Embodied agents operate in a structured world, often solving tasks with spatial, temporal, and permutation symmetries. Most algorithms for planning and model-based reinforcement learning (MBRL) do not take this rich geometric structure into account, leading to sample inefficiency and poor generalization. We introduce the Equivariant Diffuser for Generating Interactions (EDGI), an algorithm for MBRL and planning that is equivariant with respect to the product of the spatial symmetry group SE(3), the discrete-time translation group ℤ, and the object permutation group Sₙ. EDGI follows the Diffuser framework by Janner et al. (2022) in treating both learning a world model and planning in it as a conditional generative modeling problem, training a diffusion model on an offline trajectory dataset. We introduce a new SE(3) ℤ Sₙ-equivariant diffusion model that supports multiple representations.

Model-based unsupervised reinforcement learning (URL) has gained prominence for reducing environment interactions and learning general skills using intrinsic rewards. However, distractors in observations can severely affect intrinsic reward estimation, leading to a biased exploration process, especially in environments with visual inputs like images or videos. To address this challenge, we propose a bi-level optimization framework named Separation-assisted eXplorer (SeeX). In the inner optimization, SeeX trains a separated world model to extract exogenous and endogenous information, minimizing uncertainty to ensure task relevance. In the outer optimization, it learns a policy on imaginary trajectories generated within the endogenous state space to maximize task-relevant uncertainty. Evaluations on multiple locomotion and manipulation tasks demonstrate SeeX's effectiveness.

This verification model assigns a confidence score to each reasoning step, indicating the probability of arriving at the correct final answer from that point onward.We detect relative changes in the verification's confidence scores across reasoning steps to automatically annotate the reasoning process, enabling error detection even in scenarios where ground truth answers are unavailable. This alleviates the need for numerous manual annotations or the high computational costs associated with model-induced annotation approaches.We experimentally validate that the step-level confidence changes learned by the verification model trained on the final answer correctness can effectively identify errors in the reasoning steps.We demonstrate that the verification model, when trained on process annotations generated by \textsc{AutoPSV}, exhibits improved performance in selecting correct answers from multiple LLM-generated outputs.Notably, we achieve substantial improvements across five datasets in mathematics and commonsense reasoning.

Which transformer scaling regimes are able to perfectly solve different classes of algorithmic problems? While tremendous empirical advances have been attained by transformer-based neural networks, a theoretical understanding of their algorithmic reasoning capabilities in realistic parameter regimes is lacking. We investigate this question in terms of the network's depth, width, and number of extra tokens for algorithm execution. We prove that logarithmic depth is necessary and sufficient for tasks like graph connectivity, while single-layer transformers with small embedding dimensions can solve contextual retrieval tasks. We also support our theoretical analysis with ample empirical evidence using the GraphQA benchmark.

We study fair allocation of constrained resources, where a market designer optimizes overall welfare while maintaining group fairness. In many large-scale settings, utilities are not known in advance, but are instead observed after realizing the allocation. We therefore estimate agent utilities using machine learning. Optimizing over estimates requires trading-off between mean utilities and their predictive variances. We discuss these trade-offs under two paradigms for preference modeling – in the stochastic optimization regime, the market designer has access to a probability distribution over utilities, and in the robust optimization regime they have access to an uncertainty set containing the true utilities with high probability.

Probabilistic circuits (PCs) have emerged as a powerful framework compactly representing probability distributions for efficient and exact probabilistic inference. It has been shown that PCs with general directed acyclic graph (DAG) structure can be understood as a mixture of exponentially (in its height) many components, each of which is a product distributions over univariate marginals. However, existing structure learning algorithms for PCs often generate tree-structured circuits, or using tree-structured circuits as intermediate steps to compress them into DAG-structured circuits. This leads to an intriguing question on whether there exists an exponential gap between DAGs and trees for the PC structure.In this paper, we provide a negative answer to this conjecture by proving that, for n variables, there is a quasi-polynomial upper bound n {O(\log n)} on the size of an equivalent tree computing the same probability distribution. On the other hand, we will also show that given a depth restriction on the tree, there is a super-polynomial separation between tree and DAG-structured PCs. Our work takes an important step towards understanding the expressive power of tree-structured PCs, and our techniques may be of independent interest in the study of structure learning algorithms for PCs.

While finetuning language models from pairwise preferences has proven remarkably effective, the underspecified nature of natural language presents critical challenges. Direct preference feedback is uninterpretable, difficult to provide where multidimensional criteria may apply, and often inconsistent, either because it is based on incomplete instructions or provided by diverse principals. To address these challenges, we consider the two-step preference modeling procedure that first resolves the under-specification by selecting a context, and then evaluates preference with respect to the chosen context. We decompose reward modeling error according to these two steps, which suggests that supervising context in addition to context-specific preference may be a viable approach to aligning models with diverse human preferences. For this to work, the ability of models to evaluate context-specific preference is critical.

We study the optimal memorization capacity of modern Hopfield models and Kernelized Hopfield Models (KHMs), a transformer-compatible class of Dense Associative Memories.We present a tight analysis by establishing a connection between the memory configuration of KHMs and spherical codes from information theory. Specifically, we treat the stored memory set as a specialized spherical code.This enables us to cast the memorization problem in KHMs into a point arrangement problem on a hypersphere.We show that the optimal capacity of KHMs occurs when the feature space allows memories to form an optimal spherical code.This unique perspective leads to: 1. An analysis of how KHMs achieve optimal memory capacity, and identify corresponding necessary conditions. Importantly, we establish an upper capacity bound that matches the well-known exponential lower bound in the literature. This provides the first tight and optimal asymptotic memory capacity for modern Hopfield models.2.

We give a model-based agent that builds a Python program representing its knowledge of the world based on its interactions with the environment. The world model tries to explain its interactions, while also being optimistic about what reward it can achieve. We define this optimism as a logical constraint between a program and a planner. We study our agent on gridworlds, and on task planning, finding our approach is more sample-efficient compared to deep RL, more compute-efficient compared to ReAct-style agents, and that it can transfer its knowledge across environments by editing its code.

Deep neural networks have reached human-level performance on many computer vision tasks. However, the objectives used to train these networks enforce only that similar images are embedded at similar locations in the representation space, and do not directly constrain the global structure of the resulting space. Here, we explore the impact of supervising this global structure by linearly aligning it with human similarity judgments. We find that a naive approach leads to large changes in local representational structure that harm downstream performance. Thus, we propose a novel method that aligns the global structure of representations while preserving their local structure.