arXiv:2604.01339v1 Announce Type: cross Abstract: Vision transformers (ViT) rely on attention mechanism to weigh input features, and therefore attention scores have naturally been considered as explanations for its decision-making process. However, attention scores are almost always non-zero, resulting in noisy and diffused attention maps and limiting interpretability. Can we quantify uncertainty measures of attention scores and obtain regularized attention scores? To this end, we consider attention scores of ViT in a statistical framework where independent noise would lead to insignificant yet non-zero scores. Leveraging statistical learning techniques, we introduce the bootstrapping for attention scores which generates a baseline distribution of attention scores by resampling input features. Such a bootstrap distribution is then used to estimate significances and posterior probabilities of attention scores. In natural and medical images, the proposed \emph{Attention Regularization} approach demonstrates a straightforward removal of spurious attention arising from noise, drastically improving shrinkage and sparsity. Quantitative evaluations are conducted using both simulation and real-world datasets. Our study highlights bootstrapping as a practical regularization tool when using attention scores as explanations for ViT. Code available: https://github.com/ncchung/AttentionRegularization

arXiv:2508.14285v3 Announce Type: replace-cross Abstract: Fine-tuning large language models (LLMs) with low-rank adaptation (LoRA) is a cost-effective way to incorporate information from a specific dataset. However, when a problem requires incorporating information from multiple datasets - as in few shot learning - generalization across datasets can be limited, driving up training costs. As a consequence, other approaches such as in-context learning are typically used in this setting. To address this challenge, we introduce an efficient method for adapting the weights of LLMs to multiple distributions, Amortized Bayesian Meta-Learning for LoRA (ABMLL). This method builds on amortized Bayesian meta-learning for smaller models, adapting this approach to LLMs by reframing where local and global variables are defined in LoRA and using a new hyperparameter to balance reconstruction accuracy and the fidelity of task-specific parameters to the global ones. ABMLL supports effective generalization across datasets and scales to large models such as Llama3-8B and Qwen2-7B, outperforming existing methods on the CrossFit and Unified-QA datasets in terms of both accuracy and expected calibration error. We show that meta-learning can also be combined with in-context learning, resulting in further improvements in both these datasets and legal and chemistry applications.

arXiv:2601.11016v2 Announce Type: replace-cross Abstract: In this paper, we introduce a framework for contextual distributionally robust optimization (DRO) that considers the causal and continuous structure of the underlying distribution by developing interpretable and tractable decision rules that prescribe decisions using covariates. We first introduce the causal Sinkhorn discrepancy (CSD), an entropy-regularized causal Wasserstein distance that encourages continuous transport plans while preserving the causal consistency. We then formulate a contextual DRO model with a CSD-based ambiguity set, termed Causal Sinkhorn DRO (Causal-SDRO), and derive its strong dual reformulation where the worst-case distribution is characterized as a mixture of Gibbs distributions. To solve the corresponding infinite-dimensional policy optimization, we propose the Soft Regression Forest (SRF) decision rule, which approximates optimal policies within arbitrary measurable function spaces. The SRF preserves the interpretability of classical decision trees while being fully parametric, differentiable, and Lipschitz smooth, enabling intrinsic interpretation from both global and local perspectives. To solve the Causal-SDRO with parametric decision rules, we develop an efficient stochastic compositional gradient algorithm that converges to an $\varepsilon$-stationary point at a rate of $O(\varepsilon^{-4})$, matching the convergence rate of standard stochastic gradient descent. Finally, we validate our method through numerical experiments on synthetic and real-world datasets, demonstrating its superior performance and interpretability.

arXiv:2603.02491v2 Announce Type: replace-cross Abstract: As artificial agents become increasingly capable, what internal structure is *necessary* for an agent to act competently under uncertainty? Classical results show that optimal control can be *implemented* using belief states or world models, but not that such representations are required. We prove quantitative "selection theorems" showing that strong task performance (low *average-case regret*) forces world models, belief-like memory and -- under task mixtures -- persistent variables resembling core primitives associated with emotion, along with informational modularity under block-structured tasks. Our results cover stochastic policies, partial observability, and evaluation under task distributions, without assuming optimality, determinism, or access to an explicit model. Technically, we reduce predictive modeling to binary "betting" decisions and show that regret bounds limit probability mass on suboptimal bets, enforcing the predictive distinctions needed to separate high-margin outcomes. In fully observed settings, this yields approximate recovery of the interventional transition kernel; under partial observability, it implies necessity of predictive state and belief-like memory, addressing an open question in prior world-model recovery work.

arXiv:2603.17717v2 Announce Type: replace-cross Abstract: Supervised detection of network attacks has always been a critical part of network intrusion detection systems (NIDS). Nowadays, in a pivotal time for artificial intelligence (AI), with even more sophisticated attacks that utilize advanced techniques, such as generative artificial intelligence (GenAI) and reinforcement learning, it has become a vital component if we wish to protect our personal data, which are scattered across the web. In this paper, we address two tasks, in the first unified multi-modal NIDS dataset, which incorporates flow-level data, packet payload information and temporal contextual features, from the reprocessed CIC-IDS-2017, CIC-IoT-2023, UNSW-NB15 and CIC-DDoS-2019, with the same feature space. In the first task we use machine learning (ML) algorithms, with stratified cross validation, in order to prevent network attacks, with stability and reliability. In the second task we use adversarial learning algorithms to generate synthetic data, compare them with the real ones and evaluate their fidelity, utility and privacy using the SDV framework, f-divergences, distinguishability and non-parametric statistical tests. The findings provide stable ML models for intrusion detection and generative models with high fidelity and utility, by combining the Synthetic Data Vault framework, the TRTS and TSTR tests, with non-parametric statistical tests and f-divergence measures.

arXiv:2603.28650v2 Announce Type: replace-cross Abstract: Can a safety gate permit unbounded beneficial self-modification while maintaining bounded cumulative risk? We formalize this question through dual conditions -- requiring sum delta_n 1, any classifier-based gate under overlapping safe/unsafe distributions satisfies TPR_n 0, escaping the impossibility. Formal Lipschitz bounds for pre-LayerNorm transformers under LoRA enable LLM-scale verification. The separation is strict. We validate on GPT-2 (d_LoRA = 147,456): conditional delta = 0 with TPR = 0.352. Comprehensive empirical validation is in the companion paper [D2].

arXiv:2603.29654v1 Announce Type: cross Abstract: Aligning human-interpretable concepts with the internal representations learned by modern machine learning systems remains a central challenge for interpretable AI. We introduce a geometric framework for comparing supervised human concepts with unsupervised intermediate representations extracted from foundation model embeddings. Motivated by the role of conceptual leaps in scientific discovery, we formalise the notion of concept frustration: a contradiction that arises when an unobserved concept induces relationships between known concepts that cannot be made consistent within an existing ontology. We develop task-aligned similarity measures that detect concept frustration between supervised concept-based models and unsupervised representations derived from foundation models, and show that the phenomenon is detectable in task-aligned geometry while conventional Euclidean comparisons fail. Under a linear-Gaussian generative model we derive a closed-form expression for Bayes-optimal concept-based classifier accuracy, decomposing predictive signal into known-known, known-unknown and unknown-unknown contributions and identifying analytically where frustration affects performance. Experiments on synthetic data and real language and vision tasks demonstrate that frustration can be detected in foundation model representations and that incorporating a frustrating concept into an interpretable model reorganises the geometry of learned concept representations, to better align human and machine reasoning. These results suggest a principled framework for diagnosing incomplete concept ontologies and aligning human and machine conceptual reasoning, with implications for the development and validation of safe interpretable AI for high-risk applications.

arXiv:2510.03638v4 Announce Type: replace-cross Abstract: Implicit models, an emerging model class, compute outputs by iterating a single parameter block to a fixed point. This architecture realizes an infinite-depth, weight-tied network that trains with constant memory, significantly reducing memory needs for the same level of performance compared to explicit models. While it is empirically known that these compact models can often match or even exceed the accuracy of larger explicit networks by allocating more test-time compute, the underlying mechanism remains poorly understood. We study this gap through a nonparametric analysis of expressive power. We provide a strict mathematical characterization, showing that a simple and regular implicit operator can, through iteration, progressively express more complex mappings. We prove that for a broad class of implicit models, this process lets the model's expressive power scale with test-time compute, ultimately matching a much richer function class. The theory is validated across four domains: image reconstruction, scientific computing, operations research, and LLM reasoning, demonstrating that as test-time iterations increase, the complexity of the learned mapping rises, while the solution quality simultaneously improves and stabilizes.

arXiv:2510.14582v2 Announce Type: replace-cross Abstract: Causal discovery methods can identify valid adjustment sets for causal effect estimation for a pair of target variables, even when the underlying causal graph is unknown. Global causal discovery methods focus on learning the whole causal graph and therefore enable the recovery of optimal adjustment sets, i.e., sets with the lowest asymptotic variance, but they quickly become computationally prohibitive as the number of variables grows. Local causal discovery methods offer a more scalable alternative by focusing on the local neighborhood of the target variables, but are restricted to statistically suboptimal adjustment sets. In this work, we propose Local Optimal Adjustments Discovery (LOAD), a sound and complete causal discovery approach that combines the computational efficiency of local methods with the statistical optimality of global methods. First, LOAD identifies the causal relation between the targets and tests if the causal effect is identifiable by using only local information. If it is identifiable, it finds the possible descendants of the treatment and infers the optimal adjustment set as the parents of the outcome in a modified forbidden projection. Otherwise, it returns the locally valid parent adjustment sets. In our experiments on synthetic and realistic data LOAD outperforms global methods in scalability, while providing more accurate effect estimation than local methods.

arXiv:2512.15987v2 Announce Type: replace-cross Abstract: It is widely believed that complex machine learning models generally encode features through linear representations. This is the foundational hypothesis behind a vast body of work on interpretability. A key challenge toward extracting interpretable features, however, is that they exist in superposition. In this work, we study the question of extracting features in superposition from a learning theoretic perspective. We start with the following fundamental setting: we are given query access to a function \[ f(x)=\sum_{i=1}^n \sigma_i(v_i^\top x), \] where each unit vector $v_i$ encodes a feature direction and $\sigma_i:\R\to\R$ is an arbitrary response function and our goal is to recover the $v_i$ and the function $f$. In learning-theoretic terms, superposition refers to the \emph{overcomplete regime}, when the number of features is larger than the underlying dimension (i.e. $n > d$), which has proven especially challenging for typical algorithmic approaches. Our main result is an efficient query algorithm that, from noisy oracle access to $f$, identifies all feature directions whose responses are non-degenerate and reconstructs the function $f$. Crucially, our algorithm works in a significantly more general setting than all related prior results. We allow for essentially arbitrary superpositions, only requiring that $v_i, v_j$ are not nearly identical for $i \neq j$, and allowing for general response functions $\sigma_i$. At a high level, our algorithm introduces an approach for searching in Fourier space by iteratively refining the search space to locate the hidden directions $v_i$.

arXiv:2603.22328v1 Announce Type: cross Abstract: Despite the strong predictive performance achieved by machine learning models across many application domains, assessing their trustworthiness through reliable estimates of predictive confidence remains a critical challenge. This issue arises in scenarios where the likelihood of error inferred from learned representations follows a bimodal distribution, resulting from the coexistence of confident and ambiguous predictions. Standard regression approaches often struggle to adequately express this predictive uncertainty, as they implicitly assume unimodal Gaussian noise, leading to mean-collapse behavior in such settings. Although Mixture Density Networks (MDNs) can represent different distributions, they suffer from severe optimization instability. We propose a family of distribution-aware loss functions integrating normalized RMSE with Wasserstein and Cram\'er distances. When applied to standard deep regression models, our approach recovers bimodal distributions without the volatility of mixture models. Validated across four experimental stages, our results show that the proposed Wasserstein loss establishes a new Pareto efficiency frontier: matching the stability of standard regression losses like MSE in unimodal tasks while reducing Jensen-Shannon Divergence by 45% on complex bimodal datasets. Our framework strictly dominates MDNs in both fidelity and robustness, offering a reliable tool for aleatoric uncertainty estimation in trustworthy AI systems.

arXiv:2603.22900v1 Announce Type: cross Abstract: Optimizing survival outcomes, such as patient survival or customer retention, is a critical objective in data-driven decision-making. Off-Policy Evaluation~(OPE) provides a powerful framework for assessing such decision-making policies using logged data alone, without the need for costly or risky online experiments in high-stakes applications. However, typical estimators are not designed to handle right-censored survival outcomes, as they ignore unobserved survival times beyond the censoring time, leading to systematic underestimation of the true policy performance. To address this issue, we propose a novel framework for OPE and Off-Policy Learning~(OPL) tailored for survival outcomes under censoring. Specifically, we introduce IPCW-IPS and IPCW-DR, which employ the Inverse Probability of Censoring Weighting technique to explicitly deal with censoring bias. We theoretically establish that our estimators are unbiased and that IPCW-DR achieves double robustness, ensuring consistency if either the propensity score or the outcome model is correct. Furthermore, we extend this framework to constrained OPL to optimize policy value under budget constraints. We demonstrate the effectiveness of our proposed methods through simulation studies and illustrate their practical impacts using public real-world data for both evaluation and learning tasks.

arXiv:2603.23220v1 Announce Type: cross Abstract: We study learning under regime variation, where the learner, its memory state, and the evaluative conditions may evolve over time. This paper is a foundational and structural contribution: its goal is to define the core learning-theoretic objects required for such settings and to establish their first theorem-supporting consequences. The paper develops a regime-varying framework centered on admissible transport, protected-core preservation, and evaluator-aware learning evolution. It records the immediate closure consequences of admissibility, develops a structural obstruction argument for faithful fixed-ontology reduction in genuinely multi-regime settings, and introduces a protected-stability template together with explicit numerical and symbolic witnesses on controlled subclasses, including convex and deductive settings. It also establishes theorem-layer results on evaluator factorization, morphisms, composition, and partial kernel-level alignment across semantically commensurable layers. A worked two-regime example makes the admissibility certificate, protected evaluative core, and regime-variation cost explicit on a controlled subclass. The symbolic component is deliberately restricted in scope: the paper establishes a first kernel-level compatibility result together with a controlled monotonic deductive witness. The manuscript should therefore be read as introducing a structured learning-theoretic framework for regime-varying learning together with its first theorem-supporting layer, not as a complete quantitative theory of all learning systems.

arXiv:2603.23398v1 Announce Type: cross Abstract: Energy-based models for discrete domains, such as graphs, explicitly capture relative likelihoods, naturally enabling composable probabilistic inference tasks like conditional generation or enforcing constraints at test-time. However, discrete energy-based models typically struggle with efficient and high-quality sampling, as off-support regions often contain spurious local minima, trapping samplers and causing training instabilities. This has historically resulted in a fidelity gap relative to discrete diffusion models. We introduce Graph Energy Matching (GEM), a generative framework for graphs that closes this fidelity gap. Motivated by the transport map optimization perspective of the Jordan-Kinderlehrer-Otto (JKO) scheme, GEM learns a permutation-invariant potential energy that simultaneously provides transport-aligned guidance from noise toward data and refines samples within regions of high data likelihood. Further, we introduce a sampling protocol that leverages an energy-based switch to seamlessly bridge: (i) rapid, gradient-guided transport toward high-probability regions to (ii) a mixing regime for exploration of the learned graph distribution. On molecular graph benchmarks, GEM matches or exceeds strong discrete diffusion baselines. Beyond sample quality, explicit modeling of relative likelihood enables targeted exploration at inference time, facilitating compositional generation, property-constrained sampling, and geodesic interpolation between graphs.

arXiv:2504.14094v3 Announce Type: replace-cross Abstract: Concept-based Models aim to improve interpretability by predicting high-level intermediate concepts, representing a promising approach for deployment in high-risk scenarios. However, they are known to suffer from information leakage, whereby models exploit unintended information encoded within the learned concepts. We introduce an information-theoretic framework to rigorously characterise and quantify leakage, and define two complementary measures: the concepts-task leakage (CTL) and interconcept leakage (ICL) scores. We show that these measures are strongly predictive of model behaviour under interventions and outperform existing alternatives. Using this framework, we identify the primary causes of leakage and, as a case study, analyse how it manifests in Concept Embedding Models, revealing interconcept and alignment leakage in addition to the concepts-task leakage present by design. Finally, we present a set of practical guidelines for designing concept-based models to reduce leakage and ensure interpretability.

arXiv:2510.08294v2 Announce Type: replace-cross Abstract: We address the open question of counterfactual identification for high-dimensional multivariate outcomes from observational data. Pearl (2000) argues that counterfactuals must be identifiable (i.e., recoverable from the observed data distribution) to justify causal claims. A recent line of work on counterfactual inference shows promising results but lacks identification, undermining the causal validity of its estimates. To address this, we establish a foundation for multivariate counterfactual identification using continuous-time flows, including non-Markovian settings under standard criteria. We characterise the conditions under which flow matching yields a unique, monotone, and rank-preserving counterfactual transport map with tools from dynamic optimal transport, ensuring consistent inference. Building on this, we validate the theory in controlled scenarios with counterfactual ground-truth and demonstrate improvements in axiomatic counterfactual soundness on real images.

arXiv:2601.13698v2 Announce Type: replace-cross Abstract: Fairness and privacy are two vital pillars of trustworthy machine learning. Despite extensive research on these individual topics, their relationship has received significantly less attention. In this paper, we utilize an information-theoretic measure Chernoff Information to characterize the fundamental trade-off between fairness, privacy, and accuracy, as induced by the input data distribution. We first propose Chernoff Difference, a notion of data fairness, along with its noisy variant, Noisy Chernoff Difference, which allows us to analyze both fairness and privacy simultaneously. Through simple Gaussian examples, we show that Noisy Chernoff Difference exhibits three qualitatively distinct behaviors depending on the underlying data distribution. To extend this analysis beyond synthetic settings, we develop the Chernoff Information Neural Estimator (CINE), the first neural network-based estimator of Chernoff Information for unknown distributions. We apply CINE to analyze the Noisy Chernoff Difference on real-world datasets. Together, this work fills a critical gap in the literature by providing a principled, data-dependent characterization of the fairness-privacy interaction.

arXiv:2603.12288v1 Announce Type: cross Abstract: Tabular machine learning presents a paradox: modern models achieve state-of-the-art performance using high-dimensional (high-D), collinear, error-prone data, defying the "Garbage In, Garbage Out" mantra. To help resolve this, we synthesize principles from Information Theory, Latent Factor Models, and Psychometrics, clarifying that predictive robustness arises not solely from data cleanliness, but from the synergy between data architecture and model capacity. Partitioning predictor-space "noise" into "Predictor Error" and "Structural Uncertainty" (informational deficits from stochastic generative mappings), we prove that leveraging high-D sets of error-prone predictors asymptotically overcomes both types of noise, whereas cleaning a low-D set is fundamentally bounded by Structural Uncertainty. We demonstrate why "Informative Collinearity" (dependencies from shared latent causes) enhances reliability and convergence efficiency, and explain why increased dimensionality reduces the latent inference burden, enabling feasibility with finite samples. To address practical constraints, we propose "Proactive Data-Centric AI" to identify predictors that enable robustness efficiently. We also derive boundaries for Systematic Error Regimes and show why models that absorb "rogue" dependencies can mitigate assumption violations. Linking latent architecture to Benign Overfitting, we offer a first step towards a unified view of robustness to Outcome Error and predictor-space noise, while also delineating when traditional DCAI's focus on label cleaning remains powerful. By redefining data quality from item-level perfection to portfolio-level architecture, we provide a theoretical rationale for "Local Factories" -- learning from live, uncurated enterprise "data swamps" -- supporting a deployment paradigm shift from "Model Transfer" to "Methodology Transfer'' to overcome static generalizability limitations.

arXiv:2603.12349v1 Announce Type: cross Abstract: Scientific discovery increasingly relies on AI systems to select candidates for expensive experimental validation, yet no principled, budget-aware evaluation framework exists for comparing selection strategies -- a gap intensified by large language models (LLMs), which generate plausible scientific proposals without reliable downstream evaluation. We introduce the Budget-Sensitive Discovery Score (BSDS), a formally verified metric -- 20 theorems machine-checked by the Lean 4 proof assistant -- that jointly penalizes false discoveries (lambda-weighted FDR) and excessive abstention (gamma-weighted coverage gap) at each budget level. Its budget-averaged form, the Discovery Quality Score (DQS), provides a single summary statistic that no proposer can inflate by performing well at a cherry-picked budget. As a case study, we apply BSDS/DQS to: do LLMs add marginal value to an existing ML pipeline for drug discovery candidate selection? We evaluate 39 proposers -- 11 mechanistic variants, 14 zero-shot LLM configurations, and 14 few-shot LLM configurations -- using SMILES representations on MoleculeNet HIV (41,127 compounds, 3.5% active, 1,000 bootstrap replicates) under both random and scaffold splits. Three findings emerge. First, the simple RF-based Greedy-ML proposer achieves the best DQS (-0.046), outperforming all MLP variants and LLM configurations. Second, no LLM surpasses the Greedy-ML baseline under zero-shot or few-shot evaluation on HIV or Tox21, establishing that LLMs provide no marginal value over an existing trained classifier. Third, the proposer hierarchy generalizes across five MoleculeNet benchmarks spanning 0.18%-46.2% prevalence, a non-drug AV safety domain, and a 9x7 grid of penalty parameters (tau >= 0.636, mean tau = 0.863). The framework applies to any setting where candidates are selected under budget constraints and asymmetric error costs.

arXiv:2603.12893v1 Announce Type: cross Abstract: Reinforcement learning (RL) has become a standard technique for post-training diffusion-based image synthesis models, as it enables learning from reward signals to explicitly improve desirable aspects such as image quality and prompt alignment. In this paper, we propose an online RL variant that reduces the variance in the model updates by sampling paired trajectories and pulling the flow velocity in the direction of the more favorable image. Unlike existing methods that treat each sampling step as a separate policy action, we consider the entire sampling process as a single action. We experiment with both high-quality vision language models and off-the-shelf quality metrics for rewards, and evaluate the outputs using a broad set of metrics. Our method converges faster and yields higher output quality and prompt alignment than previous approaches.