Generative models that maximize model likelihood have gained traction in many practical settings. Among them, perturbation based approaches underpin many strong likelihood estimation models, yet they often face slow convergence and limited theoretical understanding. In this paper, we derive a tighter likelihood bound for noise driven models to improve both the accuracy and efficiency of maximum likelihood learning. Our key insight extends the classical KL divergence Fisher information relationship to arbitrary noise perturbations, going beyond the Gaussian assumption and enabling structured noise distributions. This formulation allows flexible use of randomized noise distributions that naturally account for sensor artifacts, quantization effects, and data distribution smoothing, while remaining compatible with standard diffusion training. Treating the diffusion process as a Gaussian channel, we further express the mismatched entropy between data and model, showing that the proposed objective upper bounds the negative log-likelihood (NLL). In experiments, our models achieve competitive NLL on CIFAR-10 and SOTA results on ImageNet across multiple resolutions, all without data augmentation, and the framework extends naturally to discrete data.

Understanding how patterns of interaction between neural populations reorganize with behavior is central to systems neuroscience and to applications that decode or modulate brain activity. These interactions are often framed under the umbrella of brain connectivity, distinguished as structural (anatomical pathways), functional (statistical dependencies), and effective (directed influence)--complementary lenses on how distributed circuits communicate and adapt to task demands [1, 2]. Reviews emphasize both the promise and the challenges of connectivity-centric approaches, particularly the need to capture short-timescale dynamics while maintaining interpretability [3, 4]. Graph-based formulations make this agenda concrete: representing brain regions as nodes and their relationships as edges enables quantitative analysis of modularity, hubs, and task-dependent reconfiguration [5, 6]. Such network perspectives motivate methods that go beyond static, correlation-only descriptions toward dynamic, directed estimates that better align with mechanistic questions. We focus on intracranial local field potentials (LFPs), a high-temporal-resolution measure of population activity recorded simultaneously from multiple deep-brain regions [7, 8, 9, 10]. Multi-region LFP imposes unique modeling requirements: (i) many micro-contacts per region must be consolidated into coherent region-level trajectories; (ii) neural activity reconfigures across well-defined behavioral phases; and (iii) the spatial layout of contacts is high-dimensional and non-Euclidean [11]. Existing pipelines often average across behavior with a single correlation-based graph [2] or impose hard-coded anatomical connectivity [12, 13], limiting their ability to capture phase-specific, directed interactions. Recent machine learning advances in graph learning from neural time series highlight the opportunity but do not yet fill this gap.

Marked Temporal Point Process (MTPP) has been well studied to model the event distribution in marked event streams, which can be used to predict the mark and arrival time of the next event. However, existing studies overlook that the distribution of event marks is highly imbalanced in many real-world applications, with some marks being frequent but others rare. The imbalance poses a significant challenge to the performance of the next event prediction, especially for events of rare marks. To address this issue, we propose a thresholding method, which learns thresholds to tune the mark probability normalized by the mark's prior probability to optimize mark prediction, rather than predicting the mark directly based on the mark probability as in existing studies. In conjunction with this method, we predict the mark first and then the time. In particular, we develop a novel neural MTPP model to support effective time sampling and estimation of mark probability without computationally expensive numerical improper integration. Extensive experiments on real-world datasets demonstrate the superior performance of our solution against various baselines for the next event mark and time prediction. The code is available at https://github.com/undes1red/IFNMTPP.

We consider the problem of online dynamic mechanism design for sequential auctions in unknown environments, where the underlying market and, thus, the bidders' values vary over time as interactions between the seller and the bidders progress. We model the sequential auctions as an infinite-horizon average-reward Markov decision process (MDP). In each round, the seller determines an allocation and sets a payment for each bidder, while each bidder receives a private reward and submits a sealed bid to the seller. The state, which represents the underlying market, evolves according to an unknown transition kernel and the seller's allocation policy without episodic resets. We first extend the Vickrey-Clarke-Groves (VCG) mechanism to sequential auctions, thereby obtaining a dynamic counterpart that preserves the desired properties: efficiency, truthfulness, and individual rationality. We then focus on the online setting and develop a reinforcement learning algorithm for the seller to learn the underlying MDP and implement a mechanism that closely resembles the dynamic VCG mechanism. We show that the learned mechanism approximately satisfies efficiency, truthfulness, and individual rationality and achieves guaranteed performance in terms of various notions of regret.

Listwise reranking with large language models (LLMs) enhances top-ranked results in retrieval-based applications. Due to the limit in context size and high inference cost of long context, reranking is typically performed over a fixed size of small subsets, with the final ranking aggregated from these partial results. This fixed computation disregards query difficulty and document distribution, leading to inefficiencies. We propose AcuRank, an adaptive reranking framework that dynamically adjusts both the amount and target of computation based on uncertainty estimates over document relevance. Using a Bayesian TrueSkill model, we iteratively refine relevance estimates until reaching sufficient confidence levels, and our explicit modeling of ranking uncertainty enables principled control over reranking behavior and avoids unnecessary updates to confident predictions. Results on the TREC-DL and BEIR benchmarks show that our method consistently achieves a superior accuracy-efficiency trade-off and scales better with compute than fixed-computation baselines. These results highlight the effectiveness and generalizability of our method across diverse retrieval tasks and LLM-based reranking models.

Generative flow networks are able to sample, via sequential construction, high-reward, complex objects according to a reward function. However, such reward functions are often estimated approximately from noisy data, leading to epistemic uncertainty in the learnt policy. We present an approach to quantify this uncertainty by constructing a surrogate model composed of a polynomial chaos expansion, fit on a small ensemble of trained flow networks. This model learns the relationship between reward functions, parametrised in a low-dimensional space, and the probability distributions over actions at each step along a trajectory of the flow network. The surrogate model can then be used for inexpensive Monte Carlo sampling to estimate the uncertainty in the policy given uncertain rewards. We illustrate the performance of our approach on a discrete and continuous grid-world, symbolic regression, and a Bayesian structure learning task.

Abstract-- We present a fully decentralized routing framework for multi-robot exploration missions operating under the constraints of a Lunar Delay-T olerant Network (LDTN). In this setting, autonomous rovers must relay collected data to a lander under intermittent connectivity and unknown mobility patterns. We formulate the problem as a Partially Observable Markov Decision Problem (POMDP) and propose a Graph Attention-based Multi-Agent Reinforcement Learning (GA T - MARL) policy that performs Centralized Training, Decentralized Execution (CTDE). Our method relies only on local observations and does not require global topology updates or packet replication, unlike classical approaches such as shortest path and controlled flooding-based algorithms. Through Monte Carlo simulations in randomized exploration environments, GA T -MARL provides higher delivery rates, no duplications, and fewer packet losses, and is able to leverage short-term mobility forecasts; offering a scalable solution for future space robotic systems for planetary exploration, as demonstrated by successful generalization to larger rover teams. The renewed interest in planetary and lunar surface exploration has accelerated the development of autonomous multi-robot systems.

Recent advances such as self-consistency and test-time reinforcement learning (TTRL) improve the reliability of large language models (LLMs) without additional supervision, yet their underlying mechanisms and statistical guarantees remain poorly understood. We present a unified framework for certifiable inference in LLMs, showing that majority voting provides a statistical certificate of self-consistency: under mild assumptions, the aggregated answer coincides with the mode of the model's terminal distribution with high probability. We derive finite-sample and anytime-valid concentration bounds that quantify this confidence, and introduce the Martingale Majority Certificate (MMC), a sequential stopping rule that adaptively determines when sufficient samples have been drawn. We further prove that label-free post-training methods such as TTRL implicitly sharpen the answer distribution by exponentially tilting it toward its mode, thereby reducing the number of samples required for certification. Building on this insight, we propose new post-training objectives that explicitly optimise this trade-off between sharpness and bias. Together, these results explain and connect two central test-time scaling strategies, self-consistency and TTRL, within a single statistical framework for label-free, certifiable reliability in reasoning LLMs.

Understanding causal relationships in multivariate time series is crucial in many scenarios, such as those dealing with financial or neurological data. Many such time series exhibit multiple regimes, i.e., consecutive temporal segments with a priori unknown boundaries, with each regime having its own causal structure. Inferring causal dependencies and regime shifts is critical for analyzing the underlying processes. However, causal structure learning in this setting is challenging due to (1) non-stationarity, i.e., each regime can have its own causal graph and mixing function, and (2) complex noise distributions, which may be nonGaussian or heteroscedastic. Existing causal discovery approaches cannot address these challenges, since generally assume stationarity or Gaussian noise with constant variance. Hence, we introduce FANTOM, a unified framework for causal discovery that handles non-stationary processes along with non-Gaussian and heteroscedastic noises. FANTOM simultaneously infers the number of regimes and their corresponding indices and learns each regime's Directed Acyclic Graph. It uses a Bayesian Expectation Maximization algorithm that maximizes the evidence lower bound of the data log-likelihood. On the theoretical side, we prove, under mild assumptions, that temporal heteroscedastic causal models, introduced in FANTOM's formulation, are identifiable in both stationary and non-stationary settings. In addition, extensive experiments on synthetic and real data show that FANTOM outperforms existing methods.

Thanks to the remarkable human-like capabilities of machine learning (ML) models in perceptual and cognitive tasks, frameworks integrating ML within rational agent architectures are gaining traction. Yet, the landscape remains fragmented and incoherent, often focusing on embedding ML into generic agent containers while overlooking the expressive power of rational architectures--such as Belief-Desire-Intention (BDI) agents. This paper presents a fine-grained systematisation of existing approaches, using the BDI paradigm as a reference. Our analysis illustrates the fast-evolving literature on rational agents enhanced by ML, and identifies key research opportunities and open challenges for designing effective rational ML agents.