Large-scale physical systems defined on irregular grids pose significant scalability challenges for deep learning methods, especially in the presence of long-range interactions and multi-scale coupling. Traditional approaches that compute all pairwise interactions, such as attention, become computationally prohibitive as they scale quadratically with the number of nodes. We present Erwin, a hierarchical transformer inspired by methods from computational many-body physics, which combines the efficiency of tree-based algorithms with the expressivity of attention mechanisms. Erwin employs ball tree partitioning to organize computation, which enables linear-time attention by processing nodes in parallel within local neighborhoods of fixed size. Through progressive coarsening and refinement of the ball tree structure, complemented by a novel cross-ball interaction mechanism, it captures both fine-grained local details and global features. We demonstrate Erwin's effectiveness across multiple domains, including cosmology, molecular dynamics, and particle fluid dynamics, where it consistently outperforms baseline methods both in accuracy and computational efficiency.

Reinforcement Learning (RL) has the potential to enable robots to learn from their own actions in the real world. Unfortunately, RL can be prohibitively expensive, in terms of on-robot runtime, due to inefficient exploration when learning from a sparse reward signal. Designing dense reward functions is labour-intensive and requires domain expertise. In our work, we propose GCR (Goal-Contrastive Rewards), a dense reward function learning method that can be trained on passive video demonstrations. By using videos without actions, our method is easier to scale, as we can use arbitrary videos. GCR combines two loss functions, an implicit value loss function that models how the reward increases when traversing a successful trajectory, and a goal-contrastive loss that discriminates between successful and failed trajectories. We perform experiments in simulated manipulation environments across RoboMimic and MimicGen tasks, as well as in the real world using a Franka arm and a Spot quadruped. We find that GCR leads to a more-sample efficient RL, enabling model-free RL to solve about twice as many tasks as our baseline reward learning methods. We also demonstrate positive cross-embodiment transfer from videos of people and of other robots performing a task. Appendix: \url{https://tinyurl.com/gcr-appendix-2}.

We present a formulation of flow matching as variational inference, which we refer to as variational flow matching (VFM). Based on this formulation we develop CatFlow, a flow matching method for categorical data. CatFlow is easy to implement, computationally efficient, and achieves strong results on graph generation tasks. In VFM, the objective is to approximate the posterior probability path, which is a distribution over possible end points of a trajectory. We show that VFM admits both the CatFlow objective and the original flow matching objective as special cases. We also relate VFM to score-based models, in which the dynamics are stochastic rather than deterministic, and derive a bound on the model likelihood based on a reweighted VFM objective. We evaluate CatFlow on one abstract graph generation task and two molecular generation tasks. In all cases, CatFlow exceeds or matches performance of the current state-of-the-art models.

We consider inverse reinforcement learning problems with concave utilities. Concave Utility Reinforcement Learning (CURL) is a generalisation of the standard RL objective, which employs a concave function of the state occupancy measure, rather than a linear function. CURL has garnered recent attention for its ability to represent instances of many important applications including the standard RL such as imitation learning, pure exploration, constrained MDPs, offline RL, human-regularized RL, and others. Inverse reinforcement learning is a powerful paradigm that focuses on recovering an unknown reward function that can rationalize the observed behaviour of an agent. There has been recent theoretical advances in inverse RL where the problem is formulated as identifying the set of feasible reward functions. However, inverse RL for CURL problems has not been considered previously. In this paper we show that most of the standard IRL results do not apply to CURL in general, since CURL invalidates the classical Bellman equations. This calls for a new theoretical framework for the inverse CURL problem. Using a recent equivalence result between CURL and Mean-field Games, we propose a new definition for the feasible rewards for I-CURL by proving that this problem is equivalent to an inverse game theory problem in a subclass of mean-field games. We present initial query and sample complexity results for the I-CURL problem under assumptions such as Lipschitz-continuity. Finally, we outline future directions and applications in human--AI collaboration enabled by our results.

We present variational inference with sequential sample-average approximation (VISA), a method for approximate inference in computationally intensive models, such as those based on numerical simulations. VISA extends importance-weighted forward-KL variational inference by employing a sequence of sample-average approximations, which are considered valid inside a trust region. This makes it possible to reuse model evaluations across multiple gradient steps, thereby reducing computational cost. We perform experiments on high-dimensional Gaussians, Lotka-Volterra dynamics, and a Pickover attractor, which demonstrate that VISA can achieve comparable approximation accuracy to standard importance-weighted forward-KL variational inference with computational savings of a factor two or more for conservatively chosen learning rates.

Many diagnostic errors occur because clinicians cannot easily access relevant information in patient Electronic Health Records (EHRs). In this work we propose a method to use LLMs to identify pieces of evidence in patient EHR data that indicate increased or decreased risk of specific diagnoses; our ultimate aim is to increase access to evidence and reduce diagnostic errors. In particular, we propose a Neural Additive Model to make predictions backed by evidence with individualized risk estimates at time-points where clinicians are still uncertain, aiming to specifically mitigate delays in diagnosis and errors stemming from an incomplete differential. To train such a model, it is necessary to infer temporally fine-grained retrospective labels of eventual "true" diagnoses. We do so with LLMs, to ensure that the input text is from before a confident diagnosis can be made. We use an LLM to retrieve an initial pool of evidence, but then refine this set of evidence according to correlations learned by the model. We conduct an in-depth evaluation of the usefulness of our approach by simulating how it might be used by a clinician to decide between a pre-defined list of differential diagnoses.

Statisticians and machine learners analyze observed data by synthesizing models of those data. These models take a variety of forms, with several of the most widely used being directed graphical models, probabilistic programs, and structural causal models (SCMs). Applications of these frameworks have included cognitive modeling [7, 20], simulation-based inference [9], and model-based planning [12, 21]. Unfortunately, the richer the model class, the weaker the mathematical tools available to reason rigorously about it: SCMs built on linear equations with Gaussian noise admit easy inference, while graphical models have a clear meaning and a wide array of inference algorithms but encode a limited family of models. Probabilistic programs can encode any computably sampleable distribution, but the definition of their densities commonly relies on operational analogies with directed graphical models.

Incorporating geometric inductive biases into models can aid interpretability and generalization, but encoding to a specific geometric structure can be challenging due to the imposed topological constraints. In this paper, we theoretically and empirically characterize obstructions to training encoders with geometric latent spaces. We show that local optima can arise due to singularities (e.g. self-intersection) or due to an incorrect degree or winding number. We then discuss how normalizing flows can potentially circumvent these obstructions by defining multimodal variational distributions. Inspired by this observation, we propose a new flow-based model that maps data points to multimodal distributions over geometric spaces and empirically evaluate our model on 2 domains. We observe improved stability during training and a higher chance of converging to a homeomorphic encoder.

Imitation learning of robot policies from few demonstrations is crucial in open-ended applications. We propose a new method, Interaction Warping, for learning SE(3) robotic manipulation policies from a single demonstration. We infer the 3D mesh of each object in the environment using shape warping, a technique for aligning point clouds across object instances. Then, we represent manipulation actions as keypoints on objects, which can be warped with the shape of the object. We show successful one-shot imitation learning on three simulated and real-world object re-arrangement tasks. We also demonstrate the ability of our method to predict object meshes and robot grasps in the wild.

We propose CHiLL (Crafting High-Level Latents), an approach for natural-language specification of features for linear models. CHiLL prompts LLMs with expert-crafted queries to generate interpretable features from health records. The resulting noisy labels are then used to train a simple linear classifier. Generating features based on queries to an LLM can empower physicians to use their domain expertise to craft features that are clinically meaningful for a downstream task of interest, without having to manually extract these from raw EHR. We are motivated by a real-world risk prediction task, but as a reproducible proxy, we use MIMIC-III and MIMIC-CXR data and standard predictive tasks (e.g., 30-day readmission) to evaluate this approach. We find that linear models using automatically extracted features are comparably performant to models using reference features, and provide greater interpretability than linear models using "Bag-of-Words" features. We verify that learned feature weights align well with clinical expectations.