In-context learning (ICL) is a hallmark capability of transformers, through which trained models learn to adapt to new tasks by leveraging information from the input context. Prior work has shown that ICL emerges in transformers due to the presence of special circuits called induction heads. Given the equivalence between induction heads and conditional k-grams, a recent line of work modeling sequential inputs as Markov processes has revealed the fundamental impact of model depth on its ICL capabilities: while a two-layer transformer can efficiently represent a conditional 1-gram model, its single-layer counterpart cannot solve the task unless it is exponentially large. However, for higher order Markov sources, the best known constructions require at least three layers (each with a single attention head) - leaving open the question: can a two-layer single-head transformer represent any kth-order Markov process? In this paper, we precisely address this and theoretically show that a two-layer transformer with one head per layer can indeed represent any conditional k-gram. Thus, our result provides the tightest known characterization of the interplay between transformer depth and Markov order for ICL. Building on this, we further analyze the learning dynamics of our two-layer construction, focusing on a simplified variant for first-order Markov chains, illustrating how effective in-context representations emerge during training. Together, these results deepen our current understanding of transformer-based ICL and illustrate how even shallow architectures can surprisingly exhibit strong ICL capabilities on structured sequence modeling tasks.

Understanding and identifying controlled direct effects (CDEs) is crucial across numerous scientific domains, including public health. While existing methods can identify these effects from causal directed acyclic graphs (DAGs), the true underlying structure is often unknown in practice. Essential graphs, which represent a Markov equivalence class of DAGs characterized by the same set of $d$-separations, provide a more practical and realistic alternative. However, learning the full essential graph is computationally intensive and typically depends on strong, untestable assumptions. In this work, we characterize a local class of graphs, defined relative to a target variable, that share a specific subset of $d$-separations, and introduce a graphical representation of this class, called the local essential graph (LEG). We then present LocPC, a novel algorithm designed to recover the LEG from an observed distribution using only local conditional independence tests. Building on LocPC, we propose LocPC-CDE, an algorithm that discovers the portion of the LEG that is both sufficient and necessary to identify a CDE, bypassing the need of retrieving the full essential graph. Compared to global methods, our algorithms require less conditional independence tests and operate under weaker assumptions while maintaining theoretical guarantees. We illustrate the effectiveness of our approach through simulation studies.

We present Distributional RewArds for Generative OptimizatioN (DRAGON), a versatile framework for fine-tuning media generation models towards a desired outcome. Compared with traditional reinforcement learning with human feedback (RLHF) or pairwise preference approaches such as direct preference optimization (DPO), DRAGON is more flexible. It can optimize reward functions that evaluate either individual examples or distributions of them, making it compatible with a broad spectrum of instance-wise, instance-to-distribution, and distribution-to-distribution rewards. Leveraging this versatility, we construct novel reward functions by selecting an encoder and a set of reference examples to create an exemplar distribution. When cross-modal encoders such as CLAP are used, the reference may be of a different modality (text versus audio). Then, DRAGON gathers online and on-policy generations, scores them with the reward function to construct a positive demonstration set and a negative set, and leverages the contrast between the two finite sets to approximate distributional reward optimization. For evaluation, we fine-tune an audio-domain text-to-music diffusion model with 20 reward functions, including a custom music aesthetics model, CLAP score, Vendi diversity, and Frechet audio distance (FAD). We further compare instance-wise (per-song) and full-dataset FAD settings while ablating multiple FAD encoders and reference sets. Over all 20 target rewards, DRAGON achieves an 81.45% average win rate. Moreover, reward functions based on exemplar sets enhance generations and are comparable to model-based rewards. With an appropriate exemplar set, DRAGON achieves a 60.95% human-voted music quality win rate without training on human preference annotations. DRAGON is a new approach to designing and optimizing reward functions for improving human-perceived quality. Demos at https://ml-dragon.github.io/web

Technological systems increasingly mediate human information exchange, spanning interactions among humans as well as between humans and artificial agents. The unprecedented scale and reliance on information disseminated through these systems substantially expand the scope of information-based influence that can both enable and undermine sound decision-making. Consequently, understanding and protecting decision-making today faces growing challenges, as individuals and organizations must navigate evolving opportunities and information-based threats across varied domains and information environments. While these risks are widely recognized, research remains fragmented: work evaluating information-based threat phenomena has progressed largely in isolation from foundational studies of human information processing. In this review, we synthesize insights from both domains to identify shared cognitive mechanisms that mediate vulnerability to information-based threats and shape behavioral outcomes. Finally, we outline directions for future research aimed at integrating these perspectives, emphasizing the importance of such integration for mitigating human vulnerabilities and aligning human-machine representations.

Modern scientific simulations, observations, and large-scale experiments generate data at volumes that often exceed the limits of storage, processing, and analysis. This challenge drives the development of data reduction methods that efficiently manage massive datasets while preserving essential physical features and quantities of interest. In many scientific workflows, it is also crucial to enable data recovery from compressed representations - a task known as super-resolution - with guarantees on the preservation of key physical characteristics. A notable example is checkpointing and restarting, which is essential for long-running simulations to recover from failures, resume after interruptions, or examine intermediate results. In this work, we introduce a novel framework for scientific data compression and super-resolution, grounded in recent advances in learning exponential families. Our method preserves and quantifies uncertainty in physical quantities of interest and supports flexible trade-offs between compression ratio and reconstruction fidelity.

Sampling from a target distribution induced by training data is central to Bayesian learning, with Stochastic Gradient Langevin Dynamics (SGLD) serving as a key tool for scalable posterior sampling and decentralized variants enabling learning when data are distributed across a network of agents. This paper introduces DIGing-SGLD, a decentralized SGLD algorithm designed for scalable Bayesian learning in multi-agent systems operating over time-varying networks. Existing decentralized SGLD methods are restricted to static network topologies, and many exhibit steady-state sampling bias caused by network effects, even when full batches are used. DIGing-SGLD overcomes these limitations by integrating Langevin-based sampling with the gradient-tracking mechanism of the DIGing algorithm, originally developed for decentralized optimization over time-varying networks, thereby enabling efficient and bias-free sampling without a central coordinator. To our knowledge, we provide the first finite-time non-asymptotic Wasserstein convergence guarantees for decentralized SGLD-based sampling over time-varying networks, with explicit constants. Under standard strong convexity and smoothness assumptions, DIGing-SGLD achieves geometric convergence to an $O(\sqrtη)$ neighborhood of the target distribution, where $η$ is the stepsize, with dependence on the target accuracy matching the best-known rates for centralized and static-network SGLD algorithms using constant stepsize. Numerical experiments on Bayesian linear and logistic regression validate the theoretical results and demonstrate the strong empirical performance of DIGing-SGLD under dynamically evolving network conditions.

This paper proposes a novel Bayesian framework for solving Poisson inverse problems by devising a Monte Carlo sampling algorithm which accounts for the underlying non-Euclidean geometry. To address the challenges posed by the Poisson likelihood -- such as non-Lipschitz gradients and positivity constraints -- we derive a Bayesian model which leverages exact and asymptotically exact data augmentations. In particular, the augmented model incorporates two sets of splitting variables both derived through a Bregman divergence based on the Burg entropy. Interestingly the resulting augmented posterior distribution is characterized by conditional distributions which benefit from natural conjugacy properties and preserve the intrinsic geometry of the latent and splitting variables. This allows for efficient sampling via Gibbs steps, which can be performed explicitly for all conditionals, except the one incorporating the regularization potential. For this latter, we resort to a Hessian Riemannian Langevin Monte Carlo (HRLMC) algorithm which is well suited to handle priors with explicit or easily computable score functions. By operating on a mirror manifold, this Langevin step ensures that the sampling satisfies the positivity constraints and more accurately reflects the underlying problem structure. Performance results obtained on denoising, deblurring, and positron emission tomography (PET) experiments demonstrate that the method achieves competitive performance in terms of reconstruction quality compared to optimization- and sampling-based approaches.

This note presents an analytical framework for decision-making in drone swarm systems operating under uncertainty, based on the integration of Partially Observable Markov Decision Processes (POMDP) with Deep Deterministic Policy Gradient (DDPG) reinforcement learning. The proposed approach enables adaptive control and cooperative behavior of unmanned aerial vehicles (UAVs) within a cognitive AI platform, where each agent learns optimal energy management and navigation policies from dynamic environmental states. We extend the standard DDPG architecture with a belief-state representation derived from Bayesian filtering, allowing for robust decision-making in partially observable environments. In this paper, for the Gaussian case, we numerically compare the performance of policies derived from DDPG to optimal policies for discretized versions of the original continuous problem. Simulation results demonstrate that the POMDP-DDPG-based swarm control model significantly improves mission success rates and energy efficiency compared to baseline methods. The developed framework supports distributed learning and decision coordination across multiple agents, providing a foundation for scalable cognitive swarm autonomy. The outcomes of this research contribute to the advancement of energy-aware control algorithms for intelligent multi-agent systems and can be applied in security, environmental monitoring, and infrastructure inspection scenarios.

Multi-agent reinforcement learning (MARL) has made significant strides in enabling coordinated behaviors among autonomous agents. However, most existing approaches assume that communication is instantaneous, reliable, and has unlimited bandwidth; these conditions are rarely met in real-world deployments. This survey systematically reviews recent advances in robust and efficient communication strategies for MARL under realistic constraints, including message perturbations, transmission delays, and limited bandwidth. Furthermore, because the challenges of low-latency reliability, bandwidth-intensive data sharing, and communication-privacy trade-offs are central to practical MARL systems, we focus on three applications involving cooperative autonomous driving, distributed simultaneous localization and mapping, and federated learning. Finally, we identify key open challenges and future research directions, advocating a unified approach that co-designs communication, learning, and robustness to bridge the gap between theoretical MARL models and practical implementations.

Multi-token prediction (MTP) is a prominent strategy to significantly speed up generation in large language models (LLMs), including byte-level LLMs, which are tokeniser-free but prohibitively slow. However, existing MTP methods often sacrifice expressiveness by assuming independence between future tokens. In this work, we investigate the trade-off between expressiveness and latency in MTP within the framework of probabilistic circuits (PCs). Our framework, named MTPC, allows one to explore different ways to encode the joint distributions over future tokens by selecting different circuit architectures, generalising classical models such as (hierarchical) mixture models, hidden Markov models and tensor networks. We show the efficacy of MTPC by retrofitting existing byte-level LLMs, such as EvaByte. Our experiments show that, when combined with speculative decoding, MTPC significantly speeds up generation compared to MTP with independence assumptions, while guaranteeing to retain the performance of the original verifier LLM. We also rigorously study the optimal trade-off between expressiveness and latency when exploring the possible parameterisations of MTPC, such as PC architectures and partial layer sharing between the verifier and draft LLMs.