Daily Papers

Stability guarantees are crucial when ensuring a fully autonomous robot does not take undesirable or potentially harmful actions. Unfortunately, global stability guarantees are hard to provide in dynamical systems learned from data, especially when the learned dynamics are governed by neural networks. We propose a novel methodology to learn neural contractive dynamical systems, where our neural architecture ensures contraction, and hence, global stability. To efficiently scale the method to high-dimensional dynamical systems, we develop a variant of the variational autoencoder that learns dynamics in a low-dimensional latent representation space while retaining contractive stability after decoding. We further extend our approach to learning contractive systems on the Lie group of rotations to account for full-pose end-effector dynamic motions. The result is the first highly flexible learning architecture that provides contractive stability guarantees with capability to perform obstacle avoidance. Empirically, we demonstrate that our approach encodes the desired dynamics more accurately than the current state-of-the-art, which provides less strong stability guarantees.

Score-based diffusion modeling is a generative machine learning algorithm that can be used to sample from complex distributions. They achieve this by learning a score function, i.e., the gradient of the log-probability density of the data, and reversing a noising process using the same. Once trained, score-based diffusion models not only generate new samples but also enable zero-shot conditioning of the generated samples on observed data. This promises a novel paradigm for data and model fusion, wherein the implicitly learned distributions of pretrained score-based diffusion models can be updated given the availability of online data in a Bayesian formulation. In this article, we apply such a concept to the super-resolution of a high-dimensional dynamical system, given the real-time availability of low-resolution and experimentally observed sparse sensor measurements from multimodal data. Additional analysis on how score-based sampling can be used for uncertainty estimates is also provided. Our experiments are performed for a super-resolution task that generates the ERA5 atmospheric dataset given sparse observations from a coarse-grained representation of the same and/or from unstructured experimental observations of the IGRA radiosonde dataset. We demonstrate accurate recovery of the high dimensional state given multiple sources of low-fidelity measurements. We also discover that the generative model can balance the influence of multiple dataset modalities during spatiotemporal reconstructions.

Despite advances in learning-based methods, finding valid Lyapunov functions for nonlinear dynamical systems remains challenging. Current neural network approaches face two main issues: challenges in scalable verification and limited interpretability. To address these, we propose an end-to-end framework using transformers to construct analytical Lyapunov functions (local), which simplifies formal verification, enhances interpretability, and provides valuable insights for control engineers. Our framework consists of a transformer-based trainer that generates candidate Lyapunov functions and a falsifier that verifies candidate expressions and refines the model via risk-seeking policy gradient. Unlike Alfarano et al. (2024), which utilizes pre-training and seeks global Lyapunov functions for low-dimensional systems, our model is trained from scratch via reinforcement learning (RL) and succeeds in finding local Lyapunov functions for high-dimensional and non-polynomial systems. Given the analytical nature of the candidates, we employ efficient optimization methods for falsification during training and formal verification tools for the final verification. We demonstrate the efficiency of our approach on a range of nonlinear dynamical systems with up to ten dimensions and show that it can discover Lyapunov functions not previously identified in the control literature.

Machine learning architectures, including transformers and recurrent neural networks (RNNs) have revolutionized forecasting in applications ranging from text processing to extreme weather. Notably, advanced network architectures, tuned for applications such as natural language processing, are transferable to other tasks such as spatiotemporal forecasting tasks. However, there is a scarcity of ablation studies to illustrate the key components that enable this forecasting accuracy. The absence of such studies, although explainable due to the associated computational cost, intensifies the belief that these models ought to be considered as black boxes. In this work, we decompose the key architectural components of the most powerful neural architectures, namely gating and recurrence in RNNs, and attention mechanisms in transformers. Then, we synthesize and build novel hybrid architectures from the standard blocks, performing ablation studies to identify which mechanisms are effective for each task. The importance of considering these components as hyper-parameters that can augment the standard architectures is exhibited on various forecasting datasets, from the spatiotemporal chaotic dynamics of the multiscale Lorenz 96 system, the Kuramoto-Sivashinsky equation, as well as standard real world time-series benchmarks. A key finding is that neural gating and attention improves the performance of all standard RNNs in most tasks, while the addition of a notion of recurrence in transformers is detrimental. Furthermore, our study reveals that a novel, sparsely used, architecture which integrates Recurrent Highway Networks with neural gating and attention mechanisms, emerges as the best performing architecture in high-dimensional spatiotemporal forecasting of dynamical systems.

Large-scale recordings of neural activity are providing new opportunities to study neural population dynamics. A powerful method for analyzing such high-dimensional measurements is to deploy an algorithm to learn the low-dimensional latent dynamics. LFADS (Latent Factor Analysis via Dynamical Systems) is a deep learning method for inferring latent dynamics from high-dimensional neural spiking data recorded simultaneously in single trials. This method has shown a remarkable performance in modeling complex brain signals with an average inference latency in milliseconds. As our capacity of simultaneously recording many neurons is increasing exponentially, it is becoming crucial to build capacity for deploying low-latency inference of the computing algorithms. To improve the real-time processing ability of LFADS, we introduce an efficient implementation of the LFADS models onto Field Programmable Gate Arrays (FPGA). Our implementation shows an inference latency of 41.97 mus for processing the data in a single trial on a Xilinx U55C.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

Predicting the behavior of complex systems is critical in many scientific and engineering domains, and hinges on the model's ability to capture their underlying dynamics. Existing methods encode the intrinsic dynamics of high-dimensional observations through latent representations and predict autoregressively. However, these latent representations lose the inherent spatial structure of spatiotemporal dynamics, leading to the predictor's inability to effectively model spatial interactions and neglect emerging dynamics during long-term prediction. In this work, we propose SparseDiff, introducing a test-time adaptation strategy to dynamically update the encoding scheme to accommodate emergent spatiotemporal structures during the long-term evolution of the system. Specifically, we first design a codebook-based sparse encoder, which coarsens the continuous spatial domain into a sparse graph topology. Then, we employ a graph neural ordinary differential equation to model the dynamics and guide a diffusion decoder for reconstruction. SparseDiff autoregressively predicts the spatiotemporal evolution and adjust the sparse topological structure to adapt to emergent spatiotemporal patterns by adaptive re-encoding. Extensive evaluations on representative systems demonstrate that SparseDiff achieves an average prediction error reduction of 49.99\% compared to baselines, requiring only 1\% of the spatial resolution.

Multi-vector document retrieval systems, such as ColPali, excel in fine-grained matching for complex queries but incur significant storage and computational costs due to their reliance on high-dimensional patch embeddings and late-interaction scoring. To address these challenges, we propose HPC-ColPali, a Hierarchical Patch Compression framework that enhances the efficiency of ColPali while preserving its retrieval accuracy. Our approach integrates three innovative techniques: (1) K-Means quantization, which compresses patch embeddings into 1-byte centroid indices, achieving up to 32times storage reduction; (2) attention-guided dynamic pruning, utilizing Vision-Language Model attention weights to retain only the top-p% most salient patches, reducing late-interaction computation by up to 60\% with less than 2\% nDCG@10 loss; and (3) optional binary encoding of centroid indices into b-bit strings (b=lceillog_2 Krceil), enabling rapid Hamming distance-based similarity search for resource-constrained environments. Evaluated on the ViDoRe and SEC-Filings datasets, HPC-ColPali achieves 30--50\% lower query latency under HNSW indexing while maintaining high retrieval precision. When integrated into a Retrieval-Augmented Generation pipeline for legal summarization, it reduces hallucination rates by 30\% and halves end-to-end latency. These advancements establish HPC-ColPali as a scalable and efficient solution for multi-vector document retrieval across diverse applications. Code is available at https://github.com/DngBack/HPC-ColPali.

The theory of open quantum systems lays the foundations for a substantial part of modern research in quantum science and engineering. Rooted in the dimensionality of their extended Hilbert spaces, the high computational complexity of simulating open quantum systems calls for the development of strategies to approximate their dynamics. In this paper, we present an approach for tackling open quantum system dynamics. Using an exact probabilistic formulation of quantum physics based on positive operator-valued measure (POVM), we compactly represent quantum states with autoregressive transformer neural networks; such networks bring significant algorithmic flexibility due to efficient exact sampling and tractable density. We further introduce the concept of String States to partially restore the symmetry of the autoregressive transformer neural network and improve the description of local correlations. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator using a forward-backward trapezoid method and find the steady state via a variational formulation. Our approach is benchmarked on prototypical one and two-dimensional systems, finding results which closely track the exact solution and achieve higher accuracy than alternative approaches based on using Markov chain Monte Carlo to sample restricted Boltzmann machines. Our work provides general methods for understanding quantum dynamics in various contexts, as well as techniques for solving high-dimensional probabilistic differential equations in classical setups.

Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body -- two close positions in a higher-level mesh correspond to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods. Our code is available at https://github.com/yuyudeep/hcmt.

Large language models (LLMs) pre-trained on vast internet-scale data have showcased remarkable capabilities across diverse domains. Recently, there has been escalating interest in deploying LLMs for robotics, aiming to harness the power of foundation models in real-world settings. However, this approach faces significant challenges, particularly in grounding these models in the physical world and in generating dynamic robot motions. To address these issues, we introduce a novel paradigm in which we use few-shot prompts collected from the physical environment, enabling the LLM to autoregressively generate low-level control commands for robots without task-specific fine-tuning. Experiments across various robots and environments validate that our method can effectively prompt a robot to walk. We thus illustrate how LLMs can proficiently function as low-level feedback controllers for dynamic motion control even in high-dimensional robotic systems. The project website and source code can be found at: https://prompt2walk.github.io/ .

Reduced-order modeling (ROM) of time-dependent and parameterized differential equations aims to accelerate the simulation of complex high-dimensional systems by learning a compact latent manifold representation that captures the characteristics of the solution fields and their time-dependent dynamics. Although high-fidelity numerical solvers generate the training datasets, they have thus far been excluded from the training process, causing the learned latent dynamics to drift away from the discretized governing physics. This mismatch often limits generalization and forecasting capabilities. In this work, we propose Physics-informed ROM (Φ-ROM) by incorporating differentiable PDE solvers into the training procedure. Specifically, the latent space dynamics and its dependence on PDE parameters are shaped directly by the governing physics encoded in the solver, ensuring a strong correspondence between the full and reduced systems. Our model outperforms state-of-the-art data-driven ROMs and other physics-informed strategies by accurately generalizing to new dynamics arising from unseen parameters, enabling long-term forecasting beyond the training horizon, maintaining continuity in both time and space, and reducing the data cost. Furthermore, Φ-ROM learns to recover and forecast the solution fields even when trained or evaluated with sparse and irregular observations of the fields, providing a flexible framework for field reconstruction and data assimilation. We demonstrate the framework's robustness across various PDE solvers and highlight its broad applicability by providing an open-source JAX implementation that is readily extensible to other PDE systems and differentiable solvers, available at https://phi-rom.github.io.

Ensuring safety and meeting temporal specifications are critical challenges for long-term robotic tasks. Signal temporal logic (STL) has been widely used to systematically and rigorously specify these requirements. However, traditional methods of finding the control policy under those STL requirements are computationally complex and not scalable to high-dimensional or systems with complex nonlinear dynamics. Reinforcement learning (RL) methods can learn the policy to satisfy the STL specifications via hand-crafted or STL-inspired rewards, but might encounter unexpected behaviors due to ambiguity and sparsity in the reward. In this paper, we propose a method to directly learn a neural network controller to satisfy the requirements specified in STL. Our controller learns to roll out trajectories to maximize the STL robustness score in training. In testing, similar to Model Predictive Control (MPC), the learned controller predicts a trajectory within a planning horizon to ensure the satisfaction of the STL requirement in deployment. A backup policy is designed to ensure safety when our controller fails. Our approach can adapt to various initial conditions and environmental parameters. We conduct experiments on six tasks, where our method with the backup policy outperforms the classical methods (MPC, STL-solver), model-free and model-based RL methods in STL satisfaction rate, especially on tasks with complex STL specifications while being 10X-100X faster than the classical methods.

Large-scale LLM pretraining now runs across 10^5--10^6 accelerators, making failures routine and elasticity mandatory. We posit that an elastic-native training system must jointly deliver (i) parameter consistency, (ii) low mean time to recovery (MTTR), (iii) high post-change throughput, and (iv) computation consistency. No prior system achieves all four simultaneously. To achieve these goals, we present ElasWave, which delivers per-step fault tolerance via multi-dimensional scheduling across graph, dataflow, DVFS, and RNG. ElasWave reshapes and reshards micro-batches while preserving the global batch size and gradient scale. It performs online pipeline resharding with asynchronous parameter migration and interleaves ZeRO partitions, reducing parameter recovery processes to disjoint rank-to-rank transfers. It further leverages DVFS to absorb pipeline bubbles and reshards RNG to keep computation consistency. Together, a dynamic communicator enables in-place communication group edits, while per-step in-memory snapshots support online verification and redistribution. We evaluate ElasWave on 96 NPUs and benchmark it against state-of-the-art baselines: throughput improves by 1.35times over ReCycle and 1.60times over TorchFT; communicator recovery completes within one second (up to 82times/3.6times faster than full/partial rebuilds); migration MTTR drops by as much as 51%; and convergence deviation is reduced by approximately 78%.

We introduce controlgym, a library of thirty-six safety-critical industrial control settings, and ten infinite-dimensional partial differential equation (PDE)-based control problems. Integrated within the OpenAI Gym/Gymnasium (Gym) framework, controlgym allows direct applications of standard reinforcement learning (RL) algorithms like stable-baselines3. Our control environments complement those in Gym with continuous, unbounded action and observation spaces, motivated by real-world control applications. Moreover, the PDE control environments uniquely allow the users to extend the state dimensionality of the system to infinity while preserving the intrinsic dynamics. This feature is crucial for evaluating the scalability of RL algorithms for control. This project serves the learning for dynamics & control (L4DC) community, aiming to explore key questions: the convergence of RL algorithms in learning control policies; the stability and robustness issues of learning-based controllers; and the scalability of RL algorithms to high- and potentially infinite-dimensional systems. We open-source the controlgym project at https://github.com/xiangyuan-zhang/controlgym.