Daily Papers

Time series forecasting is essential in various domains. Compared to relying solely on endogenous variables (i.e., target variables), considering exogenous variables (i.e., covariates) provides additional predictive information and often leads to more accurate predictions. However, existing methods for time series forecasting with exogenous variables (TSF-X) have the following shortcomings: 1) they do not leverage future exogenous variables, 2) they fail to fully account for the correlation between endogenous and exogenous variables. In this study, to better leverage exogenous variables, especially future exogenous variables, we propose DAG, which utilizes Dual correlAtion network along both the temporal and channel dimensions for time series forecasting with exoGenous variables. Specifically, we propose two core components: the Temporal Correlation Module and the Channel Correlation Module. Both modules consist of a correlation discovery submodule and a correlation injection submodule. The former is designed to capture the correlation effects of historical exogenous variables on future exogenous variables and on historical endogenous variables, respectively. The latter injects the discovered correlation relationships into the processes of forecasting future endogenous variables based on historical endogenous variables and future exogenous variables.

Time series clustering promises to uncover hidden structural patterns in data with applications across healthcare, finance, industrial systems, and other critical domains. However, without validated ground truth information, researchers cannot objectively assess clustering quality or determine whether poor results stem from absent structures in the data, algorithmic limitations, or inappropriate validation methods, raising the question whether clustering is "more art than science" (Guyon et al., 2009). To address these challenges, we introduce CSTS (Correlation Structures in Time Series), a synthetic benchmark for evaluating the discovery of correlation structures in multivariate time series data. CSTS provides a clean benchmark that enables researchers to isolate and identify specific causes of clustering failures by differentiating between correlation structure deterioration and limitations of clustering algorithms and validation methods. Our contributions are: (1) a comprehensive benchmark for correlation structure discovery with distinct correlation structures, systematically varied data conditions, established performance thresholds, and recommended evaluation protocols; (2) empirical validation of correlation structure preservation showing moderate distortion from downsampling and minimal effects from distribution shifts and sparsification; and (3) an extensible data generation framework enabling structure-first clustering evaluation. A case study demonstrates CSTS's practical utility by identifying an algorithm's previously undocumented sensitivity to non-normal distributions, illustrating how the benchmark enables precise diagnosis of methodological limitations. CSTS advances rigorous evaluation standards for correlation-based time series clustering.

Ask a pretrained biomedical language model whether "cortisol 28 ug/dL" and "stock-market volatility" are related, and it returns a cosine similarity of 0.83 on a scale where 1.0 means identical. The two share no mechanism. This is not a corner case: every off-the-shelf biomedical encoder we tested (BioBERT, PubMedBERT, BioM-ELECTRA) scores unrelated cross-domain pairs between 0.76 and 0.92 when the answer should be near zero. Accuracy on cross-domain discrimination is 0%. Retrieval systems survive this, because a language model downstream filters the noise. A Large Behavioural Model (LBM), a foundation model whose subject is a person rather than a sentence, does not: it reasons over a graph of a user's life and treats embedding proximity as evidence that two events are causally linked. False proximity writes a false causal edge, and everything downstream inherits the error. Here, embedding geometry is not a tuning knob; it is correctness. We report the fix. A contrastive pass over 72,034 pairs raises PubMedBERT BIOSSES correlation from 0.633 to 0.828 and within-vs-across-domain separation from 1.05x to 1.63x. A second pass, BODHI, mines hard negatives from edges absent in a biomedical knowledge graph and lifts separation to 2.30x and the discrimination gap to +0.392, at a 4.5% BIOSSES cost. On an Intel Xeon 6737P with AMX, OpenVINO cuts single-query latency from 1367 ms to 10 ms (133x) and reaches 555 sentences/sec. One finding contradicts standard advice: FP16 beats INT8 on this silicon at every serving batch size, and we explain why. The same model on a no-AMX Ice Lake instance runs 13-27x slower. We release the benchmark suite, training corpora, the BODHI generator, and the OpenVINO scripts.

Correlation does not imply causation, but patterns of statistical association between variables can be exploited to infer a causal structure (even with purely observational data) with the burgeoning field of causal discovery. As a purely observational science, astrophysics has much to gain by exploiting these new methods. The supermassive black hole (SMBH)--galaxy interaction has long been constrained by observed scaling relations, that is low-scatter correlations between variables such as SMBH mass and the central velocity dispersion of stars in a host galaxy's bulge. This study, using advanced causal discovery techniques and an up-to-date dataset, reveals a causal link between galaxy properties and dynamically-measured SMBH masses. We apply a score-based Bayesian framework to compute the exact conditional probabilities of every causal structure that could possibly describe our galaxy sample. With the exact posterior distribution, we determine the most likely causal structures and notice a probable causal reversal when separating galaxies by morphology. In elliptical galaxies, bulge properties (built from major mergers) tend to influence SMBH growth, while in spiral galaxies, SMBHs are seen to affect host galaxy properties, potentially through feedback in gas-rich environments. For spiral galaxies, SMBHs progressively quench star formation, whereas in elliptical galaxies, quenching is complete, and the causal connection has reversed. Our findings support theoretical models of hierarchical assembly of galaxies and active galactic nuclei feedback regulating galaxy evolution. Our study suggests the potentiality for further exploration of causal links in astrophysical and cosmological scaling relations, as well as any other observational science.

Large Language Models (LLMs) show promise in biomedicine but lack true causal understanding, relying instead on correlations. This paper envisions causal LLM agents that integrate multimodal data (text, images, genomics, etc.) and perform intervention-based reasoning to infer cause-and-effect. Addressing this requires overcoming key challenges: designing safe, controllable agentic frameworks; developing rigorous benchmarks for causal evaluation; integrating heterogeneous data sources; and synergistically combining LLMs with structured knowledge (KGs) and formal causal inference tools. Such agents could unlock transformative opportunities, including accelerating drug discovery through automated hypothesis generation and simulation, enabling personalized medicine through patient-specific causal models. This research agenda aims to foster interdisciplinary efforts, bridging causal concepts and foundation models to develop reliable AI partners for biomedical progress.

Activation patching is a standard method in mechanistic interpretability for localizing the components of a model responsible for specific behaviors, but it is computationally expensive to apply at scale. Attribution patching offers a faster, gradient-based approximation, yet suffers from noise and reduced reliability in deep, highly non-linear networks. In this work, we introduce Relevance Patching (RelP), which replaces the local gradients in attribution patching with propagation coefficients derived from Layer-wise Relevance Propagation (LRP). LRP propagates the network's output backward through the layers, redistributing relevance to lower-level components according to local propagation rules that ensure properties such as relevance conservation or improved signal-to-noise ratio. Like attribution patching, RelP requires only two forward passes and one backward pass, maintaining computational efficiency while improving faithfulness. We validate RelP across a range of models and tasks, showing that it more accurately approximates activation patching than standard attribution patching, particularly when analyzing residual stream and MLP outputs in the Indirect Object Identification (IOI) task. For instance, for MLP outputs in GPT-2 Large, attribution patching achieves a Pearson correlation of 0.006, whereas RelP reaches 0.956, highlighting the improvement offered by RelP. Additionally, we compare the faithfulness of sparse feature circuits identified by RelP and Integrated Gradients (IG), showing that RelP achieves comparable faithfulness without the extra computational cost associated with IG.

Gene expression analysis holds the key to many biomedical discoveries, yet extracting insights from raw transcriptomic data remains formidable due to the complexity of multiple large, semi-structured files and the need for extensive domain expertise. Current automation approaches are often limited by either inflexible workflows that break down in edge cases or by fully autonomous agents that lack the necessary precision for rigorous scientific inquiry. GenoMAS charts a different course by presenting a team of LLM-based scientists that integrates the reliability of structured workflows with the adaptability of autonomous agents. GenoMAS orchestrates six specialized LLM agents through typed message-passing protocols, each contributing complementary strengths to a shared analytic canvas. At the heart of GenoMAS lies a guided-planning framework: programming agents unfold high-level task guidelines into Action Units and, at each juncture, elect to advance, revise, bypass, or backtrack, thereby maintaining logical coherence while bending gracefully to the idiosyncrasies of genomic data. On the GenoTEX benchmark, GenoMAS reaches a Composite Similarity Correlation of 89.13% for data preprocessing and an F_1 of 60.48% for gene identification, surpassing the best prior art by 10.61% and 16.85% respectively. Beyond metrics, GenoMAS surfaces biologically plausible gene-phenotype associations corroborated by the literature, all while adjusting for latent confounders. Code is available at https://github.com/Liu-Hy/GenoMAS.

Structured pruning is essential for efficient deployment of Large Language Models (LLMs). The varying sensitivity of LLM sub-blocks to pruning necessitates the identification of optimal non-uniformly pruned models. Existing methods evaluate the importance of layers, attention heads, or weight channels in isolation. Such localized focus ignores the complex global structural dependencies that exist across the model. Training-aware structured pruning addresses global dependencies, but its computational cost can be just as expensive as post-pruning training. To alleviate the computational burden of training-aware pruning and capture global structural dependencies, we propose TraceNAS, a training-free Neural Architecture Search (NAS) framework that jointly explores structured pruning of LLM depth and width. TraceNAS identifies pruned models that maintain a high degree of loss landscape alignment with the pretrained model using a scale-invariant zero-shot proxy, effectively selecting models that exhibit maximal performance potential during post-pruning training. TraceNAS is highly efficient, enabling high-fidelity discovery of pruned models on a single GPU in 8.5 hours, yielding a 10times reduction in GPU-hours compared to training-aware methods. Evaluations on the Llama and Qwen families demonstrate that TraceNAS is competitive with training-aware baselines across commonsense and reasoning benchmarks.

We introduce DiscoPhon, a multilingual benchmark for evaluating unsupervised phoneme discovery from discrete speech units. DiscoPhon covers 6 dev and 6 test languages, chosen to span a wide range of phonemic contrasts. Given only 10 hours of speech in a previously unseen language, systems must produce discrete units that are mapped to a predefined phoneme inventory, through either a many-to-one or a one-to-one assignment. The resulting sequences are evaluated for unit quality, recognition and segmentation. We provide four pretrained multilingual HuBERT and SpidR baselines, and show that phonemic information is available enough in current models for derived units to correlate well with phonemes, though with variations across languages.

Financial metrics like the Sharpe ratio are pivotal in evaluating investment performance by balancing risk and return. However, traditional metrics often struggle with robustness and generalization, particularly in dynamic and volatile market conditions. This paper introduces AlphaSharpe, a novel framework leveraging large language models (LLMs) to iteratively evolve and optimize financial metrics to discover enhanced risk-return metrics that outperform traditional approaches in robustness and correlation with future performance metrics by employing iterative crossover, mutation, and evaluation. Key contributions of this work include: (1) a novel use of LLMs to generate and refine financial metrics with implicit domain-specific knowledge, (2) a scoring mechanism to ensure that evolved metrics generalize effectively to unseen data, and (3) an empirical demonstration of 3x predictive power for future risk-returns, and 2x portfolio performance. Experimental results in a real-world dataset highlight the superiority of discovered metrics, making them highly relevant to portfolio managers and financial decision-makers. This framework not only addresses the limitations of existing metrics but also showcases the potential of LLMs in advancing financial analytics, paving the way for informed and robust investment strategies.

Interpreting the internal reasoning of vision-language models is essential for deploying AI in safety-critical domains. Concept-based explainability provides a human-aligned lens by representing a model's behavior through semantically meaningful components. However, existing methods are largely restricted to images and overlook the cross-modal interactions. Text-image embeddings, such as those produced by CLIP, suffer from a modality gap, where visual and textual features follow distinct distributions, limiting interpretability. Canonical Correlation Analysis (CCA) offers a principled way to align features from different distributions, but has not been leveraged for multi-modal concept-level analysis. We show that the objectives of CCA and InfoNCE are closely related, such that optimizing CCA implicitly optimizes InfoNCE, providing a simple, training-free mechanism to enhance cross-modal alignment without affecting the pre-trained InfoNCE objective. Motivated by this observation, we couple concept-based explainability with CCA, introducing Concept CCA (CoCCA), a framework that aligns cross-modal embeddings while enabling interpretable concept decomposition. We further extend it and propose Sparse Concept CCA (SCoCCA), which enforces sparsity to produce more disentangled and discriminative concepts, facilitating improved activation, ablation, and semantic manipulation. Our approach generalizes concept-based explanations to multi-modal embeddings and achieves state-of-the-art performance in concept discovery, evidenced by reconstruction and manipulation tasks such as concept ablation.

Extending the forecasting time is a critical demand for real applications, such as extreme weather early warning and long-term energy consumption planning. This paper studies the long-term forecasting problem of time series. Prior Transformer-based models adopt various self-attention mechanisms to discover the long-range dependencies. However, intricate temporal patterns of the long-term future prohibit the model from finding reliable dependencies. Also, Transformers have to adopt the sparse versions of point-wise self-attentions for long series efficiency, resulting in the information utilization bottleneck. Going beyond Transformers, we design Autoformer as a novel decomposition architecture with an Auto-Correlation mechanism. We break with the pre-processing convention of series decomposition and renovate it as a basic inner block of deep models. This design empowers Autoformer with progressive decomposition capacities for complex time series. Further, inspired by the stochastic process theory, we design the Auto-Correlation mechanism based on the series periodicity, which conducts the dependencies discovery and representation aggregation at the sub-series level. Auto-Correlation outperforms self-attention in both efficiency and accuracy. In long-term forecasting, Autoformer yields state-of-the-art accuracy, with a 38% relative improvement on six benchmarks, covering five practical applications: energy, traffic, economics, weather and disease. Code is available at this repository: https://github.com/thuml/Autoformer.

Understanding and interpreting dynamics of functional materials in situ is a grand challenge in physics and materials science due to the difficulty of experimentally probing materials at varied length and time scales. X-ray photon correlation spectroscopy (XPCS) is uniquely well-suited for characterizing materials dynamics over wide-ranging time scales, however spatial and temporal heterogeneity in material behavior can make interpretation of experimental XPCS data difficult. In this work we have developed an unsupervised deep learning (DL) framework for automated classification and interpretation of relaxation dynamics from experimental data without requiring any prior physical knowledge of the system behavior. We demonstrate how this method can be used to rapidly explore large datasets to identify samples of interest, and we apply this approach to directly correlate bulk properties of a model system to microscopic dynamics. Importantly, this DL framework is material and process agnostic, marking a concrete step towards autonomous materials discovery.

Neural language models trained on large crowdsourced corpora frequently exploit spurious surface patterns tied to target labels without true linguistic or causal relevance, boosting benchmark performance while failing on adversarial or out-of-distribution inputs. Existing approaches either require manual specification of the feature vocabulary or automate discovery only partially, leaving the gap between dataset-level correlation and model-level exploitation unaddressed. We present U N M ASK, a fully automated pipeline that discovers, causally verifies, and mitigates spurious correlations in text classifiers without additional human annotation. Given unlabeled training examples, U N M ASK generates candidate surface patterns as executable boolean expressions, filters them through a statistical validation protocol with independent replication, and establishes causal model dependence via verified counterfactual interventions. Causally confirmed features then serve as annotation-free group definitions for Deep Feature Reweighting, eliminating the group labels that standard DFR requires. Applied to BERT and RoBERTa trained on MNLI, our pipeline independently rediscovers established lexical-overlap and negation biases, verifying 9 of 10 features on BERT and 6 on RoBERTa, and improving HANS accuracy by up to 12.58 pp. On CivilComments-WILDS, programmatic groups match the 70.1% worst- group accuracy of hand-labeled DFR (Kirichenko et al., 2023) without demographic annotation. We further demonstrate that the discovery and validation stages generalize to reward model preference data, surfacing interpretable spurious correlations in RewardBench2.

Sparse autoencoders (SAEs) are a technique for sparse decomposition of neural network activations into human-interpretable features. However, current SAEs suffer from feature absorption, where specialized features capture instances of general features creating representation holes, and feature composition, where independent features merge into composite representations. In this work, we introduce Orthogonal SAE (OrtSAE), a novel approach aimed to mitigate these issues by enforcing orthogonality between the learned features. By implementing a new training procedure that penalizes high pairwise cosine similarity between SAE features, OrtSAE promotes the development of disentangled features while scaling linearly with the SAE size, avoiding significant computational overhead. We train OrtSAE across different models and layers and compare it with other methods. We find that OrtSAE discovers 9% more distinct features, reduces feature absorption (by 65%) and composition (by 15%), improves performance on spurious correlation removal (+6%), and achieves on-par performance for other downstream tasks compared to traditional SAEs.

The Global CVE initiative (GCVE) proposes a decentralized, open, and extensible model for vulnerability identification, publication, and enrichment. It addresses a gap in today's vulnerability ecosystem: centralized systems provide rigorous control and widely recognized identifiers, while many producers publish advisories independently without a shared fabric for discovery, correlation, enrichment, and reuse. This paper presents GCVE as a socio-technical standardization effort combining autonomous GCVE Numbering Authorities, lightweight allocation rules, distributed publication, open Best Current Practices, and practical reference implementations. The model preserves global uniqueness while allowing participants to publish according to their operational needs. It also broadens the concept of a vulnerability record to cover assignments, disclosures, sightings, rejected identifiers, observations, exploited vulnerability information, and enrichment records. The paper describes how the GCVE BCP process supports technical interoperability and amendable operational practice, including practical guidance for vulnerability handling and disclosure. It also examines the extension mechanism, including AI-oriented extensions, as a way to evolve the standard without centralizing control. A particular focus is placed on vulnerability-lookup as the reference implementation. It aggregates multiple sources, supports GCVE publication and consumption, implements distributed Known Exploited Vulnerability data, and enables automatically enriched vulnerability data streams. Building on lessons from the MISP ecosystem, GCVE frames vulnerability coordination not only as identifier allocation, but as open infrastructure for collective security knowledge production.

We study the problem of detecting the correlation between two Gaussian databases XinR^{ntimes d} and Y^{ntimes d}, each composed of n users with d features. This problem is relevant in the analysis of social media, computational biology, etc. We formulate this as a hypothesis testing problem: under the null hypothesis, these two databases are statistically independent. Under the alternative, however, there exists an unknown permutation sigma over the set of n users (or, row permutation), such that X is rho-correlated with Y^sigma, a permuted version of Y. We determine sharp thresholds at which optimal testing exhibits a phase transition, depending on the asymptotic regime of n and d. Specifically, we prove that if rho^2dto0, as dtoinfty, then weak detection (performing slightly better than random guessing) is statistically impossible, irrespectively of the value of n. This compliments the performance of a simple test that thresholds the sum all entries of X^TY. Furthermore, when d is fixed, we prove that strong detection (vanishing error probability) is impossible for any rho<rho^star, where rho^star is an explicit function of d, while weak detection is again impossible as long as rho^2dto0. These results close significant gaps in current recent related studies.

Causal discovery, i.e., inferring underlying cause-effect relationships from observations of a scene or system, is an inherent mechanism in human cognition, but has been shown to be highly challenging to automate. The majority of approaches in the literature aiming for this task consider constrained scenarios with fully observed variables or data from stationary time-series. In this work we aim for causal discovery in a more general class of scenarios, scenes with non-stationary behavior over time. For our purposes we here regard a scene as a composition objects interacting with each other over time. Non-stationarity is modeled as stationarity conditioned on an underlying variable, a state, which can be of varying dimension, more or less hidden given observations of the scene, and also depend more or less directly on these observations. We propose a probabilistic deep learning approach called State-Dependent Causal Inference (SDCI) for causal discovery in such conditionally stationary time-series data. Results in two different synthetic scenarios show that this method is able to recover the underlying causal dependencies with high accuracy even in cases with hidden states.

Causal discovery, the process of recovering underlying causal structures from observational data, is a fundamental pursuit across scientific disciplines. Over the past decades, numerous algorithms have been developed to tackle this challenge through workflows tailored to the specific causal mechanisms underlying each type of dataset, demonstrating effectiveness across a wide range of applications. However, as the volume and heterogeneity of real-world data continue to grow, this dataset-specific approach inevitably leads to a fragmented, test-driven paradigm that struggles to scale to the demands of modern scientific discovery. To address this, we formulate the Causal Discovery Foundation Model (CDFM) as a unified, general-purpose framework for zero-shot structural inference. To ensure reliable generalization across unknown domains, we first investigate the theoretical boundaries of causal identifiability, revealing the indispensable role of causal prior mechanisms in this process. Building on these insights, we formulate a principled variational framework that treats unknown causal mechanisms as latent variables and mathematically decomposes the intractable marginal likelihood into distinct, tractable learning modules. The variational decomposition provides a conceptual design principle for the architecture design of CDFM, while comprehensive causal knowledge guides the large-scale synthesis of our pretraining data. By pretraining on a massive, highly diverse space of synthetic structural causal models, CDFM successfully internalizes complex statistical asymmetries. Extensive experiments demonstrate that CDFM consistently outperforms traditional algorithms, driving a paradigm shift toward a general-purpose causal discovery foundation model.

Autonomous scientific discovery systems offer the potential to accelerate research by automating the process of hypothesis generation and validation. However, current systems operate within constrained search spaces or require predefined research questions, limiting their capacity for true open-ended inquiry. Furthermore, while they generate hypotheses iteratively, they largely lack the ability to explicitly synthesize their own accumulated findings to uncover complex, interconnected phenomena. We introduce DiscoPER, an autonomous large language model-powered framework that conducts open-ended research by dynamically generating and executing code to explore datasets without pre-specified research objectives. To ensure rigorous scientific validity, every proposed discovery must pass statistical testing. To overcome the limitations of isolated search, our framework introduces a second-order reasoning mechanism that periodically analyzes its own accumulated discoveries. By treating prior discoveries as empirical data, DiscoPER identifies structural patterns, confounds, and epistemic gaps, actively redirecting hypothesis exploration toward uncharted regions of the search space. The search space is further expanded by incorporating tool use, enabling the system to explore hypotheses beyond structured metadata by seamlessly processing and extracting useful information from multimodal sources like images. Evaluated on iNatDisco, a new multimodal ecological knowledge benchmark with pattern-level ground truth obtained from peer-reviewed literature, DiscoPER recovers 8 of 9 known patterns with a 72.7% hypothesis support rate, outperforming both classical causal discovery and LLM-guided baselines. Ablations show that DiscoPER scales with more data, and confirms the benefits of second-order meta-reflection.

Pre-trained models have revolutionized natural language understanding. However, researchers have found they can encode artifacts undesired in many applications, such as professions correlating with one gender more than another. We explore such gendered correlations as a case study for how to address unintended correlations in pre-trained models. We define metrics and reveal that it is possible for models with similar accuracy to encode correlations at very different rates. We show how measured correlations can be reduced with general-purpose techniques, and highlight the trade offs different strategies have. With these results, we make recommendations for training robust models: (1) carefully evaluate unintended correlations, (2) be mindful of seemingly innocuous configuration differences, and (3) focus on general mitigations.

Most existing causal discovery methods rely on the assumption of no latent confounders, limiting their applicability in solving real-life problems. In this paper, we introduce a novel, versatile framework for causal discovery that accommodates the presence of causally-related hidden variables almost everywhere in the causal network (for instance, they can be effects of observed variables), based on rank information of covariance matrix over observed variables. We start by investigating the efficacy of rank in comparison to conditional independence and, theoretically, establish necessary and sufficient conditions for the identifiability of certain latent structural patterns. Furthermore, we develop a Rank-based Latent Causal Discovery algorithm, RLCD, that can efficiently locate hidden variables, determine their cardinalities, and discover the entire causal structure over both measured and hidden ones. We also show that, under certain graphical conditions, RLCD correctly identifies the Markov Equivalence Class of the whole latent causal graph asymptotically. Experimental results on both synthetic and real-world personality data sets demonstrate the efficacy of the proposed approach in finite-sample cases.

Formula alpha mining, which generates predictive signals from financial data, is critical for quantitative investment. Although various algorithmic approaches-such as genetic programming, reinforcement learning, and large language models-have significantly expanded the capacity for alpha discovery, systematic evaluation remains a key challenge. Existing evaluation metrics predominantly include backtesting and correlation-based measures. Backtesting is computationally intensive, inherently sequential, and sensitive to specific strategy parameters. Correlation-based metrics, though efficient, assess only predictive ability and overlook other crucial properties such as temporal stability, robustness, diversity, and interpretability. Additionally, the closed-source nature of most existing alpha mining models hinders reproducibility and slows progress in this field. To address these issues, we propose AlphaEval, a unified, parallelizable, and backtest-free evaluation framework for automated alpha mining models. AlphaEval assesses the overall quality of generated alphas along five complementary dimensions: predictive power, stability, robustness to market perturbations, financial logic, and diversity. Extensive experiments across representative alpha mining algorithms demonstrate that AlphaEval achieves evaluation consistency comparable to comprehensive backtesting, while providing more comprehensive insights and higher efficiency. Furthermore, AlphaEval effectively identifies superior alphas compared to traditional single-metric screening approaches. All implementations and evaluation tools are open-sourced to promote reproducibility and community engagement.

Learning causal graphs from multivariate time series is a ubiquitous challenge in all application domains dealing with time-dependent systems, such as in Earth sciences, biology, or engineering, to name a few. Recent developments for this causal discovery learning task have shown considerable skill, notably the specific time-series adaptations of the popular conditional independence-based learning framework. However, uncertainty estimation is challenging for conditional independence-based methods. Here, we introduce a novel bootstrap approach designed for time series causal discovery that preserves the temporal dependencies and lag structure. It can be combined with a range of time series causal discovery methods and provides a measure of confidence for the links of the time series graphs. Furthermore, next to confidence estimation, an aggregation, also called bagging, of the bootstrapped graphs by majority voting results in bagged causal discovery methods. In this work, we combine this approach with the state-of-the-art conditional-independence-based algorithm PCMCI+. With extensive numerical experiments we empirically demonstrate that, in addition to providing confidence measures for links, Bagged-PCMCI+ improves in precision and recall as compared to its base algorithm PCMCI+, at the cost of higher computational demands. These statistical performance improvements are especially pronounced in the more challenging settings (short time sample size, large number of variables, high autocorrelation). Our bootstrap approach can also be combined with other time series causal discovery algorithms and can be of considerable use in many real-world applications.

The discovery of causal relations from observed data has attracted significant interest from disciplines such as economics, social sciences, and biology. In practical applications, considerable knowledge of the underlying systems is often unavailable, and real data are usually associated with nonlinear causal structures, which makes the direct use of most conventional causality analysis methods difficult. This study proposes a novel quantum Peter-Clark (qPC) algorithm for causal discovery that does not require any assumptions about the underlying model structures. Based on conditional independence tests in a class of reproducing kernel Hilbert spaces characterized by quantum circuits, the proposed algorithm can explore causal relations from the observed data drawn from arbitrary distributions. We conducted systematic experiments on fundamental graphs of causal structures, demonstrating that the qPC algorithm exhibits better performance, particularly with smaller sample sizes compared to its classical counterpart. Furthermore, we proposed a novel optimization approach based on Kernel Target Alignment (KTA) for determining hyperparameters of quantum kernels. This method effectively reduced the risk of false positives in causal discovery, enabling more reliable inference. Our theoretical and experimental results demonstrate that the quantum algorithm can empower classical algorithms for accurate inference in causal discovery, supporting them in regimes where classical algorithms typically fail. In addition, the effectiveness of this method was validated using the datasets on Boston housing prices, heart disease, and biological signaling systems as real-world applications. These findings highlight the potential of quantum-based causal discovery methods in addressing practical challenges, particularly in small-sample scenarios, where traditional approaches have shown significant limitations.

Pairwise dependence measures such as correlation and causality are fundamental to temporal data mining, yet there is still no principled and robust way to quantify dependence between heterogeneous data types, especially between continuous time series and discrete temporal event sequences. Existing approaches rely on ad hoc transformations or mutual-information estimators that are highly sensitive to quantization, repeated values, and event redundancy, leading to biased or unstable results in practice. We propose a nonparametric mutual information estimator that directly measures the dependence between time series and event sequences without data transformation, learning, or ad hoc discretization. Our method models the continuous-discrete duality of real-world time series to handle quantization and repeated-value artifacts and introduces a latent event clustering strategy to mitigate bias from event co-occurrence and redundancy. Together, these yield a robust and unified framework that bridges discrete and continuous mutual information. We evaluate the proposed estimator on four representative tasks: discrete-continuous time-delayed mutual information for causality analysis, global and local temporal repetition discovery, discrete covariate selection for time series forecasting, and continuous feature selection for classification. Experiments on synthetic and real-world datasets show consistent improvements over existing methods in accuracy, robustness, and interpretability, positioning our approach as a general-purpose dependence operator for heterogeneous temporal data, similar to Pearson correlation for homogeneous time series. Code available at: https://github.com/HaojiHu/Multimodal-Temporal-Data-Quantification

Large language models are being widely used across industries to generate content that contributes directly to key performance metrics, such as conversion rates. Pretrained models, however, often fall short when it comes to aligning with human preferences or optimizing for business objectives. As a result, fine-tuning with good-quality labeled data is essential to guide models to generate content that achieves better results. Controlled experiments, like A/B tests, can provide such data, but they are often expensive and come with significant engineering and logistical challenges. Meanwhile, companies have access to a vast amount of historical (observational) data that remains underutilized. In this work, we study the challenges and opportunities of fine-tuning LLMs using observational data. We show that while observational outcomes can provide valuable supervision, directly fine-tuning models on such data can lead them to learn spurious correlations. We present empirical evidence of this issue using various real-world datasets and propose DeconfoundLM, a method that explicitly removes the effect of known confounders from reward signals. Using simulation experiments, we demonstrate that DeconfoundLM improves the recovery of causal relationships and mitigates failure modes found in fine-tuning methods that ignore or naively incorporate confounding variables. Our findings highlight that while observational data presents risks, with the right causal corrections, it can be a powerful source of signal for LLM alignment. Please refer to the project page for code and related resources.

We used a dataset of daily Bloomberg Financial Market Summaries from 2010 to 2023, reposted on large financial media, to determine how global news headlines may affect stock market movements using ChatGPT and a two-stage prompt approach. We document a statistically significant positive correlation between the sentiment score and future equity market returns over short to medium term, which reverts to a negative correlation over longer horizons. Validation of this correlation pattern across multiple equity markets indicates its robustness across equity regions and resilience to non-linearity, evidenced by comparison of Pearson and Spearman correlations. Finally, we provide an estimate of the optimal horizon that strikes a balance between reactivity to new information and correlation.

It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time. Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper, we develop a framework for causal discovery from such data, called Constraint-based causal Discovery from heterogeneous/NOnstationary Data (CD-NOD), to find causal skeleton and directions and estimate the properties of mechanism changes. First, we propose an enhanced constraint-based procedure to detect variables whose local mechanisms change and recover the skeleton of the causal structure over observed variables. Second, we present a method to determine causal orientations by making use of independent changes in the data distribution implied by the underlying causal model, benefiting from information carried by changing distributions. After learning the causal structure, next, we investigate how to efficiently estimate the "driving force" of the nonstationarity of a causal mechanism. That is, we aim to extract from data a low-dimensional representation of changes. The proposed methods are nonparametric, with no hard restrictions on data distributions and causal mechanisms, and do not rely on window segmentation. Furthermore, we find that data heterogeneity benefits causal structure identification even with particular types of confounders. Finally, we show the connection between heterogeneity/nonstationarity and soft intervention in causal discovery. Experimental results on various synthetic and real-world data sets (task-fMRI and stock market data) are presented to demonstrate the efficacy of the proposed methods.

We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for this problem. We construct a novel semi-metric on the set of vertices, which we call the correlation metric, that indicates to our clustering algorithms whether pairs of nodes should be in the same cluster. The paper demonstrates empirically that, compared to prior work, our algorithms sacrifice little in the objective quality to obtain significantly better run-time. Moreover, our algorithms scale to larger networks that are effectively intractable for known algorithms.

Learning causal structure from observational data often assumes that we observe independent and identically distributed (i.\,i.\,d) data. The traditional approach aims to find a graphical representation that encodes the same set of conditional independence relationships as those present in the observed distribution. It is known that under i.\,i.\,d assumption, even with infinite data, there is a limit to how fine-grained a causal structure we can identify. To overcome this limitation, recent work has explored using data originating from different, related environments to learn richer causal structure. These approaches implicitly rely on the independent causal mechanisms (ICM) principle, which postulates that the mechanism giving rise to an effect given its causes and the mechanism which generates the causes do not inform or influence each other. Thus, components of the causal model can independently change from environment to environment. Despite its wide application in machine learning and causal inference, there is a lack of statistical formalization of the ICM principle and how it enables identification of richer causal structures from grouped data. Here we present new causal de Finetti theorems which offer a first statistical formalization of ICM principle and show how causal structure identification is possible from exchangeable data. Our work provides theoretical justification for a broad range of techniques leveraging multi-environment data to learn causal structure.

The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the complexity of the problem statement. Here, we focus on establishing partial optimality conditions for the special case of complete graphs and cubic objective functions. In addition, we define and implement algorithms for testing these conditions and examine their effect numerically, on two datasets.

Partial correlations quantify linear association between two variables adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix. For compositional data, the covariance structure is specified from log ratios of variables, so unless we try to "open" the data via a normalization, this implies changes in the definition and interpretation of partial correlations. In the present work, we elucidate how results derived by Aitchison (1986) lead to a natural definition of partial correlation that has a number of advantages over current measures of association. For this, we show that the residuals of log-ratios between a variable with a reference, when adjusting for all remaining variables including the reference, are reference-independent. Since the reference itself can be controlled for, correlations between residuals are defined for the variables directly without the necessity to recur to ratios except when specifying which variables are partialled out. Thus, perhaps surprisingly, partial correlations do not have the problems commonly found with measures of pairwise association on compositional data. They are well-defined between two variables, are properly scaled, and allow for negative association. By design, they are subcompositionally incoherent, but they share this property with conventional partial correlations (where results change when adjusting for the influence of fewer variables). We discuss the equivalence with normalization-based approaches whenever the normalizing variables are controlled for. We also discuss the partial variances and correlations we obtain from a previously studied data set of Roman glass cups.

Deep neural networks often rely on spurious correlations to make predictions, which hinders generalization beyond training environments. For instance, models that associate cats with bed backgrounds can fail to predict the existence of cats in other environments without beds. Mitigating spurious correlations is crucial in building trustworthy models. However, the existing works lack transparency to offer insights into the mitigation process. In this work, we propose an interpretable framework, Discover and Cure (DISC), to tackle the issue. With human-interpretable concepts, DISC iteratively 1) discovers unstable concepts across different environments as spurious attributes, then 2) intervenes on the training data using the discovered concepts to reduce spurious correlation. Across systematic experiments, DISC provides superior generalization ability and interpretability than the existing approaches. Specifically, it outperforms the state-of-the-art methods on an object recognition task and a skin-lesion classification task by 7.5% and 9.6%, respectively. Additionally, we offer theoretical analysis and guarantees to understand the benefits of models trained by DISC. Code and data are available at https://github.com/Wuyxin/DISC.

Despite the widespread application of latent factor analysis, existing methods suffer from the following weaknesses: requiring the number of factors to be known, lack of theoretical guarantees for learning the model structure, and nonidentifiability of the parameters due to rotation invariance properties of the likelihood. We address these concerns by proposing a fast correlation thresholding (CT) algorithm that simultaneously learns the number of latent factors and a rotationally identifiable model structure. Our novel approach translates this structure learning problem into the search for so-called independent maximal cliques in a thresholded correlation graph that can be easily constructed from the observed data. Our clique analysis technique scales well up to thousands of variables, while competing methods are not applicable in a reasonable amount of running time. We establish a finite-sample error bound and high-dimensional consistency for the structure learning of our method. Through a series of simulation studies and a real data example, we show that the CT algorithm is an accurate method for learning the structure of factor analysis models and is robust to violations of its assumptions.

Causal discovery aims to recover directed causal relations from observational and interventional data, providing a basis for mechanistic understanding and reliable decision-making. Causal discovery foundation models (CDFMs) seek to amortize this problem by mapping a dataset directly to a causal graph in a single forward pass, avoiding per-dataset testing, search, or optimization. However, existing CDFMs remain limited, often failing to consistently match strong classical methods, and we find that a key bottleneck is how causal pretraining tasks are constructed. Based on this observation, we propose TabCausal, a data-driven CDFM trained with broad causal pretraining over diverse graph priors, structural mechanisms, noise models, dimensions, sample sizes, and intervention regimes. A dynamic task construction strategy composes these causal environments into varied discovery tasks, enabling more transferable structural learning from observational and mixed-interventional data. On large-scale synthetic benchmarks, TabCausal achieves better macro-averaged performance than a diverse set of causal discovery baselines. To further bridge abstract synthetic generators and realistic causal reasoning scenarios, we introduce a protocol-guided and LLM-audited semantic causal environment benchmark, where domain-grounded SCMs generate interpretable observational and interventional datasets for out-of-distribution analysis. Across both synthetic and semantic environments, TabCausal demonstrates robust structure recovery, especially under interventional evidence, highlighting broad causal pretraining as a key ingredient for transferable amortized causal discovery.

We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional independence and dependence relations between measured variables, even when latent variables and selection bias may be present, there are sufficient conditions for reliably concluding that there is a causal path from one variable to another, and sufficient conditions for reliably concluding when no such causal path exists.

Recent work has shown promising results in causal discovery by leveraging interventional data with gradient-based methods, even when the intervened variables are unknown. However, previous work assumes that the correspondence between samples and interventions is known, which is often unrealistic. We envision a scenario with an extensive dataset sampled from multiple intervention distributions and one observation distribution, but where we do not know which distribution originated each sample and how the intervention affected the system, i.e., interventions are entirely latent. We propose a method based on neural networks and variational inference that addresses this scenario by framing it as learning a shared causal graph among an infinite mixture (under a Dirichlet process prior) of intervention structural causal models. Experiments with synthetic and real data show that our approach and its semi-supervised variant are able to discover causal relations in this challenging scenario.

Understanding the performance of machine learning (ML) models across diverse data distributions is critically important for reliable applications. Despite recent empirical studies positing a near-perfect linear correlation between in-distribution (ID) and out-of-distribution (OOD) accuracies, we empirically demonstrate that this correlation is more nuanced under subpopulation shifts. Through rigorous experimentation and analysis across a variety of datasets, models, and training epochs, we demonstrate that OOD performance often has a nonlinear correlation with ID performance in subpopulation shifts. Our findings, which contrast previous studies that have posited a linear correlation in model performance during distribution shifts, reveal a "moon shape" correlation (parabolic uptrend curve) between the test performance on the majority subpopulation and the minority subpopulation. This non-trivial nonlinear correlation holds across model architectures, hyperparameters, training durations, and the imbalance between subpopulations. Furthermore, we found that the nonlinearity of this "moon shape" is causally influenced by the degree of spurious correlations in the training data. Our controlled experiments show that stronger spurious correlation in the training data creates more nonlinear performance correlation. We provide complementary experimental and theoretical analyses for this phenomenon, and discuss its implications for ML reliability and fairness. Our work highlights the importance of understanding the nonlinear effects of model improvement on performance in different subpopulations, and has the potential to inform the development of more equitable and responsible machine learning models.

Causal discovery is fundamental to scientific understanding and reliable decision-making. Existing approaches face critical limitations: purely data-driven methods suffer from statistical indistinguishability and modeling assumptions, while recent LLM-based methods either ignore statistical evidence or incorporate unverified priors that can mislead result. To this end, we propose CauScientist, a collaborative framework that synergizes LLMs as hypothesis-generating "data scientists" with probabilistic statistics as rigorous "verifiers". CauScientist employs hybrid initialization to select superior starting graphs, iteratively refines structures through LLM-proposed modifications validated by statistical criteria, and maintains error memory to guide efficient search space. Experiments demonstrate that CauScientist substantially outperforms purely data-driven baselines, achieving up to 53.8% F1 score improvement and enhancing recall from 35.0% to 100.0%. Notably, while standalone LLM performance degrades with graph complexity, CauScientist reduces structural hamming distance (SHD) by 44.0% compared to Qwen3-32B on 37-node graphs. Our project page is at https://github.com/OpenCausaLab/CauScientist.

We study the problem of identifying an anomalous subset of streams under correlated noise, motivated by monitoring and security in cyber-physical systems. This problem can be viewed as a form of combinatorial pure exploration, where each stream plays the role of an arm and measurements must be allocated sequentially under uncertainty. Existing combinatorial bandit and hypothesis testing methods typically assume independent observations and fail to exploit correlation for efficient measurement design. We propose ECC-AHT, an adaptive algorithm that selects continuous, constrained measurements to maximize Chernoff information between competing hypotheses, enabling active noise cancellation through differential sensing. ECC-AHT achieves optimal sample complexity guarantees and significantly outperforms state-of-the-art baselines in both synthetic and real-world correlated environments. The code is available on https://github.com/VincentdeCristo/ECC-AHT

This article studies the change in the prediction accuracy of a response variable when the number of predictors increases, and all variables follow a multivariate normal distribution. Assuming that the correlations between variables are independently drawn, I show that adding variables leads to globally increasing returns to scale when the mean of the correlation distribution is zero. The speed of learning depends positively on the variance of the correlation distribution. I use simulations to study the more complex case of correlation distributions with a non-zero mean and find a pattern of decreasing returns followed by increasing returns to scale - as long as the variance of correlations is not degenerate, in which case globally decreasing returns emerge. I train a collaborative filtering algorithm using the MovieLens 1M dataset to analyze returns from adding variables in a more realistic setting and find globally increasing returns to scale across 2,000 variables. The results suggest significant scale advantages from additional variables in prediction tasks.

Ongoing efforts that span over decades show a rise of AI methods for accelerating scientific discovery, yet accelerating discovery in mathematics remains a persistent challenge for AI. Specifically, AI methods were not effective in creation of formulas for mathematical constants because each such formula must be correct for infinite digits of precision, with "near-true" formulas providing no insight toward the correct ones. Consequently, formula discovery lacks a clear distance metric needed to guide automated discovery in this realm. In this work, we propose a systematic methodology for categorization, characterization, and pattern identification of such formulas. The key to our methodology is introducing metrics based on the convergence dynamics of the formulas, rather than on the numerical value of the formula. These metrics enable the first automated clustering of mathematical formulas. We demonstrate this methodology on Polynomial Continued Fraction formulas, which are ubiquitous in their intrinsic connections to mathematical constants, and generalize many mathematical functions and structures. We test our methodology on a set of 1,768,900 such formulas, identifying many known formulas for mathematical constants, and discover previously unknown formulas for pi, ln(2), Gauss', and Lemniscate's constants. The uncovered patterns enable a direct generalization of individual formulas to infinite families, unveiling rich mathematical structures. This success paves the way towards a generative model that creates formulas fulfilling specified mathematical properties, accelerating the rate of discovery of useful formulas.

In order to minimize the generalization error in neural networks, a novel technique to identify overfitting phenomena when training the learner is formally introduced. This enables support of a reliable and trustworthy early stopping condition, thus improving the predictive power of that type of modeling. Our proposal exploits the correlation over time in a collection of online indicators, namely characteristic functions for indicating if a set of hypotheses are met, associated with a range of independent stopping conditions built from a canary judgment to evaluate the presence of overfitting. That way, we provide a formal basis for decision making in terms of interrupting the learning process. As opposed to previous approaches focused on a single criterion, we take advantage of subsidiarities between independent assessments, thus seeking both a wider operating range and greater diagnostic reliability. With a view to illustrating the effectiveness of the halting condition described, we choose to work in the sphere of natural language processing, an operational continuum increasingly based on machine learning. As a case study, we focus on parser generation, one of the most demanding and complex tasks in the domain. The selection of cross-validation as a canary function enables an actual comparison with the most representative early stopping conditions based on overfitting identification, pointing to a promising start toward an optimal bias and variance control.

Tangles were originally introduced as a concept to formalize regions of high connectivity in graphs. In recent years, they have also been discovered as a link between structural graph theory and data science: when interpreting similarity in data sets as connectivity between points, finding clusters in the data essentially amounts to finding tangles in the underlying graphs. This paper further explores the potential of tangles in data sets as a means for a formal study of clusters. Real-world data often follow a normal distribution. Accounting for this, we develop a quantitative theory of tangles in data sets drawn from Gaussian mixtures. To this end, we equip the data with a graph structure that models similarity between the points and allows us to apply tangle theory to the data. We provide explicit conditions under which tangles associated with the marginal Gaussian distributions exist asymptotically almost surely. This can be considered as a sufficient formal criterion for the separabability of clusters in the data.

A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data analysis: the theory of statistical inference assumes a fixed collection of hypotheses to be tested, or learning algorithms to be applied, selected non-adaptively before the data are gathered, whereas in practice data is shared and reused with hypotheses and new analyses being generated on the basis of data exploration and the outcomes of previous analyses. In this work we initiate a principled study of how to guarantee the validity of statistical inference in adaptive data analysis. As an instance of this problem, we propose and investigate the question of estimating the expectations of m adaptively chosen functions on an unknown distribution given n random samples. We show that, surprisingly, there is a way to estimate an exponential in n number of expectations accurately even if the functions are chosen adaptively. This gives an exponential improvement over standard empirical estimators that are limited to a linear number of estimates. Our result follows from a general technique that counter-intuitively involves actively perturbing and coordinating the estimates, using techniques developed for privacy preservation. We give additional applications of this technique to our question.

Stock price forecasting has remained an extremely challenging problem for many decades due to the high volatility of the stock market. Recent efforts have been devoted to modeling complex stock correlations toward joint stock price forecasting. Existing works share a common neural architecture that learns temporal patterns from individual stock series and then mixes up temporal representations to establish stock correlations. However, they only consider time-aligned stock correlations stemming from all the input stock features, which suffer from two limitations. First, stock correlations often occur momentarily and in a cross-time manner. Second, the feature effectiveness is dynamic with market variation, which affects both the stock sequential patterns and their correlations. To address the limitations, this paper introduces MASTER, a MArkert-Guided Stock TransformER, which models the momentary and cross-time stock correlation and leverages market information for automatic feature selection. MASTER elegantly tackles the complex stock correlation by alternatively engaging in intra-stock and inter-stock information aggregation. Experiments show the superiority of MASTER compared with previous works and visualize the captured realistic stock correlation to provide valuable insights.

Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the well-known Pearson correlation coefficient, the most important is that distance correlation equals zero if and only if the random vectors are independent. There are two different estimators of the distance correlation available in the literature. The first one, proposed by Székely et al. (2007), is based on an asymptotically unbiased estimator of the distance covariance which turns out to be a V-statistic. The second one builds on an unbiased estimator of the distance covariance proposed in Székely et al. (2014), proved to be an U-statistic by Székely and Huo (2016). This study evaluates their efficiency (mean squared error) and compares computational times for both methods under different dependence structures. Under conditions of independence or near-independence, the V-estimates are biased, while the U-estimator frequently cannot be computed due to negative values. To address this challenge, a convex linear combination of the former estimators is proposed and studied, yielding good results regardless of the level of dependence.

Causal discovery for both cross-sectional and temporal data has traditionally followed a dataset-specific paradigm, where a new model is fitted for each individual dataset. Such an approach limits the potential of multi-dataset pretraining. The concept of large causal models (LCMs) envisions a class of pre-trained neural architectures specifically designed for temporal causal discovery. Prior approaches are constrained to small variable counts, degrade with larger inputs, and rely heavily on synthetic data, limiting generalization. We propose a principled framework for LCMs, combining diverse synthetic generators with realistic time-series datasets, allowing learning at scale. Extensive experiments on synthetic, semi-synthetic and realistic benchmarks show that LCMs scale effectively to higher variable counts and deeper architectures while maintaining strong performance. Trained models achieve competitive or superior accuracy compared to classical and neural baselines, particularly in out-of-distribution settings, while enabling fast, single-pass inference. Results demonstrate LCMs as a promising foundation-model paradigm for temporal causal discovery. Experiments and model weights are available at https://github.com/kougioulis/LCM-paper/.

We introduce the concept of Automated Causal Discovery (AutoCD), defined as any system that aims to fully automate the application of causal discovery and causal reasoning methods. AutoCD's goal is to deliver all causal information that an expert human analyst would and answer a user's causal queries. We describe the architecture of such a platform, and illustrate its performance on synthetic data sets. As a case study, we apply it on temporal telecommunication data. The system is general and can be applied to a plethora of causal discovery problems.

Causal Discovery plays a pivotal role in revealing relationships among observed variables, particularly in the temporal setup. While the majority of CD methods rely on synthetic data for evaluation, and recently for training, these fall short in accurately mirroring real-world scenarios; an effect even more evident in temporal data. Generation techniques depending on simplified assumptions on causal structure, effects and time, limit the quality and diversity of the simulated data. In this work, we introduce Temporal Causal-based Simulation (TCS), a robust framework for generating realistic time-series data and their associated temporal causal graphs. The approach is structured in three phases: estimating the true lagged causal structure of the data, approximating the functional dependencies between variables and learning the noise distribution of the corresponding causal model, each part of which can be explicitly tailored based on data assumptions and characteristics. Through an extensive evaluation process, we highlight that single detection methods for generated data discrimination prove inadequate, accentuating it as a multifaceted challenge. For this, we detail a Min-max optimization phase that draws on AutoML techniques. Our contributions include a flexible, model-agnostic pipeline for generating realistic temporal causal data, a thorough evaluation setup which enhances the validity of the generated datasets and insights into the challenges posed by realistic data generation. Through experiments involving not only real but also semi-synthetic and purely synthetic datasets, we demonstrate that while sampling realistic causal data remains a complex task, our method enriches the domain of generating sensible causal-based temporal data.

We propose a novel framework that leverages LLMs for full causal graph discovery. While previous LLM-based methods have used a pairwise query approach, this requires a quadratic number of queries which quickly becomes impractical for larger causal graphs. In contrast, the proposed framework uses a breadth-first search (BFS) approach which allows it to use only a linear number of queries. We also show that the proposed method can easily incorporate observational data when available, to improve performance. In addition to being more time and data-efficient, the proposed framework achieves state-of-the-art results on real-world causal graphs of varying sizes. The results demonstrate the effectiveness and efficiency of the proposed method in discovering causal relationships, showcasing its potential for broad applicability in causal graph discovery tasks across different domains.

Pairwise clustering, in general, partitions a set of items via a known similarity function. In our treatment, clustering is modeled as a transductive prediction problem. Thus rather than beginning with a known similarity function, the function instead is hidden and the learner only receives a random sample consisting of a subset of the pairwise similarities. An additional set of pairwise side-information may be given to the learner, which then determines the inductive bias of our algorithms. We measure performance not based on the recovery of the hidden similarity function, but instead on how well we classify each item. We give tight bounds on the number of misclassifications. We provide two algorithms. The first algorithm SACA is a simple agglomerative clustering algorithm which runs in near linear time, and which serves as a baseline for our analyses. Whereas the second algorithm, RGCA, enables the incorporation of side-information which may lead to improved bounds at the cost of a longer running time.

A variety of recent papers discuss the application of Shapley values, a concept for explaining coalitional games, for feature attribution in machine learning. However, the correct way to connect a machine learning model to a coalitional game has been a source of controversy. The two main approaches that have been proposed differ in the way that they condition on known features, using either (1) an interventional or (2) an observational conditional expectation. While previous work has argued that one of the two approaches is preferable in general, we argue that the choice is application dependent. Furthermore, we argue that the choice comes down to whether it is desirable to be true to the model or true to the data. We use linear models to investigate this choice. After deriving an efficient method for calculating observational conditional expectation Shapley values for linear models, we investigate how correlation in simulated data impacts the convergence of observational conditional expectation Shapley values. Finally, we present two real data examples that we consider to be representative of possible use cases for feature attribution -- (1) credit risk modeling and (2) biological discovery. We show how a different choice of value function performs better in each scenario, and how possible attributions are impacted by modeling choices.

Machine learning systems are known to be sensitive to spurious correlations between biased features of the inputs (e.g., background, texture, and secondary objects) and the corresponding labels. These features and their correlations with the labels are known as "spurious" because they tend to change with shifts in real-world data distributions, which can negatively impact the model's generalization and robustness. In this survey, we provide a comprehensive review of this issue, along with a taxonomy of current state-of-the-art methods for addressing spurious correlations in machine learning models. Additionally, we summarize existing datasets, benchmarks, and metrics to aid future research. The paper concludes with a discussion of the recent advancements and future research challenges in this field, aiming to provide valuable insights for researchers in the related domains.

The traditional i.i.d.-based learning paradigm faces inherent challenges in addressing causal relationships, which has become increasingly evident with the rise of applications in causal representation learning. Our understanding of causality naturally requires a perspective as the creator rather than observer, as the ``what...if'' questions only hold within the possible world we conceive. The traditional perspective limits capturing dynamic causal outcomes and leads to compensatory efforts such as the reliance on hidden confounders. This paper lays the groundwork for the new perspective, which enables the relation-first modeling paradigm for causality. Also, it introduces the Relation-Indexed Representation Learning (RIRL) as a practical implementation, supported by experiments that validate its efficacy.

Causal discovery with latent confounders is an important but challenging task in many scientific areas. Despite the success of some overcomplete independent component analysis (OICA) based methods in certain domains, they are computationally expensive and can easily get stuck into local optima. We notice that interestingly, by making use of higher-order cumulants, there exists a closed-form solution to OICA in specific cases, e.g., when the mixing procedure follows the One-Latent-Component structure. In light of the power of the closed-form solution to OICA corresponding to the One-Latent-Component structure, we formulate a way to estimate the mixing matrix using the higher-order cumulants, and further propose the testable One-Latent-Component condition to identify the latent variables and determine causal orders. By iteratively removing the share identified latent components, we successfully extend the results on the One-Latent-Component structure to the Multi-Latent-Component structure and finally provide a practical and asymptotically correct algorithm to learn the causal structure with latent variables. Experimental results illustrate the asymptotic correctness and effectiveness of the proposed method.

Differentially private learning algorithms inject noise into the learning process. While the most common private learning algorithm, DP-SGD, adds independent Gaussian noise in each iteration, recent work on matrix factorization mechanisms has shown empirically that introducing correlations in the noise can greatly improve their utility. We characterize the asymptotic learning utility for any choice of the correlation function, giving precise analytical bounds for linear regression and as the solution to a convex program for general convex functions. We show, using these bounds, how correlated noise provably improves upon vanilla DP-SGD as a function of problem parameters such as the effective dimension and condition number. Moreover, our analytical expression for the near-optimal correlation function circumvents the cubic complexity of the semi-definite program used to optimize the noise correlation matrix in previous work. We validate our theory with experiments on private deep learning. Our work matches or outperforms prior work while being efficient both in terms of compute and memory.

Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical difficulties of estimating time-varying and high-dimensional covariance matrices often limits existing methods to handling at most a few hundred dimensions or requires making strong assumptions on the dependence between series. We propose to combine an RNN-based time series model with a Gaussian copula process output model with a low-rank covariance structure to reduce the computational complexity and handle non-Gaussian marginal distributions. This permits to drastically reduce the number of parameters and consequently allows the modeling of time-varying correlations of thousands of time series. We show on several real-world datasets that our method provides significant accuracy improvements over state-of-the-art baselines and perform an ablation study analyzing the contributions of the different components of our model.

High-dimensional, underdetermined and highly correlated systems are common in data science practice, especially when analyzing physical measurements. In such settings, feature selection poses a fundamental challenge because multiple distinct sparse subsets may explain the response equally well. Their identification is crucial not only for predictive modeling but also for generating domain-specific insights into the underlying mechanisms. Yet, conventional methods typically isolate a single solution, obscuring the full spectrum of plausible explanations. This work introduces GEMSS (Gaussian Ensemble for Multiple Sparse Solutions), a variational algorithm designed to simultaneously discover multiple, diverse sparse feature combinations. The method employs a structured spike-and-slab prior for sparsity, a mixture of Gaussians to approximate the intractable multimodal posterior, and a Jaccard-based penalty to further control solution diversity. A single objective function is optimized via stochastic gradient descent. The method is tested on 128 comprehensive experiments by a novel benchmarking framework designed to generate artificial problems with multiple sparse solutions of equal predictive properties. This allows us to measure the retrieval of ground truth features rather than only evaluating predictive performance -- characteristics more fitting to our practical needs. A comparative analysis shows that GEMSS consistently outperforms five prominent feature selection methods adapted through the ALFESE framework. Finally, we demonstrate practical usability through 3 challenging real-world datasets from metabolomics and physical chemistry: GEMSS successfully isolates multiple distinct yet quality solutions. GEMSS is available as a PyPI package 'gemss'. The corresponding repository github.com/kat-er-ina/gemss/ includes the full codebase and a free, no-code application GEMSS Explorer.

Extracting causal relationships from observed correlations is a growing area in probabilistic reasoning, originating with the seminal work of Pearl and others from the early 1990s. This paper develops a new, categorically oriented view based on a clear distinction between syntax (string diagrams) and semantics (stochastic matrices), connected via interpretations as structure-preserving functors. A key notion in the identification of causal effects is that of an intervention, whereby a variable is forcefully set to a particular value independent of any prior propensities. We represent the effect of such an intervention as an endofunctor which performs `string diagram surgery' within the syntactic category of string diagrams. This diagram surgery in turn yields a new, interventional distribution via the interpretation functor. While in general there is no way to compute interventional distributions purely from observed data, we show that this is possible in certain special cases using a calculational tool called comb disintegration. We demonstrate the use of this technique on a well-known toy example, where we predict the causal effect of smoking on cancer in the presence of a confounding common cause. After developing this specific example, we show this technique provides simple sufficient conditions for computing interventions which apply to a wide variety of situations considered in the causal inference literature.

Scientific discovery via symbolic regression is often viewed as statistically and computationally intractable because the hypothesis space of expressions grows combinatorially with depth. This paper revisits the statistical side through the lens of PAC learning, focusing on compositional function trees built from a finite vocabulary of smooth operators (e.g., {+,times,sin,exp} and affine maps). We prove that the relevant generalization quantity, Rademacher complexity, hence the excess risk, does not necessarily blow up exponentially with the number of distinct symbolic structures, but is controlled by (i) the depth d and (ii) the Lipschitz constants of the base operators along the composed computation graph. Concretely, under mild Lipschitz conditions on operators and bounded affine leaves, a finite-union bound over a vocabulary of size K=|H_{base}| together with Maurer-type vector contraction yields R_n(H_{comp}^{d}) leq (Kb2L)^{d-1}R_n(H_{comp}^{1}) with arity bound b; corresponding high-probability risk bounds scale as O(L^{d}/n) when K,b=O(1) and R_n(H_{comp}^{1})=O(n^{-1/2}). We complement the theory with a modular codebase that trains differentiable operator trees (not MLPs) on synthetic "physics-like" targets of controlled depth and shows that the empirical generalization gap correlates positively with the predicted complexity term (L^{d})/n.

Mutual information (MI) is a fundamental measure of statistical dependence between two variables, yet accurate estimation from finite data remains notoriously difficult. No estimator is universally reliable, and common approaches fail in the high-dimensional, undersampled regimes typical of modern experiments. Recent machine learning-based estimators show promise, but their accuracy depends sensitively on dataset size, structure, and hyperparameters, with no accepted tests to detect failures. We close these gaps through a systematic evaluation of classical and neural MI estimators across standard benchmarks and new synthetic datasets tailored to challenging high-dimensional, undersampled regimes. We contribute: (i) a practical protocol for reliable MI estimation with explicit checks for statistical consistency; (ii) confidence intervals (error bars around estimates) that existing neural MI estimator do not provide; and (iii) a new class of probabilistic critics designed for high-dimensional, high-information settings. We demonstrate the effectiveness of our protocol with computational experiments, showing that it consistently matches or surpasses existing methods while uniquely quantifying its own reliability. We show that reliable MI estimation is sometimes achievable even in severely undersampled, high-dimensional datasets, provided they admit accurate low-dimensional representations. This broadens the scope of applicability of neural MI estimators and clarifies when such estimators can be trusted.

This paper proposes a methodology for discovering meaningful properties in data by exploring the latent space of unsupervised deep generative models. We combine manipulation of individual latent variables to extreme values with methods inspired by causal inference into an approach we call causal disentanglement with extreme values (CDEV) and show that this method yields insights for model interpretability. With this, we can test for what properties of unknown data the model encodes as meaningful, using it to glean insight into the communication system of sperm whales (Physeter macrocephalus), one of the most intriguing and understudied animal communication systems. The network architecture used has been shown to learn meaningful representations of speech; here, it is used as a learning mechanism to decipher the properties of another vocal communication system in which case we have no ground truth. The proposed methodology suggests that sperm whales encode information using the number of clicks in a sequence, the regularity of their timing, and audio properties such as the spectral mean and the acoustic regularity of the sequences. Some of these findings are consistent with existing hypotheses, while others are proposed for the first time. We also argue that our models uncover rules that govern the structure of units in the communication system and apply them while generating innovative data not shown during training. This paper suggests that an interpretation of the outputs of deep neural networks with causal inference methodology can be a viable strategy for approaching data about which little is known and presents another case of how deep learning can limit the hypothesis space. Finally, the proposed approach can be extended to other architectures and datasets.

We introduce Invariant Risk Minimization (IRM), a learning paradigm to estimate invariant correlations across multiple training distributions. To achieve this goal, IRM learns a data representation such that the optimal classifier, on top of that data representation, matches for all training distributions. Through theory and experiments, we show how the invariances learned by IRM relate to the causal structures governing the data and enable out-of-distribution generalization.

Inspired by the fact that the neural network, as the mainstream for machine learning, has brought successes in many application areas, here we propose to use this approach for decoding hidden correlation among pseudo-random data and predicting events accordingly. With a simple neural network structure and a typical training procedure, we demonstrate the learning and prediction power of the neural network in extremely random environment. Finally, we postulate that the high sensitivity and efficiency of the neural network may allow to critically test if there could be any fundamental difference between quantum randomness and pseudo randomness, which is equivalent to the question: Does God play dice?

Models driven by spurious correlations often yield poor generalization performance. We propose the counterfactual (CF) alignment method to detect and quantify spurious correlations of black box classifiers. Our methodology is based on counterfactual images generated with respect to one classifier being input into other classifiers to see if they also induce changes in the outputs of these classifiers. The relationship between these responses can be quantified and used to identify specific instances where a spurious correlation exists. This is validated by observing intuitive trends in face-attribute and waterbird classifiers, as well as by fabricating spurious correlations and detecting their presence, both visually and quantitatively. Furthermore, utilizing the CF alignment method, we demonstrate that we can evaluate robust optimization methods (GroupDRO, JTT, and FLAC) by detecting a reduction in spurious correlations.

Conventional causal discovery methods rely on centralized data, which is inconsistent with the decentralized nature of data in many real-world situations. This discrepancy has motivated the development of federated causal discovery (FCD) approaches. However, existing FCD methods may be limited by their potentially restrictive assumptions of identifiable functional causal models or homogeneous data distributions, narrowing their applicability in diverse scenarios. In this paper, we propose a novel FCD method attempting to accommodate arbitrary causal models and heterogeneous data. We first utilize a surrogate variable corresponding to the client index to account for the data heterogeneity across different clients. We then develop a federated conditional independence test (FCIT) for causal skeleton discovery and establish a federated independent change principle (FICP) to determine causal directions. These approaches involve constructing summary statistics as a proxy of the raw data to protect data privacy. Owing to the nonparametric properties, FCIT and FICP make no assumption about particular functional forms, thereby facilitating the handling of arbitrary causal models. We conduct extensive experiments on synthetic and real datasets to show the efficacy of our method. The code is available at https://github.com/lokali/FedCDH.git.

Several studies have compared the in-distribution (ID) and out-of-distribution (OOD) performance of models in computer vision and NLP. They report a frequent positive correlation and some surprisingly never even observe an inverse correlation indicative of a necessary trade-off. The possibility of inverse patterns is important to determine whether ID performance can serve as a proxy for OOD generalization capabilities. This paper shows with multiple datasets that inverse correlations between ID and OOD performance do happen in real-world data - not only in theoretical worst-case settings. We also explain theoretically how these cases can arise even in a minimal linear setting, and why past studies could miss such cases due to a biased selection of models. Our observations lead to recommendations that contradict those found in much of the current literature. - High OOD performance sometimes requires trading off ID performance. - Focusing on ID performance alone may not lead to optimal OOD performance. It may produce diminishing (eventually negative) returns in OOD performance. - In these cases, studies on OOD generalization that use ID performance for model selection (a common recommended practice) will necessarily miss the best-performing models, making these studies blind to a whole range of phenomena.

The robustness of machine learning models can be compromised by spurious correlations between non-causal features in the input data and target labels. A common way to test for such correlations is to train on data where the label is strongly tied to some non-causal cue, then evaluate on examples where that tie no longer holds. This idea is well established for classification tasks, but for semantic segmentation the specific failure modes are not well understood. We show that a model may achieve reasonable overlap while assigning the wrong semantic label, swapping one plausible foreground class for another, even when object boundaries are largely correct. We focus on this semantic label-flip behaviour and quantify it with a simple diagnostic (Flip) that counts how often ground truth foreground pixels are assigned the wrong foreground identity while remaining predicted as foreground. In a setting where category and scene are correlated during training, increasing the correlation consistently widens the gap between common and rare test conditions and increases these within-object label swaps on counterfactual groups. Overall, our results motivate assessing segmentation robustness under distribution shift beyond overlap by decomposing foreground errors into correct pixels, flipped-identity pixels, and missed-to-background pixels. We also propose an entropy-based, ground truth label-free `flip-risk' score, which is computed from foreground identity uncertainty, and show that it can flag flip-prone cases at inference time. Code is available at https://github.com/acharaakshit/label-flips.

This paper proposes an approach to analyze an event log of a business process in order to generate case-level recommendations of treatments that maximize the probability of a given outcome. Users classify the attributes in the event log into controllable and non-controllable, where the former correspond to attributes that can be altered during an execution of the process (the possible treatments). We use an action rule mining technique to identify treatments that co-occur with the outcome under some conditions. Since action rules are generated based on correlation rather than causation, we then use a causal machine learning technique, specifically uplift trees, to discover subgroups of cases for which a treatment has a high causal effect on the outcome after adjusting for confounding variables. We test the relevance of this approach using an event log of a loan application process and compare our findings with recommendations manually produced by process mining experts.

Spurious correlations allow flexible models to predict well during training but poorly on related test distributions. Recent work has shown that models that satisfy particular independencies involving correlation-inducing nuisance variables have guarantees on their test performance. Enforcing such independencies requires nuisances to be observed during training. However, nuisances, such as demographics or image background labels, are often missing. Enforcing independence on just the observed data does not imply independence on the entire population. Here we derive mmd estimators used for invariance objectives under missing nuisances. On simulations and clinical data, optimizing through these estimates achieves test performance similar to using estimators that make use of the full data.

Time series play a fundamental role in many domains, capturing a plethora of information about the underlying data-generating processes. When a process generates multiple synchronized signals we are faced with multidimensional time series. In this context a fundamental problem is that of motif mining, where we seek patterns repeating twice with minor variations, spanning some of the dimensions. State of the art exact solutions for this problem run in time quadratic in the length of the input time series. We provide a scalable method to find the top-k motifs in multidimensional time series with probabilistic guarantees on the quality of the results. Our algorithm runs in time subquadratic in the length of the input, and returns the exact solution with probability at least 1-δ, where δ is a user-defined parameter. The algorithm is designed to be adaptive to the input distribution, self-tuning its parameters while respecting user-defined limits on the memory to use. Our theoretical analysis is complemented by an extensive experimental evaluation, showing that our algorithm is orders of magnitude faster than the state of the art.

Real-world regression often exhibits shortcuts: attributes that are spuriously correlated with continuous targets in training, yet unreliable under deployment shifts; regressing targets using such shortcuts may fail catastrophically at test time. Existing studies on spurious correlations focus primarily on classification, where labels are categorical and groups are naturally defined. However, many real-world tasks require continuous prediction, where hard label boundaries or discrete group-label pairs do not exist. We define Deep Spurious Regression (DSR) as learning from regression data with attribute-label confounding, addressing continuous spurious correlations, and generalizing to all attribute-label combinations at test time. Motivated by the intrinsic difference between classification and regression shortcuts, we propose to exploit the similarity among spurious attributes in both label and feature spaces, thereby accounting for nearby targets and related groups while calibrating both label and learned feature distributions across attributes. Extensive experiments on common real-world DSR datasets that span computer vision, environmental sensing, and large language model (LLM) regression verify the superior performance of our strategies. Our work fills the gap in benchmarks and techniques for studying spurious correlations in continuous prediction.

We are born with the ability to learn concepts by comparing diverse observations. This helps us to understand the new world in a compositional manner and facilitates extrapolation, as objects naturally consist of multiple concepts. In this work, we argue that the cognitive mechanism of comparison, fundamental to human learning, is also vital for machines to recover true concepts underlying the data. This offers correctness guarantees for the field of concept learning, which, despite its impressive empirical successes, still lacks general theoretical support. Specifically, we aim to develop a theoretical framework for the identifiability of concepts with multiple classes of observations. We show that with sufficient diversity across classes, hidden concepts can be identified without assuming specific concept types, functional relations, or parametric generative models. Interestingly, even when conditions are not globally satisfied, we can still provide alternative guarantees for as many concepts as possible based on local comparisons, thereby extending the applicability of our theory to more flexible scenarios. Moreover, the hidden structure between classes and concepts can also be identified nonparametrically. We validate our theoretical results in both synthetic and real-world settings.

Interpreting the inner function of neural networks is crucial for the trustworthy development and deployment of these black-box models. Prior interpretability methods focus on correlation-based measures to attribute model decisions to individual examples. However, these measures are susceptible to noise and spurious correlations encoded in the model during the training phase (e.g., biased inputs, model overfitting, or misspecification). Moreover, this process has proven to result in noisy and unstable attributions that prevent any transparent understanding of the model's behavior. In this paper, we develop a robust interventional-based method grounded by causal analysis to capture cause-effect mechanisms in pre-trained neural networks and their relation to the prediction. Our novel approach relies on path interventions to infer the causal mechanisms within hidden layers and isolate relevant and necessary information (to model prediction), avoiding noisy ones. The result is task-specific causal explanatory graphs that can audit model behavior and express the actual causes underlying its performance. We apply our method to vision models trained on classification tasks. On image classification tasks, we provide extensive quantitative experiments to show that our approach can capture more stable and faithful explanations than standard attribution-based methods. Furthermore, the underlying causal graphs reveal the neural interactions in the model, making it a valuable tool in other applications (e.g., model repair).

Anomaly detection methods can be very useful in identifying unusual or interesting patterns in data. A recently proposed conditional anomaly detection framework extends anomaly detection to the problem of identifying anomalous patterns on a subset of attributes in the data. The anomaly always depends (is conditioned) on the value of remaining attributes. The work presented in this paper focuses on instance-based methods for detecting conditional anomalies. The methods depend heavily on the distance metric that lets us identify examples in the dataset that are most critical for detecting the anomaly. To optimize the performance of such methods we study and devise a metric learning method that learns the distance metric to reflect best the conditional anomaly pattern.

Suppose Alice trains an open-weight language model and Bob uses a blackbox derivative of Alice's model to produce text. Can Alice prove that Bob is using her model, either by querying Bob's derivative model (query setting) or from the text alone (observational setting)? We formulate this question as an independence testing problem--in which the null hypothesis is that Bob's model or text is independent of Alice's randomized training run--and investigate it through the lens of palimpsestic memorization in language models: models are more likely to memorize data seen later in training, so we can test whether Bob is using Alice's model using test statistics that capture correlation between Bob's model or text and the ordering of training examples in Alice's training run. If Alice has randomly shuffled her training data, then any significant correlation amounts to exactly quantifiable statistical evidence against the null hypothesis, regardless of the composition of Alice's training data. In the query setting, we directly estimate (via prompting) the likelihood Bob's model gives to Alice's training examples and order; we correlate the likelihoods of over 40 fine-tunes of various Pythia and OLMo base models ranging from 1B to 12B parameters with the base model's training data order, achieving a p-value on the order of at most 1e-8 in all but six cases. In the observational setting, we try two approaches based on estimating 1) the likelihood of Bob's text overlapping with spans of Alice's training examples and 2) the likelihood of Bob's text with respect to different versions of Alice's model we obtain by repeating the last phase (e.g., 1%) of her training run on reshuffled data. The second approach can reliably distinguish Bob's text from as little as a few hundred tokens; the first does not involve any retraining but requires many more tokens (several hundred thousand) to achieve high power.

Scientific discovery is a cumulative process and requires new ideas to be situated within an ever-expanding landscape of existing knowledge. An emerging and critical challenge is how to identify conceptually relevant prior work from rapidly growing literature, and assess how a new idea differentiates from existing research. Current embedding approaches typically conflate distinct conceptual aspects into single representations and cannot support fine-grained literature retrieval; meanwhile, LLM-based evaluators are subject to sycophancy biases, failing to provide discriminative novelty assessment. To tackle these challenges, we introduce the Ideation Space, a structured representation that decomposes scientific knowledge into three distinct dimensions, i.e., research problem, methodology, and core findings, each learned through contrastive training. This framework enables principled measurement of conceptual distance between ideas, and modeling of ideation transitions that capture the logical connections within a proposed idea. Building upon this representation, we propose a Hierarchical Sub-Space Retrieval framework for efficient, targeted literature retrieval, and a Decomposed Novelty Assessment algorithm that identifies which aspects of an idea are novel. Extensive experiments demonstrate substantial improvements, where our approach achieves Recall@30 of 0.329 (16.7% over baselines), our ideation transition retrieval reaches Hit Rate@30 of 0.643, and novelty assessment attains 0.37 correlation with expert judgments. In summary, our work provides a promising paradigm for future research on accelerating and evaluating scientific discovery.

This paper introduces the Manifold Probe, a supervised method for discovering representation manifolds in superposition. The method generalizes linear regression probes by learning the space of features of a concept that can be linearly predicted from the representations, and then learning the directions used to encode them. We demonstrate the probe on representations of time and space in Llama 2-7b, finding manifolds which linearly represent an interpretable set of features in each case. In the case of time, we show that by steering along the manifold, we can influence the model's completions about the years in which famous songs, movies and books were released, providing evidence that the Manifold Probe can discover manifolds which are causally involved in model behaviour.

We consider learning representations (features) in the setting in which we have access to multiple unlabeled views of the data for learning while only one view is available for downstream tasks. Previous work on this problem has proposed several techniques based on deep neural networks, typically involving either autoencoder-like networks with a reconstruction objective or paired feedforward networks with a batch-style correlation-based objective. We analyze several techniques based on prior work, as well as new variants, and compare them empirically on image, speech, and text tasks. We find an advantage for correlation-based representation learning, while the best results on most tasks are obtained with our new variant, deep canonically correlated autoencoders (DCCAE). We also explore a stochastic optimization procedure for minibatch correlation-based objectives and discuss the time/performance trade-offs for kernel-based and neural network-based implementations.

Literature-Based Discovery (LBD) aims to discover new scientific knowledge by mining papers and generating hypotheses. Standard LBD is limited to predicting pairwise relations between discrete concepts (e.g., drug-disease links), and ignores critical contexts like experimental settings (e.g., a specific patient population where a drug is evaluated) and background motivations (e.g., to find drugs without specific side effects). We address these limitations with a novel formulation of contextualized-LBD (C-LBD): generating scientific hypotheses in natural language, while grounding them in a context that controls the hypothesis search space. We present a modeling framework using retrieval of ``inspirations'' from past scientific papers. Our evaluations reveal that GPT-4 tends to generate ideas with overall low technical depth and novelty, while our inspiration prompting approaches partially mitigate this issue. Our work represents a first step toward building language models that generate new ideas derived from scientific literature.

The Canonical Correlation Analysis (CCA) family of methods is foundational in multiview learning. Regularised linear CCA methods can be seen to generalise Partial Least Squares (PLS) and be unified with a Generalized Eigenvalue Problem (GEP) framework. However, classical algorithms for these linear methods are computationally infeasible for large-scale data. Extensions to Deep CCA show great promise, but current training procedures are slow and complicated. First we propose a novel unconstrained objective that characterizes the top subspace of GEPs. Our core contribution is a family of fast algorithms for stochastic PLS, stochastic CCA, and Deep CCA, simply obtained by applying stochastic gradient descent (SGD) to the corresponding CCA objectives. Our algorithms show far faster convergence and recover higher correlations than the previous state-of-the-art on all standard CCA and Deep CCA benchmarks. These improvements allow us to perform a first-of-its-kind PLS analysis of an extremely large biomedical dataset from the UK Biobank, with over 33,000 individuals and 500,000 features. Finally, we apply our algorithms to match the performance of `CCA-family' Self-Supervised Learning (SSL) methods on CIFAR-10 and CIFAR-100 with minimal hyper-parameter tuning, and also present theory to clarify the links between these methods and classical CCA, laying the groundwork for future insights.

A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis introduces robust and computationally efficient methods to address several common challenges associated with high-dimensional data. In my first manuscript, I propose a coherent approach to variable screening that accommodates nonlinear associations. I develop a novel variable screening method that transcends traditional linear assumptions by leveraging mutual information, with an intended application in neuroimaging data. This approach allows for accurate identification of important variables by capturing nonlinear as well as linear relationships between the outcome and covariates. Building on this foundation, I develop new optimization methods for sparse estimation using nonconvex penalties in my second manuscript. These methods address notable challenges in current statistical computing practices, facilitating computationally efficient and robust analyses of complex datasets. The proposed method can be applied to a general class of optimization problems. In my third manuscript, I contribute to robust modeling of high-dimensional correlated observations by developing a mixed-effects model based on Tsallis power-law entropy maximization and discussed the theoretical properties of such distribution. This model surpasses the constraints of conventional Gaussian models by accommodating a broader class of distributions with enhanced robustness to outliers. Additionally, I develop a proximal nonlinear conjugate gradient algorithm that accelerates convergence while maintaining numerical stability, along with rigorous statistical properties for the proposed framework.

An industrial process includes many devices, variables, and sub-processes that are physically or electronically interconnected. These interconnections imply some level of correlation between different process variables. Since most of the alarms in a process plant are defined on process variables, alarms are also correlated. However, this can be a nuisance to operators, for one fault might trigger a, sometimes large, number of alarms. So, it is essential to find and correct correlated alarms. In this paper, we study different methods and techniques proposed to measure correlation or similarity between alarms. The similarity indices are first analytically calculated and then studied and compared. The results are also validated using Monte-Carlo simulation.

A modern challenge of Artificial Intelligence is learning multiple patterns at once (i.e.parallel learning). While this can not be accomplished by standard Hebbian associative neural networks, in this paper we show how the Multitasking Hebbian Network (a variation on theme of the Hopfield model working on sparse data-sets) is naturally able to perform this complex task. We focus on systems processing in parallel a finite (up to logarithmic growth in the size of the network) amount of patterns, mirroring the low-storage level of standard associative neural networks at work with pattern recognition. For mild dilution in the patterns, the network handles them hierarchically, distributing the amplitudes of their signals as power-laws w.r.t. their information content (hierarchical regime), while, for strong dilution, all the signals pertaining to all the patterns are raised with the same strength (parallel regime). Further, confined to the low-storage setting (i.e., far from the spin glass limit), the presence of a teacher neither alters the multitasking performances nor changes the thresholds for learning: the latter are the same whatever the training protocol is supervised or unsupervised. Results obtained through statistical mechanics, signal-to-noise technique and Monte Carlo simulations are overall in perfect agreement and carry interesting insights on multiple learning at once: for instance, whenever the cost-function of the model is minimized in parallel on several patterns (in its description via Statistical Mechanics), the same happens to the standard sum-squared error Loss function (typically used in Machine Learning).

The development of state-of-the-art (SOTA) Natural Language Processing (NLP) systems has steadily been establishing new techniques to absorb the statistics of linguistic data. These techniques often trace well-known constructs from traditional theories, and we study these connections to close gaps around key NLP methods as a means to orient future work. For this, we introduce an analytic model of the statistics learned by seminal algorithms (including GloVe and Word2Vec), and derive insights for systems that use these algorithms and the statistics of co-occurrence, in general. In this work, we derive -- to the best of our knowledge -- the first known solution to Word2Vec's softmax-optimized, skip-gram algorithm. This result presents exciting potential for future development as a direct solution to a deep learning (DL) language model's (LM's) matrix factorization. However, we use the solution to demonstrate a seemingly-universal existence of a property that word vectors exhibit and which allows for the prophylactic discernment of biases in data -- prior to their absorption by DL models. To qualify our work, we conduct an analysis of independence, i.e., on the density of statistical dependencies in co-occurrence models, which in turn renders insights on the distributional hypothesis' partial fulfillment by co-occurrence statistics.

This paper revisits datasets and evaluation criteria for Symbolic Regression, a task of expressing given data using mathematical equations, specifically focused on its potential for scientific discovery. Focused on a set of formulas used in the existing datasets based on Feynman Lectures on Physics, we recreate 120 datasets to discuss the performance of symbolic regression for scientific discovery (SRSD). For each of the 120 SRSD datasets, we carefully review the properties of the formula and its variables to design reasonably realistic sampling range of values so that our new SRSD datasets can be used for evaluating the potential of SRSD such as whether or not an SR method can (re)discover physical laws from such datasets. As an evaluation metric, we also propose to use normalized edit distances between a predicted equation and the ground-truth equation trees. While existing metrics are either binary or errors between the target values and an SR model's predicted values for a given input, normalized edit distances evaluate a sort of similarity between the ground-truth and predicted equation trees. We have conducted experiments on our new SRSD datasets using five state-of-the-art SR methods in SRBench and a simple baseline based on a recent Transformer architecture. The results show that we provide a more realistic performance evaluation and open up a new machine learning-based approach for scientific discovery. Our datasets and code repository are publicly available.

Large language models (LLMs) have achieved remarkable progress in natural language generation, yet they continue to display puzzling behaviors -- such as repetition and incoherence -- even when exhibiting low perplexity. This highlights a key limitation of conventional evaluation metrics, which emphasize local prediction accuracy while overlooking long-range structural complexity. We introduce correlation dimension, a fractal-geometric measure of self-similarity, to quantify the epistemological complexity of text as perceived by a language model. This measure captures the hierarchical recurrence structure of language, bridging local and global properties in a unified framework. Through extensive experiments, we show that correlation dimension (1) reveals three distinct phases during pretraining, (2) reflects context-dependent complexity, (3) indicates a model's tendency toward hallucination, and (4) reliably detects multiple forms of degeneration in generated text. The method is computationally efficient, robust to model quantization (down to 4-bit precision), broadly applicable across autoregressive architectures (e.g., Transformer and Mamba), and provides fresh insight into the generative dynamics of LLMs.

Redundancies and correlations in the responses of sensory neurons seem to waste neural resources but can carry cues about structured stimuli and may help the brain to correct for response errors. To assess how the retina negotiates this tradeoff, we measured simultaneous responses from populations of ganglion cells presented with natural and artificial stimuli that varied greatly in correlation structure. We found that pairwise correlations in the retinal output remained similar across stimuli with widely different spatio-temporal correlations including white noise and natural movies. Meanwhile, purely spatial correlations tended to increase correlations in the retinal response. Responding to more correlated stimuli, ganglion cells had faster temporal kernels and tended to have stronger surrounds. These properties of individual cells, along with gain changes that opposed changes in effective contrast at the ganglion cell input, largely explained the similarity of pairwise correlations across stimuli where receptive field measurements were possible.

Equation discovery aims to automate the discovery of scientific models in the form of mathematical equations from data. Technically, equation discovery is implemented by symbolic regression algorithms. Performance of symbolic regression for equation discovery is measured along two dimensions: Prediction accuracy on test data, and recovery of known groundtruth formulas. For standard regression, accuracy is typically measured on in-domain test data, for instance, by splitting a data set randomly into training and test data. While this makes sense for in-domain interpolation, which is the common goal in ordinary regression, it can be a misleading proxy for true model discovery and generalization. The obvious alternative is to measure out-of-domain accuracy. However, obtaining challenging out-of-domain test data is a non-trivial problem. Therefore, we focus on equation recovery for evaluating symbolic regression algorithms for equation discovery. The rationale is that symbolic regression algorithms that perform well in recovering known groundtruth formulas are good candidates to perform well in unknown equation discovery. Existing benchmarks for symbolic regression include equation recovery tasks, however, with only a small number of groundtruth formulas that are publicly known. Moreover, these benchmarks place less emphasis on evaluating the robustness of algorithms in terms of their behavior under changing dimensionality, sampling size, sampling distribution and sampling domain. This, however, is of central importance to practitioners wanting to discover equations for modeling natural phenomena, since data is almost certainly noisy and comes from diverse domains, distributions, and sample sizes. To fill this gap, we introduce the Equation Recovery Benchmark (ERBench), a new evaluation framework designed to rigorously assess algorithms explicitly targeting the task of equation discovery.

Self-supervised learning excels at learning representations from large amounts of data. At the same time, generative models offer the complementary property of learning information about the underlying data generation process. In this study, we aim at establishing a principled connection between these two paradigms and highlight the benefits of their complementarity. In particular, we perform an analysis of self-supervised learning objectives, elucidating the underlying probabilistic graphical models and presenting a standardized methodology for their derivation from first principles. The analysis suggests a natural means of integrating self-supervised learning with likelihood-based generative models. We instantiate this concept within the realm of cluster-based self-supervised learning and energy models, introducing a lower bound proven to reliably penalize the most important failure modes and unlocking full unification. Our theoretical findings are substantiated through experiments on synthetic and real-world data, including SVHN, CIFAR10, and CIFAR100, demonstrating that our objective function allows to jointly train a backbone network in a discriminative and generative fashion, consequently outperforming existing self-supervised learning strategies in terms of clustering, generation and out-of-distribution detection performance by a wide margin. We also demonstrate that the solution can be integrated into a neuro-symbolic framework to tackle a simple yet non-trivial instantiation of the symbol grounding problem. The code is publicly available at https://github.com/emsansone/GEDI.

Discovering effective predictive signals, or ``alphas,'' from financial data with high dimensionality and extremely low signal-to-noise ratio remains a difficult open problem. Despite progress in deep learning, genetic programming, and, more recently, large language model (LLM)--based factor generation, existing approaches still explore only a narrow region of the vast alpha search space. Neural models tend to produce opaque and fragile patterns, while symbolic or formula-based methods often yield redundant or economically ungrounded expressions that generalize poorly. Although different in form, these paradigms share a key limitation: none can conduct broad, structured, and human-like exploration that balances logical consistency with creative leaps. To address this gap, we introduce the Cognitive Alpha Mining Framework (CogAlpha), which combines code-level alpha representation with LLM-driven reasoning and evolutionary search. Treating LLMs as adaptive cognitive agents, our framework iteratively refines, mutates, and recombines alpha candidates through multi-stage prompts and financial feedback. This synergistic design enables deeper thinking, richer structural diversity, and economically interpretable alpha discovery, while greatly expanding the effective search space. Experiments on A-share equities demonstrate that CogAlpha consistently discovers alphas with superior predictive accuracy, robustness, and generalization over existing methods. Our results highlight the promise of aligning evolutionary optimization with LLM-based reasoning for automated and explainable alpha discovery. All source code will be released.

In this paper we introduce Feature Gradients, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e., in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N . This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Crucially, our algorithm is capable of finding higher-order correlations between features and targets for both the N > D and N < D regimes, as opposed to approaches that do not consider such interactions and/or only consider one regime. We provide experimental demonstration of the algorithm in small and large sample-and feature-size settings.

Causal representation learning aims to unveil latent high-level causal representations from observed low-level data. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as identifiability. A recent breakthrough explores identifiability by leveraging the change of causal influences among latent causal variables across multiple environments liu2022identifying. However, this progress rests on the assumption that the causal relationships among latent causal variables adhere strictly to linear Gaussian models. In this paper, we extend the scope of latent causal models to involve nonlinear causal relationships, represented by polynomial models, and general noise distributions conforming to the exponential family. Additionally, we investigate the necessity of imposing changes on all causal parameters and present partial identifiability results when part of them remains unchanged. Further, we propose a novel empirical estimation method, grounded in our theoretical finding, that enables learning consistent latent causal representations. Our experimental results, obtained from both synthetic and real-world data, validate our theoretical contributions concerning identifiability and consistency.

We present a straightforward statistical test to detect certain violations of the assumption that the data are Independent and Identically Distributed (IID). The specific form of violation considered is common across real-world applications: whether the examples are ordered in the dataset such that almost adjacent examples tend to have more similar feature values (e.g. due to distributional drift, or attractive interactions between datapoints). Based on a k-Nearest Neighbors estimate, our approach can be used to audit any multivariate numeric data as well as other data types (image, text, audio, etc.) that can be numerically represented, perhaps with model embeddings. Compared with existing methods to detect drift or auto-correlation, our approach is both applicable to more types of data and also able to detect a wider variety of IID violations in practice. Code: https://github.com/cleanlab/cleanlab

We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is to cluster a set of objects based on multiway interactions of different categories or types. We present improved approximation guarantees based on linear programming, and show they are tight by proving a matching integrality gap. Our results also include new approximation hardness results, a combinatorial 2-approximation whose runtime is linear in the hypergraph size, and several new connections to well-studied objectives such as vertex cover and hypergraph multiway cut.

Recent advances in LLMs have made automated scientific research the next frontline in the path to artificial superintelligence. However, these systems are bound either to tasks of narrow scope or the limited creative capabilities of LLMs. We propose Spacer, a scientific discovery system that develops creative and factually grounded concepts without external intervention. Spacer attempts to achieve this via 'deliberate decontextualization,' an approach that disassembles information into atomic units - keywords - and draws creativity from unexplored connections between them. Spacer consists of (i) Nuri, an inspiration engine that builds keyword sets, and (ii) the Manifesting Pipeline that refines these sets into elaborate scientific statements. Nuri extracts novel, high-potential keyword sets from a keyword graph built with 180,000 academic publications in biological fields. The Manifesting Pipeline finds links between keywords, analyzes their logical structure, validates their plausibility, and ultimately drafts original scientific concepts. According to our experiments, the evaluation metric of Nuri accurately classifies high-impact publications with an AUROC score of 0.737. Our Manifesting Pipeline also successfully reconstructs core concepts from the latest top-journal articles solely from their keyword sets. An LLM-based scoring system estimates that this reconstruction was sound for over 85% of the cases. Finally, our embedding space analysis shows that outputs from Spacer are significantly more similar to leading publications compared with those from SOTA LLMs.

We decompose the evidence lower bound to show the existence of a term measuring the total correlation between latent variables. We use this to motivate our beta-TCVAE (Total Correlation Variational Autoencoder), a refinement of the state-of-the-art beta-VAE objective for learning disentangled representations, requiring no additional hyperparameters during training. We further propose a principled classifier-free measure of disentanglement called the mutual information gap (MIG). We perform extensive quantitative and qualitative experiments, in both restricted and non-restricted settings, and show a strong relation between total correlation and disentanglement, when the latent variables model is trained using our framework.

Semantic Segmentation is a significant research field in Computer Vision. Despite being a widely studied subject area, many visualization tools do not exist that capture segmentation quality and dataset statistics such as a class imbalance in the same view. While the significance of discovering and introspecting the correlation between dataset statistics and AI model performance for dense prediction computer vision tasks such as semantic segmentation is well established in the computer vision literature, to the best of our knowledge, no visualization tools have been proposed to view and analyze the aforementioned tasks. Our project aims to bridge this gap by proposing three visualizations that enable users to compare dataset statistics and AI performance for segmenting all images, a single image in the dataset, explore the AI model's attention on image regions once trained and browse the quality of masks predicted by AI for any selected (by user) number of objects under the same tool. Our project tries to further increase the interpretability of the trained AI model for segmentation by visualizing its image attention weights. For visualization, we use Scatterplot and Heatmap to encode correlation and features, respectively. We further propose to conduct surveys on real users to study the efficacy of our visualization tool in computer vision and AI domain. The full system can be accessed at https://github.com/dipta007/SeeBel

Discovering causal structures with latent variables from observational data is a fundamental challenge in causal discovery. Existing methods often rely on constraint-based, iterative discrete searches, limiting their scalability to large numbers of variables. Moreover, these methods frequently assume linearity or invertibility, restricting their applicability to real-world scenarios. We present new theoretical results on the identifiability of nonlinear latent hierarchical causal models, relaxing previous assumptions in literature about the deterministic nature of latent variables and exogenous noise. Building on these insights, we develop a novel differentiable causal discovery algorithm that efficiently estimates the structure of such models. To the best of our knowledge, this is the first work to propose a differentiable causal discovery method for nonlinear latent hierarchical models. Our approach outperforms existing methods in both accuracy and scalability. We demonstrate its practical utility by learning interpretable hierarchical latent structures from high-dimensional image data and demonstrate its effectiveness on downstream tasks.

Novel Class Discovery (NCD) is a growing field where we are given during training a labeled set of known classes and an unlabeled set of different classes that must be discovered. In recent years, many methods have been proposed to address this problem, and the field has begun to mature. In this paper, we provide a comprehensive survey of the state-of-the-art NCD methods. We start by formally defining the NCD problem and introducing important notions. We then give an overview of the different families of approaches, organized by the way they transfer knowledge from the labeled set to the unlabeled set. We find that they either learn in two stages, by first extracting knowledge from the labeled data only and then applying it to the unlabeled data, or in one stage by conjointly learning on both sets. For each family, we describe their general principle and detail a few representative methods. Then, we briefly introduce some new related tasks inspired by the increasing number of NCD works. We also present some common tools and techniques used in NCD, such as pseudo labeling, self-supervised learning and contrastive learning. Finally, to help readers unfamiliar with the NCD problem differentiate it from other closely related domains, we summarize some of the closest areas of research and discuss their main differences.

Relational data augmentation is a powerful technique for enhancing data analytics and improving machine learning models by incorporating columns from external datasets. However, it is challenging to efficiently discover relevant external tables to join with a given input table. Existing approaches rely on data discovery systems to identify joinable tables from external sources, typically based on overlap or containment. However, the sheer number of tables obtained from these systems results in irrelevant joins that need to be performed; this can be computationally expensive or even infeasible in practice. We address this limitation by proposing the use of efficient mutual information (MI) estimation for finding relevant joinable tables. We introduce a new sketching method that enables efficient evaluation of relationship discovery queries by estimating MI without materializing the joins and returning a smaller set of tables that are more likely to be relevant. We also demonstrate the effectiveness of our approach at approximating MI in extensive experiments using synthetic and real-world datasets.

In this paper, we propose REASON, a novel framework that enables the automatic discovery of both intra-level (i.e., within-network) and inter-level (i.e., across-network) causal relationships for root cause localization. REASON consists of Topological Causal Discovery and Individual Causal Discovery. The Topological Causal Discovery component aims to model the fault propagation in order to trace back to the root causes. To achieve this, we propose novel hierarchical graph neural networks to construct interdependent causal networks by modeling both intra-level and inter-level non-linear causal relations. Based on the learned interdependent causal networks, we then leverage random walks with restarts to model the network propagation of a system fault. The Individual Causal Discovery component focuses on capturing abrupt change patterns of a single system entity. This component examines the temporal patterns of each entity's metric data (i.e., time series), and estimates its likelihood of being a root cause based on the Extreme Value theory. Combining the topological and individual causal scores, the top K system entities are identified as root causes. Extensive experiments on three real-world datasets with case studies demonstrate the effectiveness and superiority of the proposed framework.

Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been extensively used in the most diverse types of problems, also motivating some respective generalizations. The present work addresses further generalizations of this index, including its modification into a coincidence index capable of accounting also for the level of relative interiority between the two compared entities, as well as respective extensions for sets in continuous vector spaces, the generalization to multiset addition, densities and generic scalar fields, as well as a means to quantify the joint interdependence between two random variables. The also interesting possibility to take into account more than two sets has also been addressed, including the description of an index capable of quantifying the level of chaining between three structures. Several of the described and suggested eneralizations have been illustrated with respect to numeric case examples. It is also posited that these indices can play an important role while analyzing and integrating datasets in modeling approaches and pattern recognition activities, including as a measurement of clusters similarity or separation and as a resource for representing and analyzing complex networks.

The clustering problem, and more generally, latent factor discovery --or latent space inference-- is formulated in terms of the Wasserstein barycenter problem from optimal transport. The objective proposed is the maximization of the variability attributable to class, further characterized as the minimization of the variance of the Wasserstein barycenter. Existing theory, which constrains the transport maps to rigid translations, is extended to affine transformations. The resulting non-parametric clustering algorithms include k-means as a special case and exhibit more robust performance. A continuous version of these algorithms discovers continuous latent variables and generalizes principal curves. The strength of these algorithms is demonstrated by tests on both artificial and real-world data sets.

Earthquakes are evaluated among the most destructive disasters for human beings, as also experienced for Turkiye region. Data science has the property of discovering hidden patterns in case a sufficient volume of data is supplied. Time dependency of events, specifically being defined by co-occurrence in a specific time window, may be handled as an associate rule mining task such as a market-basket analysis application. In this regard, we assumed each day's seismic activity as a single basket of events, leading to discovering the association patterns between these events. Consequently, this study presents the most prominent association rules for the earthquakes recorded in Turkiye region in the last 5 years, each year presented separately. Results indicate statistical inference with events recorded from regions of various distances, which could be further verified with geologic evidence from the field. As a result, we believe that the current study may form a statistical basis for the future works with the aid of machine learning algorithm performed for associate rule mining.

Being able to provide explanations for a model's decision has become a central requirement for the development, deployment, and adoption of machine learning models. However, we are yet to understand what explanation methods can and cannot do. How do upstream factors such as data, model prediction, hyperparameters, and random initialization influence downstream explanations? While previous work raised concerns that explanations (E) may have little relationship with the prediction (Y), there is a lack of conclusive study to quantify this relationship. Our work borrows tools from causal inference to systematically assay this relationship. More specifically, we study the relationship between E and Y by measuring the treatment effect when intervening on their causal ancestors, i.e., on hyperparameters and inputs used to generate saliency-based Es or Ys. Our results suggest that the relationships between E and Y is far from ideal. In fact, the gap between 'ideal' case only increase in higher-performing models -- models that are likely to be deployed. Our work is a promising first step towards providing a quantitative measure of the relationship between E and Y, which could also inform the future development of methods for E with a quantitative metric.

Causal graphs provide a high-level language for making mechanisms transparent. Recent work uses Large Language Models (LLMs) to recover causal graphs of external-world processes. Instead, in this paper, we use causal graphs to model LLM inference itself, providing stakeholders with a transparent view of how the model perceives and organizes high-level concepts to produce a prediction. We propose a four-phase method for constructing such graphs. Given a target LLM and a set of textual examples, our method discovers class-discriminative, human-interpretable concepts and maps each input to LLM-perceived concept states. We then introduce an MCMC-inspired counterfactual augmentation procedure that expands the sparse observational data through chains of counterfactuals. This enables stable causal discovery with σ-CG, yielding informative, interpretable graphs. We apply our method to three LLMs across disease diagnosis, sentiment analysis, and LLM-as-a-judge classification tasks. We evaluate the learned graphs for predictive fidelity and structural stability, and the MCMC-inspired augmentation for convergence and downstream utility. Our results show that the discovered causal graphs capture meaningful dependencies consistent with LLMs' reasoning. Together, this paper provides a foundation for concept-level explainability of LLMs.

Solving complex classification tasks using deep neural networks typically requires large amounts of annotated data. However, corresponding class labels are noisy when provided by error-prone annotators, e.g., crowd workers. Training standard deep neural networks leads to subpar performances in such multi-annotator supervised learning settings. We address this issue by presenting a probabilistic training framework named multi-annotator deep learning (MaDL). A ground truth and an annotator performance model are jointly trained in an end-to-end learning approach. The ground truth model learns to predict instances' true class labels, while the annotator performance model infers probabilistic estimates of annotators' performances. A modular network architecture enables us to make varying assumptions regarding annotators' performances, e.g., an optional class or instance dependency. Further, we learn annotator embeddings to estimate annotators' densities within a latent space as proxies of their potentially correlated annotations. Together with a weighted loss function, we improve the learning from correlated annotation patterns. In a comprehensive evaluation, we examine three research questions about multi-annotator supervised learning. Our findings indicate MaDL's state-of-the-art performance and robustness against many correlated, spamming annotators.

Choosing which properties of the data to use as input to multivariate decision algorithms -- a.k.a. feature selection -- is an important step in solving any problem with machine learning. While there is a clear trend towards training sophisticated deep networks on large numbers of relatively unprocessed inputs (so-called automated feature engineering), for many tasks in physics, sets of theoretically well-motivated and well-understood features already exist. Working with such features can bring many benefits, including greater interpretability, reduced training and run time, and enhanced stability and robustness. We develop a new feature selection method based on Distance Correlation (DisCo), and demonstrate its effectiveness on the tasks of boosted top- and W-tagging. Using our method to select features from a set of over 7,000 energy flow polynomials, we show that we can match the performance of much deeper architectures, by using only ten features and two orders-of-magnitude fewer model parameters.

Causal inference is one of the hallmarks of human intelligence. While the field of CausalNLP has attracted much interest in the recent years, existing causal inference datasets in NLP primarily rely on discovering causality from empirical knowledge (e.g., commonsense knowledge). In this work, we propose the first benchmark dataset to test the pure causal inference skills of large language models (LLMs). Specifically, we formulate a novel task Corr2Cause, which takes a set of correlational statements and determines the causal relationship between the variables. We curate a large-scale dataset of more than 400K samples, on which we evaluate seventeen existing LLMs. Through our experiments, we identify a key shortcoming of LLMs in terms of their causal inference skills, and show that these models achieve almost close to random performance on the task. This shortcoming is somewhat mitigated when we try to re-purpose LLMs for this skill via finetuning, but we find that these models still fail to generalize -- they can only perform causal inference in in-distribution settings when variable names and textual expressions used in the queries are similar to those in the training set, but fail in out-of-distribution settings generated by perturbing these queries. Corr2Cause is a challenging task for LLMs, and would be helpful in guiding future research on improving LLMs' pure reasoning skills and generalizability. Our data is at https://huggingface.co/datasets/causalnlp/corr2cause. Our code is at https://github.com/causalNLP/corr2cause.

Hypothetical induction is recognized as the main reasoning type when scientists make observations about the world and try to propose hypotheses to explain those observations. Past research on hypothetical induction is under a constrained setting: (1) the observation annotations in the dataset are carefully manually handpicked sentences (resulting in a close-domain setting); and (2) the ground truth hypotheses are mostly commonsense knowledge, making the task less challenging. In this work, we tackle these problems by proposing the first dataset for social science academic hypotheses discovery, with the final goal to create systems that automatically generate valid, novel, and helpful scientific hypotheses, given only a pile of raw web corpus. Unlike previous settings, the new dataset requires (1) using open-domain data (raw web corpus) as observations; and (2) proposing hypotheses even new to humanity. A multi-module framework is developed for the task, including three different feedback mechanisms to boost performance, which exhibits superior performance in terms of both GPT-4 based and expert-based evaluation. To the best of our knowledge, this is the first work showing that LLMs are able to generate novel (''not existing in literature'') and valid (''reflecting reality'') scientific hypotheses.

Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed strategies that do not improve with experience. In this paper, we introduce the first symbolic regression method that leverages large scale pre-training. We procedurally generate an unbounded set of equations, and simultaneously pre-train a Transformer to predict the symbolic equation from a corresponding set of input-output-pairs. At test time, we query the model on a new set of points and use its output to guide the search for the equation. We show empirically that this approach can re-discover a set of well-known physical equations, and that it improves over time with more data and compute.

Agents are widely deployed as assistants over documents, tools, and code. However, they typically act only on explicit user requests, which surface only the problems the user has noticed, while many other important problems coexist, hidden in plain sight, within the broader user context, with their total number unknown in advance. We frame this as the task of discovering multiple hidden problems from context, in which coexisting problems should be uncovered, grounded in supporting evidence, and paired with concrete actions. To this end, we introduce TIDE, a template-guided iterative framework with two complementary mechanisms. Specifically, motivated by the observation that single-pass prediction anchors on the most salient cases and yields generic claims, we propose iterative discovery, which surfaces a small batch of candidates per round while conditioning on what has already been found, so subsequent rounds extend coverage; and thought templates, reusable schemas distilled from previously solved cases that specify what contextual signals to attend to and how to connect them, anchoring each prediction in a recognizable problem class. We validate TIDE on two realistic settings, personal workspaces and software repositories, across four model backbones, showing substantial gains over single-shot and parallel multi-agent baselines on task coverage, identification, and resolution.

Anomaly detection methods can be very useful in identifying unusual or interesting patterns in data. A recently proposed conditional anomaly detection framework extends anomaly detection to the problem of identifying anomalous patterns on a subset of attributes in the data. The anomaly always depends (is conditioned) on the value of remaining attributes. The work presented in this paper focuses on instance-based methods for detecting conditional anomalies. The methods rely on the distance metric to identify examples in the dataset that are most critical for detecting the anomaly. We investigate various metrics and metric learning methods to optimize the performance of the instance-based anomaly detection methods. We show the benefits of the instance-based methods on two real-world detection problems: detection of unusual admission decisions for patients with the community-acquired pneumonia and detection of unusual orders of an HPF4 test that is used to confirm Heparin induced thrombocytopenia - a life-threatening condition caused by the Heparin therapy.

Despite remarkable advances in the field, LLMs remain unreliable in distinguishing causation from correlation. Recent results from the Corr2Cause dataset benchmark reveal that state-of-the-art LLMs -- such as GPT-4 (F1 score: 29.08) -- only marginally outperform random baselines (Random Uniform, F1 score: 20.38), indicating limited capacity of generalization. To tackle this limitation, we propose a novel structured approach: rather than directly answering causal queries, we provide the model with the capability to structure its thinking by guiding the model to build a structured knowledge graph, systematically encoding the provided correlational premises, to answer the causal queries. This intermediate representation significantly enhances the model's causal capabilities. Experiments on the test subset of the Corr2Cause dataset benchmark with Qwen3-32B model (reasoning model) show substantial gains over standard direct prompting methods, improving F1 scores from 32.71 to 48.26 (over 47.5% relative increase), along with notable improvements in precision and recall. These results underscore the effectiveness of providing the model with the capability to structure its thinking and highlight its promising potential for broader generalization across diverse causal inference tasks.

We address causal reasoning in multivariate time series data generated by stochastic processes. Existing approaches are largely restricted to static settings, ignoring the continuity and emission of variations across time. In contrast, we propose a learning paradigm that directly establishes causation between events in the course of time. We present two key lemmas to compute causal contributions and frame them as reinforcement learning problems. Our approach offers formal and computational tools for uncovering and quantifying causal relationships in diffusion processes, subsuming various important settings such as discrete-time Markov decision processes. Finally, in fairly intricate experiments and through sheer learning, our framework reveals and quantifies causal links, which otherwise seem inexplicable.

On-the-fly category discovery (OCD) aims to recognize known categories while simultaneously discovering novel ones from an unlabeled online stream, using a model trained only on labeled data. Existing approaches freeze the feature extractor trained offline and employ a hash-based framework that quantizes features into binary codes as class prototypes. However, discovering novel categories with a fixed knowledge base is counterintuitive, as the learning potential of incoming data is entirely neglected. In addition, feature quantization introduces information loss, diminishes representational expressiveness, and amplifies intra-class variance. It often results in category explosion, where a single class is fragmented into multiple pseudo-classes. To overcome these limitations, we propose a test-time adaptation framework that enables learning through discovery. It incorporates two complementary strategies: a semantic-aware prototype update and a stable test-time encoder update. The former dynamically refines class prototypes to enhance classification, whereas the latter integrates new information directly into the parameter space. Together, these components allow the model to continuously expand its knowledge base with newly encountered samples. Furthermore, we introduce a margin-aware logit calibration in the offline stage to enlarge inter-class margins and improve intra-class compactness, thereby reserving embedding space for future class discovery. Experiments on standard OCD benchmarks demonstrate that our method substantially outperforms existing hash-based state-of-the-art approaches, yielding notable improvements in novel-class accuracy and effectively mitigating category explosion. The code is publicly available at blue{https://github.com/ynanwu/TALON}.

Causality testing, the act of determining cause and effect from measurements, is widely used in physics, climatology, neuroscience, econometrics and other disciplines. As a result, a large number of causality testing methods based on various principles have been developed. Causal relationships in complex systems are typically accompanied by entropic exchanges which are encoded in patterns of dynamical measurements. A data compression algorithm which can extract these encoded patterns could be used for inferring these relations. This motivates us to propose, for the first time, a generic causality testing framework based on data compression. The framework unifies existing causality testing methods and enables us to innovate a novel Compression-Complexity Causality measure. This measure is rigorously tested on simulated and real-world time series and is found to overcome the limitations of Granger Causality and Transfer Entropy, especially for noisy and non-synchronous measurements. Additionally, it gives insight on the `kind' of causal influence between input time series by the notions of positive and negative causality.