Gaussian process (GP) bandits provide a powerful framework for solving blackbox optimization of unknown functions. The characteristics of the unknown function depends heavily on the assumed GP prior. Most work in the literature assume that this prior is known but in practice this seldom holds. Instead, practitioners often rely on maximum likelihood estimation to select the hyperparameters of the prior - which lacks theoretical guarantees. In this work, we propose two algorithms for joint prior selection and regret minimization in GP bandits based on GP Thompson sampling (GP-TS): Prior-Elimination GP-TS (PE-GP-TS) and HyperPrior GP-TS (HP-GP-TS). We theoretically analyze the algorithms and establish upper bounds for their respective regret. In addition, we demonstrate the effectiveness of our algorithms compared to the alternatives through experiments with synthetic and real-world data.

This article presents MCTS-BN, an adaptation of the Monte Carlo Tree Search (MCTS) algorithm for the structural learning of Bayesian Networks (BNs). Initially designed for game tree exploration, MCTS has been repurposed to address the challenge of learning BN structures by exploring the search space of potential ancestral orders in Bayesian Networks. Then, it employs Hill Climbing (HC) to derive a Bayesian Network structure from each order. In large BNs, where the search space for variable orders becomes vast, using completely random orders during the rollout phase is often unreliable and impractical. We adopt a semi-randomized approach to address this challenge by incorporating variable orders obtained from other heuristic search algorithms such as Greedy Equivalent Search (GES), PC, or HC itself. This hybrid strategy mitigates the computational burden and enhances the reliability of the rollout process. Experimental evaluations demonstrate the effectiveness of MCTS-BN in improving BNs generated by traditional structural learning algorithms, exhibiting robust performance even when base algorithm orders are suboptimal and surpassing the gold standard when provided with favorable orders.

Abstract symbolic writing systems are semiotic codes that are ubiquitous in modern society but are otherwise absent in the animal kingdom. Anthropological evidence suggests that the earliest forms of some writing systems originally consisted of iconic pictographs, which signify their referent via visual resemblance. While previous studies have examined the emergence and, separately, the evolution of pictographic writing systems through a computational lens, most employ non-naturalistic methodologies that make it difficult to draw clear analogies to human and animal cognition. We develop a multi-agent reinforcement learning testbed for emergent communication called a Signification Game, and formulate a model of inferential communication that enables agents to leverage visual theory of mind to communicate actions using pictographs. Our model, which is situated within a broader formalism for animal communication, sheds light on the cognitive and cultural processes that led to the development of early writing systems.

What computational structures emerge in transformers trained on next-token prediction? In this work, we provide evidence that transformers implement constrained Bayesian belief updating -- a parallelized version of partial Bayesian inference shaped by architectural constraints. To do this, we integrate the model-agnostic theory of optimal prediction with mechanistic interpretability to analyze transformers trained on a tractable family of hidden Markov models that generate rich geometric patterns in neural activations. We find that attention heads carry out an algorithm with a natural interpretation in the probability simplex, and create representations with distinctive geometric structure. We show how both the algorithmic behavior and the underlying geometry of these representations can be theoretically predicted in detail -- including the attention pattern, OV-vectors, and embedding vectors -- by modifying the equations for optimal future token predictions to account for the architectural constraints of attention. Our approach provides a principled lens on how gradient descent resolves the tension between optimal prediction and architectural design.

In this manuscript, we study the learning of deep attention neural networks, defined as the composition of multiple self-attention layers, with tied and low-rank weights. We first establish a mapping of such models to sequence multi-index models, a generalization of the widely studied multi-index model to sequential covariates, for which we establish a number of general results. In the context of Bayesian-optimal learning, in the limit of large dimension $D$ and commensurably large number of samples $N$, we derive a sharp asymptotic characterization of the optimal performance as well as the performance of the best-known polynomial-time algorithm for this setting --namely approximate message-passing--, and characterize sharp thresholds on the minimal sample complexity required for better-than-random prediction performance. Our analysis uncovers, in particular, how the different layers are learned sequentially. Finally, we discuss how this sequential learning can also be observed in a realistic setup.

Graph representation learning has emerged as a cornerstone for tasks like node classification and link prediction, yet prevailing self-supervised learning (SSL) methods face challenges such as computational inefficiency, reliance on contrastive objectives, and representation collapse. Existing approaches often depend on feature reconstruction, negative sampling, or complex decoders, which introduce training overhead and hinder generalization. Further, current techniques which address such limitations fail to account for the contribution of node embeddings to a certain prediction in the absence of labeled nodes. To address these limitations, we propose a novel joint embedding predictive framework for graph SSL that eliminates contrastive objectives and negative sampling while preserving semantic and structural information. Additionally, we introduce a semantic-aware objective term that incorporates pseudo-labels derived from Gaussian Mixture Models (GMMs), enhancing node discriminability by evaluating latent feature contributions. Extensive experiments demonstrate that our framework outperforms state-of-the-art graph SSL methods across benchmarks, achieving superior performance without contrastive loss or complex decoders. Key innovations include (1) a non-contrastive, view-invariant joint embedding predictive architecture, (2) Leveraging single context and multiple targets relationship between subgraphs, and (3) GMM-based pseudo-label scoring to capture semantic contributions. This work advances graph SSL by offering a computationally efficient, collapse-resistant paradigm that bridges spatial and semantic graph features for downstream tasks. The code for our paper can be found at https://github.com/Deceptrax123/JPEB-GSSL

Large language models (LLMs) can exhibit undesirable and unexpected behavior in the blink of an eye. In a recent Anthropic demo, Claude switched from coding to Googling pictures of Yellowstone, and these sudden shifts in behavior have also been observed in reasoning patterns and jailbreaks. This phenomenon is not unique to autoregressive models: in diffusion models, key features of the final output are decided in narrow ``critical windows'' of the generation process. In this work we develop a simple, unifying theory to explain this phenomenon. We show that it emerges generically as the generation process localizes to a sub-population of the distribution it models. While critical windows have been studied at length in diffusion models, existing theory heavily relies on strong distributional assumptions and the particulars of Gaussian diffusion. In contrast to existing work our theory (1) applies to autoregressive and diffusion models; (2) makes no distributional assumptions; (3) quantitatively improves previous bounds even when specialized to diffusions; and (4) requires basic tools and no stochastic calculus or statistical physics-based machinery. We also identify an intriguing connection to the all-or-nothing phenomenon from statistical inference. Finally, we validate our predictions empirically for LLMs and find that critical windows often coincide with failures in problem solving for various math and reasoning benchmarks.

We introduce FedGVI, a probabilistic Federated Learning (FL) framework that is provably robust to both prior and likelihood misspecification. FedGVI addresses limitations in both frequentist and Bayesian FL by providing unbiased predictions under model misspecification, with calibrated uncertainty quantification. Our approach generalises previous FL approaches, specifically Partitioned Variational Inference (Ashman et al., 2022), by allowing robust and conjugate updates, decreasing computational complexity at the clients. We offer theoretical analysis in terms of fixed-point convergence, optimality of the cavity distribution, and provable robustness. Additionally, we empirically demonstrate the effectiveness of FedGVI in terms of improved robustness and predictive performance on multiple synthetic and real world classification data sets.

This paper addresses the critical challenge of latent heterogeneity in online decision-making, where individual responses to business actions vary due to unobserved characteristics. While existing approaches in data-driven decision-making have focused on observable heterogeneity through contextual features, they fall short when heterogeneity stems from unobservable factors such as lifestyle preferences and personal experiences. We propose a novel latent heterogeneous bandit framework that explicitly models this unobserved heterogeneity in customer responses, with promotion targeting as our primary example. Our methodology introduces an innovative algorithm that simultaneously learns latent group memberships and group-specific reward functions. Through theoretical analysis and empirical validation using data from a mobile commerce platform, we establish high-probability bounds for parameter estimation, convergence rates for group classification, and comprehensive regret bounds. Notably, our theoretical analysis reveals two distinct types of regret measures: a ``strong regret'' against an oracle with perfect knowledge of customer memberships, which remains non-sub-linear due to inherent classification uncertainty, and a ``regular regret'' against an oracle aware only of deterministic components, for which our algorithm achieves a sub-linear rate that is minimax optimal in horizon length and dimension. We further demonstrate that existing bandit algorithms ignoring latent heterogeneity incur constant average regret that accumulates linearly over time. Our framework provides practitioners with new tools for decision-making under latent heterogeneity and extends to various business applications, including personalized pricing, resource allocation, and inventory management.

The notion of generalization has moved away from the classical one defined in statistical learning theory towards an emphasis on out-of-domain generalization (OODG). Recently, there is a growing focus on inductive generalization, where a progression of difficulty implicitly governs the direction of domain shifts. In inductive generalization, it is often assumed that the training data lie in the easier side, while the testing data lie in the harder side. The challenge is that training data are always finite, but a learner is expected to infer an inductive principle that could be applied in an unbounded manner. This emerging regime has appeared in the literature under different names, such as length/logical/algorithmic extrapolation, but a formal definition is lacking. This work provides such a formalization that centers on the concept of model successors. Then we outline directions to adapt well-established techniques towards the learning of model successors. This work calls for restructuring of the research discussion around inductive generalization from fragmented task-centric communities to a more unified effort, focused on universal properties of learning and computation.