Shapley values, a gold standard for feature attribution in Explainable AI, face two primary challenges. First, the canonical Shapley framework assumes that the worth function is additive, yet real-world payoff constructions--driven by non-Gaussian distributions, heavy tails, feature dependence, or domain-specific loss scales--often violate this assumption, leading to distorted attributions. Secondly, achieving sparse explanations in high dimensions by computing dense Shapley values and then applying ad hoc thresholding is prohibitively costly and risks inconsistency. We introduce Sparse Isotonic Shapley Regression (SISR), a unified nonlinear explanation framework. SISR simultaneously learns a monotonic transformation to restore additivity--obviating the need for a closed-form specification--and enforces an L0 sparsity constraint on the Shapley vector, enhancing computational efficiency in large feature spaces. Its optimization algorithm leverages Pool-Adjacent-Violators for efficient isotonic regression and normalized hard-thresholding for support selection, yielding implementation ease and global convergence guarantees. Analysis shows that SISR recovers the true transformation in a wide range of scenarios and achieves strong support recovery even in high noise. Moreover, we are the first to demonstrate that irrelevant features and inter-feature dependencies can induce a true payoff transformation that deviates substantially from linearity. Experiments in regression, logistic regression, and tree ensembles demonstrate that SISR stabilizes attributions across payoff schemes, correctly filters irrelevant features while standard Shapley values suffer severe rank and sign distortions. By unifying nonlinear transformation estimation with sparsity pursuit, SISR advances the frontier of nonlinear explainability, providing a theoretically grounded and practical attribution framework.

Agentic AI systems execute a sequence of actions, such as reasoning steps or tool calls, in response to a user prompt. To evaluate the success of their trajectories, researchers have developed verifiers, such as LLM judges and process-reward models, to score the quality of each action in an agent's trajectory. Although these heuristic scores can be informative, there are no guarantees of correctness when used to decide whether an agent will yield a successful output. Here, we introduce e-valuator, a method to convert any black-box verifier score into a decision rule with provable control of false alarm rates. We frame the problem of distinguishing successful trajectories (that is, a sequence of actions that will lead to a correct response to the user's prompt) and unsuccessful trajectories as a sequential hypothesis testing problem. E-valuator builds on tools from e-processes to develop a sequential hypothesis test that remains statistically valid at every step of an agent's trajectory, enabling online monitoring of agents over arbitrarily long sequences of actions. Empirically, we demonstrate that e-valuator provides greater statistical power and better false alarm rate control than other strategies across six datasets and three agents. We additionally show that e-valuator can be used for to quickly terminate problematic trajectories and save tokens. Together, e-valuator provides a lightweight, model-agnostic framework that converts verifier heuristics into decisions rules with statistical guarantees, enabling the deployment of more reliable agentic systems.

Large language models (LLMs) produce fluent but unsupported answers - hallucinations - limiting safe deployment in high-stakes domains. We propose ECLIPSE, a framework that treats hallucination as a mismatch between a model's semantic entropy and the capacity of available evidence. We combine entropy estimation via multi-sample clustering with a novel perplexity decomposition that measures how models use retrieved evidence. We prove that under mild conditions, the resulting entropy-capacity objective is strictly convex with a unique stable optimum. We evaluate on a controlled financial question answering dataset with GPT-3.5-turbo (n=200 balanced samples with synthetic hallucinations), where ECLIPSE achieves ROC AUC of 0.89 and average precision of 0.90, substantially outperforming a semantic entropy-only baseline (AUC 0.50). A controlled ablation with Claude-3-Haiku, which lacks token-level log probabilities, shows AUC dropping to 0.59 with coefficient magnitudes decreasing by 95% - demonstrating that ECLIPSE is a logprob-native mechanism whose effectiveness depends on calibrated token-level uncertainties. The perplexity decomposition features exhibit the largest learned coefficients, confirming that evidence utilization is central to hallucination detection. We position this work as a controlled mechanism study; broader validation across domains and naturally occurring hallucinations remains future work.

Large Language Models (LLMs) are very demanding in terms of their computational resources. Low-rank decompositions of LLM weights, e.g. via Singular Value Decomposition (SVD), is a promising approach for LLM compression, but presents several practical hurdles, e.g. selecting appropriate layer-wise ranks and getting rid of its parameter redundancy. In this work, we present two physics-inspired improvements to SVD LLM compression: (1) \textbf{FermiGrad}, a gradient-descent algorithm that determines globally optimal layer-wise ranks by relaxing the discrete singular-value truncation into a continuous optimization using the Fermi function; (2) \textbf{PivGa}, an additional \textit{lossless} compression of the low-rank factors that exploits the intrinsic gauge freedom in their parametrization.

Large language models have achieved remarkable progress in complex problem-solving, but suffer from high computational costs during deployment (Kwon et al., 2023). To address this, various approaches have been proposed, including model routing (Ong et al., 2025; Dekoninck et al., 2025), speculative decoding (Leviathan et al., 2023), and adaptive reasoning strategies (Snell et al., 2024). Zeng et al. (2025) proposed PAC reasoning, which constructs a composite model ˆ f that selectively switches between an expensive expert model f and a cheaper fast model f while providing statistical guarantees on performance loss. A typical example is the thinking-nonthinking paradigm, where the expert model performs extended chain-of-thought reasoning while the fast model generates direct responses. The original PAC reasoning provides marginal guarantees, controlling the expected risk over the input distribution. A natural extension is whether we can achieve a stronger, conditional guarantee that controls the risk for each input point individually. This is analogous to the notion of object-conditional validity in conformal prediction (Vovk, 2012; Lei and Wasserman, 2014; Lei et al., 2018). 1

Diffusion models have achieved remarkable success in data-driven learning and in sampling from complex, unnormalized target distributions. Building on this progress, we reinterpret Maximum Entropy Reinforcement Learning (MaxEntRL) as a diffusion model-based sampling problem. We tackle this problem by minimizing the reverse Kullback-Leibler (KL) divergence between the diffusion policy and the optimal policy distribution using a tractable upper bound. By applying the policy gradient theorem to this objective, we derive a modified surrogate objective for MaxEntRL that incorporates diffusion dynamics in a principled way. This leads to simple diffusion-based variants of Soft Actor-Critic (SAC), Proximal Policy Optimization (PPO) and Wasserstein Policy Optimization (WPO), termed DiffSAC, DiffPPO and DiffWPO. All of these methods require only minor implementation changes to their base algorithm. We find that on standard continuous control benchmarks, DiffSAC, DiffPPO and DiffWPO achieve better returns and higher sample efficiency than SAC and PPO.

Sequential optimization of black-box functions from noisy evaluations has been widely studied, with Gaussian Process bandit algorithms such as GP-UCB guaranteeing no-regret in stationary settings. However, for time-varying objectives, it is known that no-regret is unattainable under pure bandit feedback unless strong and often unrealistic assumptions are imposed. In this article, we propose a novel method to optimize time-varying rewards in the frequentist setting, where the objective has bounded RKHS norm. Time variations are captured through uncertainty injection (UI), which enables heteroscedastic GP regression that adapts past observations to the current time step. As no-regret is unattainable in general in the strict bandit setting, we relax the latter allowing additional queries on previously observed points. Building on sparse inference and the effect of UI on regret, we propose W-SparQ-GP-UCB, an online algorithm that achieves no-regret with only a vanishing number of additional queries per iteration. To assess the theoretical limits of this approach, we establish a lower bound on the number of additional queries required for no-regret, proving the efficiency of our method. Finally, we provide a comprehensive analysis linking the degree of time-variation of the function to achievable regret rates, together with upper and lower bounds on the number of additional queries needed in each regime.

Generative modeling is typically framed as learning mapping rules, but from an observer's perspective without access to these rules, the task becomes disentangling the geometric support from the probability distribution. We propose that continuum percolation is uniquely suited to this support analysis, as the sampling process effectively projects high-dimensional density estimation onto a geometric counting problem on the support. In this work, we establish a rigorous correspondence between the topological phase transitions of random geometric graphs and the underlying data manifold in high-dimensional space. By analyzing the relationship between our proposed Percolation Shift metric and FID, we show that this metric captures structural pathologies, such as implicit mode collapse, where standard statistical metrics fail. Finally, we translate this topological phenomenon into a differentiable loss function that guides training. Experimental results confirm that this approach not only prevents manifold shrinkage but also fosters a form of synergistic improvement, where topological stability becomes a prerequisite for sustained high fidelity in both static generation and sequential decision making.

Understanding the geometry of the loss landscape near a minimum is key to explaining the implicit bias of gradient-based methods in non-convex optimization problems such as deep neural network training and deep matrix factorization. A central quantity to characterize this geometry is the maximum eigenvalue of the Hessian of the loss, which measures the sharpness of the landscape. Currently, its precise role has been obfuscated because no exact expressions for this sharpness measure were known in general settings. In this paper, we present the first exact expression for the maximum eigenvalue of the Hessian of the squared-error loss at any minimizer in general overparameterized deep matrix factorization (i.e., deep linear neural network training) problems, resolving an open question posed by Mulayoff & Michaeli (2020). This expression uncovers a fundamental property of the loss landscape of depth-2 matrix factorization problems: a minimum is flat if and only if it is spectral-norm balanced, which implies that flat minima are not necessarily Frobenius-norm balanced. Furthermore, to complement our theory, we empirically investigate an escape phenomenon observed during gradient-based training near a minimum that crucially relies on our exact expression of the sharpness. Decades of research in learning theory suggest limiting model complexity to prevent overfitting.

Generative AI systems now mediate newsfeeds, search rankings, and creative content for hundreds of millions of users, positioning a handful of private firms as de-facto arbiters of truth. Drawing on a comparative-historical lens, this article juxtaposes the Galileo Affair, a touchstone of clerical knowledge control, with contemporary Big-Tech content moderation. We integrate Foucault's power/knowledge thesis, Weber's authority types (extended to a rational-technical and emerging agentic-technical modality), and Floridi's Dataism to analyze five recurrent dimensions: disciplinary power, authority modality, data pluralism, trust versus reliance, and resistance pathways. Primary sources (Inquisition records; platform transparency reports) and recent empirical studies on AI trust provide the evidentiary base. Findings show strong structural convergences: highly centralized gatekeeping, legitimacy claims couched in transcendent principles, and systematic exclusion of marginal voices. Divergences lie in temporal velocity, global scale, and the widening gap between public reliance and trust in AI systems. Ethical challenges cluster around algorithmic opacity, linguistic inequity, bias feedback loops, and synthetic misinformation. We propose a four-pillar governance blueprint: (1) a mandatory international model-registry with versioned policy logs, (2) representation quotas and regional observatories to de-center English-language hegemony, (3) mass critical-AI literacy initiatives, and (4) public-private support for community-led data trusts. Taken together, these measures aim to narrow the trust-reliance gap and prevent GenAI from hardcoding a twenty-first-century digital orthodoxy.