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.

We propose geodesic-based optimization methods on dually flat spaces, where the geometric structure of the parameter manifold is closely related to the form of the objective function. A primary application is maximum likelihood estimation in statistical models, especially exponential families, whose model manifolds are dually flat. We show that an m-geodesic update, which directly optimizes the log-likelihood, can theoretically reach the maximum likelihood estimator in a single step. In contrast, an e-geodesic update has a practical advantage in cases where the parameter space is geodesically complete, allowing optimization without explicitly handling parameter constraints. We establish the theoretical properties of the proposed methods and validate their effectiveness through numerical experiments.

Applied researchers now routinely work with regression models that feature a large number of covariates. A primary inferential goal in econometrics is to estimate the ceteris paribus effect of a specific variable while controlling for other variables (Belloni et al., 2013a, 2018). The prevailing practice interprets the coefficient on a regressor as a causal effect, conditional on the included controls. As the plausibility of conditional unconfoundedness is often argued using a large set of covariates, practitioners have increasingly embraced high-dimensional regression models. This setting has been extensively studied, predominantly using frequentist methods. Bayesian inference, on the other hand, has long been valued for its coherent framework for handling uncertainty in statistical analysis. As highlighted by Rubin (1984), Bayesian methods provide direct answers to many empirical questions by quantifying uncertainty about unknown parameters conditional on the observed data.

The Weibull distribution is a commonly adopted choice for modeling the survival of systems subject to maintenance over time. When only proxy indicators and censored observations are available, it becomes necessary to express the distribution's parameters as functions of time-dependent covariates. Deep neural networks provide the flexibility needed to learn complex relationships between these covariates and operational lifetime, thereby extending the capabilities of traditional regression-based models. Motivated by the analysis of a fleet of military vehicles operating in highly variable and demanding environments, as well as by the limitations observed in existing methodologies, this paper introduces WTNN, a new neural network-based modeling framework specifically designed for Weibull survival studies. The proposed architecture is specifically designed to incorporate qualitative prior knowledge regarding the most influential covariates, in a manner consistent with the shape and structure of the Weibull distribution. Through numerical experiments, we show that this approach can be reliably trained on proxy and right-censored data, and is capable of producing robust and interpretable survival predictions that can improve existing approaches.