We study streaming data with categorical features where the vocabulary of categorical feature values is changing and can even grow unboundedly over time. Feature hashing is commonly used as a pre-processing step to map these categorical values into a feature space of fixed size before learning their embeddings. While these methods have been developed and evaluated for offline or batch settings, in this paper we consider online settings. We show that deterministic embeddings are sensitive to the arrival order of categories and suffer from forgetting in online learning, leading to performance deterioration. To mitigate this issue, we propose a probabilistic hash embedding (PHE) model that treats hash embeddings as stochastic and applies Bayesian online learning to learn incrementally from data. Based on the structure of PHE, we derive a scalable inference algorithm to learn model parameters and infer/update the posteriors of hash embeddings and other latent variables. Our algorithm (i) can handle an evolving vocabulary of categorical items, (ii) is adaptive to new items without forgetting old items, (iii) is implementable with a bounded set of parameters that does not grow with the number of distinct observed values on the stream, and (iv) is invariant to the item arrival order. Experiments in classification, sequence modeling, and recommendation systems in online learning setups demonstrate the superior performance of PHE while maintaining high memory efficiency (consumes as low as 2~4 memory of a one-hot embedding table). Supplementary materials are at https://github.com/aodongli/probabilistic-hash-embeddings

Stochastic Variance Reduced Gradient (SVRG) and its variants aim to speed-up training by using gradient corrections, but have seen limited success in deep learning. Here, we show surprising new foundational connections of SVRG to a recently proposed Bayesian method called posterior correction. Specifically, we show that SVRG is recovered as a special case of posterior correction over the isotropic-Gaussian family, while novel extensions are automatically obtained by using more flexible exponential families. We derive two new SVRG variants by using Gaussian families: First, a Newton-like variant that employs novel Hessian corrections, and second, an Adam-like extension that improves pretraining and finetuning of Transformer language models. This is the first work to connect SVRG to Bayes and use it to boost variational training for deep networks.

Modeling historical events poses fundamental challenges for machine learning: extreme data scarcity (N << 100), heterogeneous and noisy measurements, missing counterfactuals, and the requirement for human interpretable explanations. We present HistoricalML, a probabilistic neuro-symbolic framework that addresses these challenges through principled integration of (1) Bayesian uncertainty quantification to separate epistemic from aleatoric uncertainty, (2) structural causal models for counterfactual reasoning under confounding, (3) cooperative game theory (Shapley values) for fair allocation modeling, and (4) attention based neural architectures for context dependent factor weighting. We provide theoretical analysis showing that our approach achieves consistent estimation in the sparse data regime when strong priors from domain knowledge are available, and that Shapley based allocation satisfies axiomatic fairness guarantees that pure regression approaches cannot provide. We instantiate the framework on two historical case studies: the 19th century partition of Africa (N = 7 colonial powers) and the Second Punic War (N = 2 factions). Our model identifies Germany's +107.9 percent discrepancy as a quantifiable structural tension preceding World War I, with tension factor 36.43 and 0.79 naval arms race correlation. For the Punic Wars, Monte Carlo battle simulations achieve a 57.3 percent win probability for Carthage at Cannae and 57.8 percent for Rome at Zama, aligning with historical outcomes. Counterfactual analysis reveals that Carthaginian political support (support score 6.4 vs Napoleon's 7.1), rather than military capability, was the decisive factor.

Collaborative Combat Aircraft (CCAs) are envisioned to enable autonomous Intelligence, Surveillance, and Reconnaissance (ISR) missions in contested environments, where adversaries may act strategically to deceive or evade detection. These missions pose challenges due to model uncertainty and the need for safe, real-time decision-making. Robust Markov Decision Processes (RMDPs) provide worst-case guarantees but are limited by static ambiguity sets that capture initial uncertainty without adapting to new observations. This paper presents an adaptive RMDP framework tailored to ISR missions with CCAs. We introduce a mission-specific formulation in which aircraft alternate between movement and sensing states. Adversarial tactics are modeled as a finite set of transition kernels, each capturing assumptions about how adversarial sensing or environmental conditions affect rewards. Our approach incrementally refines policies by eliminating inconsistent threat models, allowing agents to shift from conservative to aggressive behaviors while maintaining robustness. We provide theoretical guarantees showing that the adaptive planner converges as credible sets contract to the true threat and maintains safety under uncertainty. Experiments under Gaussian and non-Gaussian threat models across diverse network topologies show higher mission rewards and fewer exposure events compared to nominal and static robust planners.

Diffusion models have emerged as a leading technique for generating images due to their ability to create high-resolution and realistic images. Despite their strong performance, diffusion models still struggle in managing image collections with significant feature differences. They often fail to capture complex features and produce conflicting results. Research has attempted to address this issue by learning different regions of an image through multiple diffusion paths and then combining them. However, this approach leads to inefficient coordination among multiple paths and high computational costs. To tackle these issues, this paper presents a Diffusion Fuzzy System (DFS), a latent-space multi-path diffusion model guided by fuzzy rules. DFS offers several advantages. First, unlike traditional multi-path diffusion methods, DFS uses multiple diffusion paths, each dedicated to learning a specific class of image features. By assigning each path to a different feature type, DFS overcomes the limitations of multi-path models in capturing heterogeneous image features. Second, DFS employs rule-chain-based reasoning to dynamically steer the diffusion process and enable efficient coordination among multiple paths. Finally, DFS introduces a fuzzy membership-based latent-space compression mechanism to reduce the computational costs of multi-path diffusion effectively. We tested our method on three public datasets: LSUN Bedroom, LSUN Church, and MS COCO. The results show that DFS achieves more stable training and faster convergence than existing single-path and multi-path diffusion models. Additionally, DFS surpasses baseline models in both image quality and alignment between text and images, and also shows improved accuracy when comparing generated images to target references.

Bayesian Neural Networks provide a principled framework for uncertainty quantification by modeling the posterior distribution of network parameters. However, exact posterior inference is computationally intractable, and widely used approximations like the Laplace method struggle with scalability and posterior accuracy in modern deep networks. In this work, we revisit sampling techniques for posterior exploration, proposing a simple variation tailored to efficiently sample from the posterior in over-parameterized networks by leveraging the low-dimensional structure of loss minima. Building on this, we introduce a model that learns a deformation of the parameter space, enabling rapid posterior sampling without requiring iterative methods. Empirical results demonstrate that our approach achieves competitive posterior approximations with improved scalability compared to recent refinement techniques. These contributions provide a practical alternative for Bayesian inference in deep learning.

AI systems deployed in the real world must contend with distractions and out-of-distribution (OOD) noise that can destabilize their policies and lead to unsafe behavior . While robust training can reduce sensitivity to some forms of noise, it is infeasible to anticipate all possible OOD conditions. T o mitigate this issue, we develop an algorithm that leverages a world model's inherent measure of surprise to reduce the impact of noise in world model-based reinforcement learning agents. W e introduce both multi-representation and single-representation rejection sampling, enabling robustness to settings with multiple faulty sensors or a single faulty sensor . While the introduction of noise typically degrades agent performance, we show that our techniques preserve performance relative to baselines under varying types and levels of noise across multiple environments within self-driving simulation domains (CARLA and Safety Gymnasium). Furthermore, we demonstrate that our methods enhance the stability of two state-of-the-art world models with markedly different underlying architectures: Cosmos and DreamerV3.

The rapid advancement of humanoid robotics has intensified the need for robust and adaptable controllers to enable stable and efficient locomotion across diverse platforms. However, developing such controllers remains a significant challenge because existing solutions are tailored to specific robot designs, requiring extensive tuning of reward functions, physical parameters, and training hyperparameters for each embodiment. To address this challenge, we introduce H-Zero, a cross-humanoid locomotion pretraining pipeline that learns a generalizable humanoid base policy. We show that pretraining on a limited set of embodiments enables zero-shot and few-shot transfer to novel humanoid robots with minimal fine-tuning. Evaluations show that the pretrained policy maintains up to 81% of the full episode duration on unseen robots in simulation while enabling few-shot transfer to unseen humanoids and upright quadrupeds within 30 minutes of fine-tuning.

Reinforcement Learning (RL) has achieved remarkable success in various domains, yet it often relies on carefully designed programmatic reward functions to guide agent behavior . Designing such reward functions can be challenging and may not generalize well across different tasks. T o address this limitation, we leverage the rich world knowledge contained in pretrained video diffusion models to provide goal-driven reward signals for RL agents without ad-hoc design of reward. Our key idea is to exploit off-the-shelf video diffusion models pretrained on large-scale video datasets as informative reward functions in terms of video-level and frame-level goals. F or video-level rewards, we first finetune a pretrained video diffusion model on domain-specific datasets and then employ its video encoder to evaluate the alignment between the latent representations of agent's trajectories and the generated goal videos. T o enable more fine-grained goal-achievement, we derive a frame-level goal by identifying the most relevant frame from the generated video using CLIP, which serves as the goal state. W e then employ a learned forward-backward representation that represents the probability of visiting the goal state from a given state-action pair as frame-level reward, promoting more coherent and goal-driven trajectories. Experiments on various Meta-W orld tasks demonstrate the effectiveness of our approach.

Group symmetries provide a powerful inductive bias for reinforcement learning (RL), enabling efficient generalization across symmetric states and actions via group-invariant Markov Decision Processes (MDPs). However, real-world environments almost never realize fully group-invariant MDPs; dynamics, actuation limits, and reward design usually break symmetries, often only locally. Under group-invariant Bellman backups for such cases, local symmetry-breaking introduces errors that propagate across the entire state-action space, resulting in global value estimation errors. To address this, we introduce Partially group-Invariant MDP (PI-MDP), which selectively applies group-invariant or standard Bellman backups depending on where symmetry holds. This framework mitigates error propagation from locally broken symmetries while maintaining the benefits of equivariance, thereby enhancing sample efficiency and generalizability. Building on this framework, we present practical RL algorithms -- Partially Equivariant (PE)-DQN for discrete control and PE-SAC for continuous control -- that combine the benefits of equivariance with robustness to symmetry-breaking. Experiments across Grid-World, locomotion, and manipulation benchmarks demonstrate that PE-DQN and PE-SAC significantly outperform baselines, highlighting the importance of selective symmetry exploitation for robust and sample-efficient RL.