The property of learning-curve monotonicity, highlighted in a recent series of work by Loog, Mey and Viering, describes algorithms which only improve in average performance given more data, for any underlying data distribution within a given family. We establish the first nontrivial monotonicity guarantees for the maximum likelihood estimator in a variety of well-specified parametric settings. For sequential prediction with log loss, we show monotonicity (in fact complete monotonicity) of the forward KL divergence for Gaussian vectors with unknown covariance and either known or unknown mean, as well as for Gamma variables with unknown scale parameter. The Gaussian setting was explicitly highlighted as open in the aforementioned works, even in dimension 1. Finally we observe that for reverse KL divergence, a folklore trick yields monotonicity for very general exponential families. All results in this paper were derived by variants of GPT-5.2 Pro. Humans did not provide any proof strategies or intermediate arguments, but only prompted the model to continue developing additional results, and verified and transcribed its proofs.

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph topology identification and statistical inference methods for multidimensional relational data. Approaches for undirected links connecting graph nodes are outlined, going all the way from correlation metrics to covariance selection, and revealing ties with smooth signal priors. To account for directional (possibly causal) relations among nodal variables and address the limitations of linear time-invariant models in handling dynamic as well as nonlinear dependencies, a principled framework is surveyed to capture these complexities through judiciously selected kernels from a prescribed dictionary. Generalizations are also described via structural equations and vector autoregressions that can exploit attributes such as low rank, sparsity, acyclicity, and smoothness to model dynamic processes over possibly time-evolving topologies. It is argued that this approach supports both batch and online learning algorithms with convergence rate guarantees, is amenable to tensor (that is, multi-way array) formulations as well as decompositions that are well-suited for multidimensional network data, and can seamlessly leverage high-order statistical information.

ABSTRACT We develop a Markov decision process (MDP) framework to autonomously make guidance decisions for satellite collision avoidance maneuver (CAM) and a reinforcement learning policy gradient (RL-PG) algorithm to enable direct optimization of guidance policy using historic CAM data. In addition to maintaining acceptable collision risks, this approach seeks to minimize the average propellant consumption of CAMs by making early maneuver decisions. We model CAM as a continuous state, discrete action and finite horizon MDP, where the critical decision is determining when to initiate the maneuver. By deciding to maneuver earlier than conventional methods, the Markov policy effectively favors CAMs that achieve comparable rates of collision risk reduction while consuming less propellant. Using historical data of tracked conjunction events, we verify this framework and conduct an extensive parameter-sensitivity study. When evaluated on synthetic conjunction events, the trained policy consumes significantly less propellant overall and per maneuver in comparison to a conventional cut-off policy that initiates maneuvers 24 hours before the time of closest approach (TCA). On historical conjunction events, the trained policy consumes more propellant overall but consumes less propellant per maneuver. For both historical and synthetic conjunction events, the trained policy is slightly more conservative in identifying conjunctions events that warrant CAMs in comparison to cutoff policies.

Causal discovery methods have traditionally been developed under two distinct regimes: independent and identically distributed (i.i.d.) and timeseries data, each governed by separate modelling assumptions. In this paper, we argue that the i.i.d. setting can and should be reframed in terms of exchangeability, a strictly more general symmetry principle. We present the implications of this reframing, alongside two core arguments: (1) a conceptual argument, based on extending the dependency of experimental causal inference on exchangeability to causal discovery; and (2) an empirical argument, showing that many existing i.i.d. causal-discovery methods are predicated on exchangeability assumptions, and that the sole extensive widely-used real-world "i.i.d." benchmark (the Tübingen dataset) consists mainly of exchangeable (and not i.i.d.) examples. Building on this insight, we introduce a novel synthetic dataset that enforces only the exchangeability assumption, without imposing the stronger i.i.d. assumption. We show that our exchangeable synthetic dataset mirrors the statistical structure of the real-world "i.i.d." dataset more closely than all other i.i.d. synthetic datasets. Furthermore, we demonstrate the predictive capability of this dataset by proposing a neural-network-based causal-discovery algorithm trained exclusively on our synthetic dataset, and which performs similarly to other state-of-the-art i.i.d. methods on the real-world benchmark.

This article looks at how reasoning works in current Large Language Models (LLMs) that function using the token-completion method. It examines their stochastic nature and their similarity to human abductive reasoning. The argument is that these LLMs create text based on learned patterns rather than performing actual abductive reasoning. When their output seems abductive, this is largely because they are trained on human-generated texts that include reasoning structures. Examples are used to show how LLMs can produce plausible ideas, mimic commonsense reasoning, and give explanatory answers without being grounded in truth, semantics, verification, or understanding, and without performing any real abductive reasoning. This dual nature, where the models have a stochastic base but appear abductive in use, has important consequences for how LLMs are evaluated and applied. They can assist with generating ideas and supporting human thinking, but their outputs must be critically assessed because they cannot identify truth or verify their explanations. The article concludes by addressing five objections to these points, noting some limitations in the analysis, and offering an overall evaluation.

Abstract--The rapid growth of Web3.0 is transforming the Internet from a centralized structure to decentralized, which empowers users with unprecedented self-sovereignty over their own data. However, in the context of decentralized data access within Web3.0, it is imperative to cope with efficiency concerns caused by the replication of redundant data, as well as security vulnerabilities caused by data inconsistency. T o address these challenges, we develop a Trustworthy Decentralized Cooperative Caching (TDC-Cache) framework for Web3.0 to ensure efficient caching and enhance system resilience against adversarial threats. This framework features a two-layer architecture, wherein the Decentralized Oracle Network (DON) layer serves as a trusted intermediary platform for decentralized caching, bridging the contents from decentralized storage and the content requests from users. In light of the complexity of Web3.0 network topologies and data flows, we propose a Deep Reinforcement Learning-Based Decentralized Caching (DRL-DC) for TDC-Cache to dynamically optimize caching strategies of distributed oracles. Furthermore, we develop a Proof of Cooperative Learning (PoCL) consensus to maintain the consistency of decentralized caching decisions within DON. Experimental results show that, compared with existing approaches, the proposed framework reduces average access latency by 20%, increases the cache hit rate by at most 18%, and improves the average success consensus rate by 10%. Overall, this paper serves as a first foray into the investigation of decentralized caching framework and strategy for Web3.0. HE rapid evolution of Web3.0 is driving the transition from traditional centralized systems to decentralized architectures. Leveraging blockchain, decentralized storage, and smart contracts, Web3.0 empowers users with unprecedented self-sovereignty over their own data through Decentralized Applications (DApps) [1].

The proliferation of probabilistic AI has prompted proposals for specialized stochastic computers. Despite promising efficiency gains, these proposals have failed to gain traction because they rely on fundamentally limited modeling techniques and exotic, unscalable hardware. In this work, we address these shortcomings by proposing an all-transistor probabilistic computer that implements powerful denoising models at the hardware level. A system-level analysis indicates that devices based on our architecture could achieve performance parity with GPUs on a simple image benchmark using approximately 10,000 times less energy.

Learning and optimal control under robust Markov decision processes (MDPs) have received increasing attention, yet most existing theory, algorithms, and applications focus on finite-horizon or discounted models. Long-run average-reward formulations, while natural in many operations research and management contexts, remain underexplored. This is primarily because the dynamic programming foundations are technically challenging and only partially understood, with several fundamental questions remaining open. This paper steps toward a general framework for average-reward robust MDPs by analyzing the constant-gain setting. We study the average-reward robust control problem with possible information asymmetries between the controller and an S-rectangular adversary. Our analysis centers on the constant-gain robust Bellman equation, examining both the existence of solutions and their relationship to the optimal average reward. Specifically, we identify when solutions to the robust Bellman equation characterize the optimal average reward and stationary policies, and we provide one-sided weak communication conditions ensuring solutions' existence. These findings expand the dynamic programming theory for average-reward robust MDPs and lay a foundation for robust dynamic decision making under long-run average criteria in operational environments.

Reproducibility is a cornerstone of scientific validation and of the authority it confers on its results. Reproducibility in machine learning evaluations leads to greater trust, confidence, and value. However, the ground truth responses used in machine learning often necessarily come from humans, among whom disagreement is prevalent, and surprisingly little research has studied the impact of effectively ignoring disagreement in these responses, as is typically the case. One reason for the lack of research is that budgets for collecting human-annotated evaluation data are limited, and obtaining more samples from multiple raters for each example greatly increases the per-item annotation costs. We investigate the trade-off between the number of items ($N$) and the number of responses per item ($K$) needed for reliable machine learning evaluation. We analyze a diverse collection of categorical datasets for which multiple annotations per item exist, and simulated distributions fit to these datasets, to determine the optimal $(N, K)$ configuration, given a fixed budget ($N \times K$), for collecting evaluation data and reliably comparing the performance of machine learning models. Our findings show, first, that accounting for human disagreement may come with $N \times K$ at no more than 1000 (and often much lower) for every dataset tested on at least one metric. Moreover, this minimal $N \times K$ almost always occurred for $K > 10$. Furthermore, the nature of the tradeoff between $K$ and $N$, or if one even existed, depends on the evaluation metric, with metrics that are more sensitive to the full distribution of responses performing better at higher levels of $K$. Our methods can be used to help ML practitioners get more effective test data by finding the optimal metrics and number of items and annotations per item to collect to get the most reliability for their budget.

While modern language models and their inner workings are incredibly complex, recent work (Golowich, Liu & Shetty; 2025) has proposed a simple and potentially tractable abstraction for them through the observation that empirically, these language models all seem to have approximately low logit rank. Roughly, this means that a matrix formed by the model's log probabilities of various tokens conditioned on certain sequences of tokens is well approximated by a low rank matrix. In this paper, our focus is on understanding how this structure can be exploited algorithmically for obtaining provable learning guarantees. Since low logit rank models can encode hard-to-learn distributions such as noisy parities, we study a query learning model with logit queries that reflects the access model for common APIs. Our main result is an efficient algorithm for learning any approximately low logit rank model from queries. We emphasize that our structural assumption closely reflects the behavior that is empirically observed in modern language models. Thus, our result gives what we believe is the first end-to-end learning guarantee for a generative model that plausibly captures modern language models.