Daily Papers

In this paper, we introduce a new class of parameterized controllers, drawing inspiration from Model Predictive Control (MPC). The controller resembles a Quadratic Programming (QP) solver of a linear MPC problem, with the parameters of the controller being trained via Deep Reinforcement Learning (DRL) rather than derived from system models. This approach addresses the limitations of common controllers with Multi-Layer Perceptron (MLP) or other general neural network architecture used in DRL, in terms of verifiability and performance guarantees, and the learned controllers possess verifiable properties like persistent feasibility and asymptotic stability akin to MPC. On the other hand, numerical examples illustrate that the proposed controller empirically matches MPC and MLP controllers in terms of control performance and has superior robustness against modeling uncertainty and noises. Furthermore, the proposed controller is significantly more computationally efficient compared to MPC and requires fewer parameters to learn than MLP controllers. Real-world experiments on vehicle drift maneuvering task demonstrate the potential of these controllers for robotics and other demanding control tasks.

With the rapid advancement of 2D generative models, preserving subject identity while enabling diverse editing has emerged as a critical research focus. Existing methods typically face inherent trade-offs between identity preservation and personalized manipulation. We introduce FlexIP, a novel framework that decouples these objectives through two dedicated components: a Personalization Adapter for stylistic manipulation and a Preservation Adapter for identity maintenance. By explicitly injecting both control mechanisms into the generative model, our framework enables flexible parameterized control during inference through dynamic tuning of the weight adapter. Experimental results demonstrate that our approach breaks through the performance limitations of conventional methods, achieving superior identity preservation while supporting more diverse personalized generation capabilities (Project Page: https://flexip-tech.github.io/flexip/).

Deep neural networks have shown promise for music audio signal processing applications, often surpassing prior approaches, particularly as end-to-end models in the waveform domain. Yet results to date have tended to be constrained by low sample rates, noise, narrow domains of signal types, and/or lack of parameterized controls (i.e. "knobs"), making their suitability for professional audio engineering workflows still lacking. This work expands on prior research published on modeling nonlinear time-dependent signal processing effects associated with music production by means of a deep neural network, one which includes the ability to emulate the parameterized settings you would see on an analog piece of equipment, with the goal of eventually producing commercially viable, high quality audio, i.e. 44.1 kHz sampling rate at 16-bit resolution. The results in this paper highlight progress in modeling these effects through architecture and optimization changes, towards increasing computational efficiency, lowering signal-to-noise ratio, and extending to a larger variety of nonlinear audio effects. Toward these ends, the strategies employed involved a three-pronged approach: model speed, model accuracy, and model generalizability. Most of the presented methods provide marginal or no increase in output accuracy over the original model, with the exception of dataset manipulation. We found that limiting the audio content of the dataset, for example using datasets of just a single instrument, provided a significant improvement in model accuracy over models trained on more general datasets.

For robots to be useful outside labs and specialized factories we need a way to teach them new useful behaviors quickly. Current approaches lack either the generality to onboard new tasks without task-specific engineering, or else lack the data-efficiency to do so in an amount of time that enables practical use. In this work we explore dense tracking as a representational vehicle to allow faster and more general learning from demonstration. Our approach utilizes Track-Any-Point (TAP) models to isolate the relevant motion in a demonstration, and parameterize a low-level controller to reproduce this motion across changes in the scene configuration. We show this results in robust robot policies that can solve complex object-arrangement tasks such as shape-matching, stacking, and even full path-following tasks such as applying glue and sticking objects together, all from demonstrations that can be collected in minutes.

Neural implicit fields are powerful for representing 3D scenes and generating high-quality novel views, but it remains challenging to use such implicit representations for creating a 3D human avatar with a specific identity and artistic style that can be easily animated. Our proposed method, AvatarCraft, addresses this challenge by using diffusion models to guide the learning of geometry and texture for a neural avatar based on a single text prompt. We carefully design the optimization framework of neural implicit fields, including a coarse-to-fine multi-bounding box training strategy, shape regularization, and diffusion-based constraints, to produce high-quality geometry and texture. Additionally, we make the human avatar animatable by deforming the neural implicit field with an explicit warping field that maps the target human mesh to a template human mesh, both represented using parametric human models. This simplifies animation and reshaping of the generated avatar by controlling pose and shape parameters. Extensive experiments on various text descriptions show that AvatarCraft is effective and robust in creating human avatars and rendering novel views, poses, and shapes. Our project page is: https://avatar-craft.github.io/.

We demonstrate the possibility of learning drone swarm controllers that are zero-shot transferable to real quadrotors via large-scale multi-agent end-to-end reinforcement learning. We train policies parameterized by neural networks that are capable of controlling individual drones in a swarm in a fully decentralized manner. Our policies, trained in simulated environments with realistic quadrotor physics, demonstrate advanced flocking behaviors, perform aggressive maneuvers in tight formations while avoiding collisions with each other, break and re-establish formations to avoid collisions with moving obstacles, and efficiently coordinate in pursuit-evasion tasks. We analyze, in simulation, how different model architectures and parameters of the training regime influence the final performance of neural swarms. We demonstrate the successful deployment of the model learned in simulation to highly resource-constrained physical quadrotors performing station keeping and goal swapping behaviors. Code and video demonstrations are available on the project website at https://sites.google.com/view/swarm-rl.

Audio-driven talking face generation has garnered significant interest within the domain of digital human research. Existing methods are encumbered by intricate model architectures that are intricately dependent on each other, complicating the process of re-editing image or video inputs. In this work, we present ControlTalk, a talking face generation method to control face expression deformation based on driven audio, which can construct the head pose and facial expression including lip motion for both single image or sequential video inputs in a unified manner. By utilizing a pre-trained video synthesis renderer and proposing the lightweight adaptation, ControlTalk achieves precise and naturalistic lip synchronization while enabling quantitative control over mouth opening shape. Our experiments show that our method is superior to state-of-the-art performance on widely used benchmarks, including HDTF and MEAD. The parameterized adaptation demonstrates remarkable generalization capabilities, effectively handling expression deformation across same-ID and cross-ID scenarios, and extending its utility to out-of-domain portraits, regardless of languages.

Diffusion models may be formulated as a time-indexed sequence of energy-based models, where the score corresponds to the negative gradient of an energy function. As opposed to learning the score directly, an energy parameterization is attractive as the energy itself can be used to control generation via Monte Carlo samplers. Architectural constraints and training instability in energy parameterized models have so far yielded inferior performance compared to directly approximating the score or denoiser. We address these deficiencies by introducing a novel training regime for the energy function through distillation of pre-trained diffusion models, resembling a Helmholtz decomposition of the score vector field. We further showcase the synergies between energy and score by casting the diffusion sampling procedure as a Feynman Kac model where sampling is controlled using potentials from the learnt energy functions. The Feynman Kac model formalism enables composition and low temperature sampling through sequential Monte Carlo.

Control barrier functions (CBFs) enable guaranteed safe multi-agent navigation in the continuous domain. The resulting navigation performance, however, is highly sensitive to the underlying hyperparameters. Traditional approaches consider fixed CBFs (where parameters are tuned apriori), and hence, typically do not perform well in cluttered and highly dynamic environments: conservative parameter values can lead to inefficient agent trajectories, or even failure to reach goal positions, whereas aggressive parameter values can lead to infeasible controls. To overcome these issues, in this paper, we propose online CBFs, whereby hyperparameters are tuned in real-time, as a function of what agents perceive in their immediate neighborhood. Since the explicit relationship between CBFs and navigation performance is hard to model, we leverage reinforcement learning to learn CBF-tuning policies in a model-free manner. Because we parameterize the policies with graph neural networks (GNNs), we are able to synthesize decentralized agent controllers that adjust parameter values locally, varying the degree of conservative and aggressive behaviors across agents. Simulations as well as real-world experiments show that (i) online CBFs are capable of solving navigation scenarios that are infeasible for fixed CBFs, and (ii), that they improve navigation performance by adapting to other agents and changes in the environment.

Recently video diffusion models have emerged as expressive generative tools for high-quality video content creation readily available to general users. However, these models often do not offer precise control over camera poses for video generation, limiting the expression of cinematic language and user control. To address this issue, we introduce CamCo, which allows fine-grained Camera pose Control for image-to-video generation. We equip a pre-trained image-to-video generator with accurately parameterized camera pose input using Pl\"ucker coordinates. To enhance 3D consistency in the videos produced, we integrate an epipolar attention module in each attention block that enforces epipolar constraints to the feature maps. Additionally, we fine-tune CamCo on real-world videos with camera poses estimated through structure-from-motion algorithms to better synthesize object motion. Our experiments show that CamCo significantly improves 3D consistency and camera control capabilities compared to previous models while effectively generating plausible object motion. Project page: https://ir1d.github.io/CamCo/

We present SimpleStories, a large synthetic story dataset in simple language, consisting of 2 million stories each in English and Japanese. Our method employs parametrization of prompts with features at multiple levels of abstraction, allowing for systematic control over story characteristics to ensure broad syntactic and semantic diversity. Building on and addressing limitations in the TinyStories dataset, our approach demonstrates that simplicity and variety can be achieved simultaneously in synthetic text generation at scale.

Human-driven vehicles (HVs) exhibit complex and diverse behaviors. Accurately modeling such behavior is crucial for validating Robot Vehicles (RVs) in simulation and realizing the potential of mixed traffic control. However, existing approaches like parameterized models and data-driven techniques struggle to capture the full complexity and diversity. To address this, in this work, we introduce CARL, a hybrid technique combining imitation learning for close proximity car-following and probabilistic sampling for larger headways. We also propose two classes of RL-based RVs: a safety RV focused on maximizing safety and an efficiency RV focused on maximizing efficiency. Our experiments show that the safety RV increases Time-to-Collision above the critical 4 second threshold and reduces Deceleration Rate to Avoid a Crash by up to 80%, while the efficiency RV achieves improvements in throughput of up to 49%. These results demonstrate the effectiveness of CARL in enhancing both safety and efficiency in mixed traffic.

Emerging video diffusion models achieve high visual fidelity but fundamentally couple scene dynamics with camera motion, limiting their ability to provide precise spatial and temporal control. We introduce a 4D-controllable video diffusion framework that explicitly decouples scene dynamics from camera pose, enabling fine-grained manipulation of both scene dynamics and camera viewpoint. Our framework takes continuous world-time sequences and camera trajectories as conditioning inputs, injecting them into the video diffusion model through a 4D positional encoding in the attention layer and adaptive normalizations for feature modulation. To train this model, we curate a unique dataset in which temporal and camera variations are independently parameterized; this dataset will be made public. Experiments show that our model achieves robust real-world 4D control across diverse timing patterns and camera trajectories, while preserving high generation quality and outperforming prior work in controllability. See our website for video results: https://19reborn.github.io/Bullet4D/

Harmonic model predictive control (HMPC) is a recent model predictive control (MPC) formulation for tracking piece-wise constant references that includes a parameterized artificial harmonic reference as a decision variable, resulting in an increased performance and domain of attraction with respect to other MPC formulations. This article presents an extension of the HMPC formulation to track periodic harmonic/sinusoidal references and discusses its use for tracking arbitrary trajectories. The proposed formulation inherits the benefits of its predecessor, namely its good performance and large domain of attraction when using small prediction horizons, and that the complexity of its optimization problem does not depend on the period of the reference. We show closed-loop results discussing its performance and comparing it to other MPC formulations.

Recent remarkable advances in large-scale text-to-image diffusion models have inspired a significant breakthrough in text-to-3D generation, pursuing 3D content creation solely from a given text prompt. However, existing text-to-3D techniques lack a crucial ability in the creative process: interactively control and shape the synthetic 3D contents according to users' desired specifications (e.g., sketch). To alleviate this issue, we present the first attempt for text-to-3D generation conditioning on the additional hand-drawn sketch, namely Control3D, which enhances controllability for users. In particular, a 2D conditioned diffusion model (ControlNet) is remoulded to guide the learning of 3D scene parameterized as NeRF, encouraging each view of 3D scene aligned with the given text prompt and hand-drawn sketch. Moreover, we exploit a pre-trained differentiable photo-to-sketch model to directly estimate the sketch of the rendered image over synthetic 3D scene. Such estimated sketch along with each sampled view is further enforced to be geometrically consistent with the given sketch, pursuing better controllable text-to-3D generation. Through extensive experiments, we demonstrate that our proposal can generate accurate and faithful 3D scenes that align closely with the input text prompts and sketches.

We present SA-Radar (Simulate Any Radar), a radar simulation approach that enables controllable and efficient generation of radar cubes conditioned on customizable radar attributes. Unlike prior generative or physics-based simulators, SA-Radar integrates both paradigms through a waveform-parameterized attribute embedding. We design ICFAR-Net, a 3D U-Net conditioned on radar attributes encoded via waveform parameters, which captures signal variations induced by different radar configurations. This formulation bypasses the need for detailed radar hardware specifications and allows efficient simulation of range-azimuth-Doppler (RAD) tensors across diverse sensor settings. We further construct a mixed real-simulated dataset with attribute annotations to robustly train the network. Extensive evaluations on multiple downstream tasks-including 2D/3D object detection and radar semantic segmentation-demonstrate that SA-Radar's simulated data is both realistic and effective, consistently improving model performance when used standalone or in combination with real data. Our framework also supports simulation in novel sensor viewpoints and edited scenes, showcasing its potential as a general-purpose radar data engine for autonomous driving applications. Code and additional materials are available at https://zhuxing0.github.io/projects/SA-Radar.

Flow matching in the continuous simplex has emerged as a promising strategy for DNA sequence design, but struggles to scale to higher simplex dimensions required for peptide and protein generation. We introduce Gumbel-Softmax Flow and Score Matching, a generative framework on the simplex based on a novel Gumbel-Softmax interpolant with a time-dependent temperature. Using this interpolant, we introduce Gumbel-Softmax Flow Matching by deriving a parameterized velocity field that transports from smooth categorical distributions to distributions concentrated at a single vertex of the simplex. We alternatively present Gumbel-Softmax Score Matching which learns to regress the gradient of the probability density. Our framework enables high-quality, diverse generation and scales efficiently to higher-dimensional simplices. To enable training-free guidance, we propose Straight-Through Guided Flows (STGFlow), a classifier-based guidance method that leverages straight-through estimators to steer the unconditional velocity field toward optimal vertices of the simplex. STGFlow enables efficient inference-time guidance using classifiers pre-trained on clean sequences, and can be used with any discrete flow method. Together, these components form a robust framework for controllable de novo sequence generation. We demonstrate state-of-the-art performance in conditional DNA promoter design, sequence-only protein generation, and target-binding peptide design for rare disease treatment.

Autonomous systems, such as self-driving cars and drones, have made significant strides in recent years by leveraging visual inputs and machine learning for decision-making and control. Despite their impressive performance, these vision-based controllers can make erroneous predictions when faced with novel or out-of-distribution inputs. Such errors can cascade into catastrophic system failures and compromise system safety. In this work, we compute Neural Reachable Tubes, which act as parameterized approximations of Backward Reachable Tubes to stress-test the vision-based controllers and mine their failure modes. The identified failures are then used to enhance the system safety through both offline and online methods. The online approach involves training a classifier as a run-time failure monitor to detect closed-loop, system-level failures, subsequently triggering a fallback controller that robustly handles these detected failures to preserve system safety. For the offline approach, we improve the original controller via incremental training using a carefully augmented failure dataset, resulting in a more robust controller that is resistant to the known failure modes. In either approach, the system is safeguarded against shortcomings that transcend the vision-based controller and pertain to the closed-loop safety of the overall system. We validate the proposed approaches on an autonomous aircraft taxiing task that involves using a vision-based controller to guide the aircraft towards the centerline of the runway. Our results show the efficacy of the proposed algorithms in identifying and handling system-level failures, outperforming methods that rely on controller prediction error or uncertainty quantification for identifying system failures.

Unsupervised learning of 3D-aware generative adversarial networks has lately made much progress. Some recent work demonstrates promising results of learning human generative models using neural articulated radiance fields, yet their generalization ability and controllability lag behind parametric human models, i.e., they do not perform well when generalizing to novel pose/shape and are not part controllable. To solve these problems, we propose VeRi3D, a generative human vertex-based radiance field parameterized by vertices of the parametric human template, SMPL. We map each 3D point to the local coordinate system defined on its neighboring vertices, and use the corresponding vertex feature and local coordinates for mapping it to color and density values. We demonstrate that our simple approach allows for generating photorealistic human images with free control over camera pose, human pose, shape, as well as enabling part-level editing.

We consider the problem of how a teacher algorithm can enable an unknown Deep Reinforcement Learning (DRL) student to become good at a skill over a wide range of diverse environments. To do so, we study how a teacher algorithm can learn to generate a learning curriculum, whereby it sequentially samples parameters controlling a stochastic procedural generation of environments. Because it does not initially know the capacities of its student, a key challenge for the teacher is to discover which environments are easy, difficult or unlearnable, and in what order to propose them to maximize the efficiency of learning over the learnable ones. To achieve this, this problem is transformed into a surrogate continuous bandit problem where the teacher samples environments in order to maximize absolute learning progress of its student. We present a new algorithm modeling absolute learning progress with Gaussian mixture models (ALP-GMM). We also adapt existing algorithms and provide a complete study in the context of DRL. Using parameterized variants of the BipedalWalker environment, we study their efficiency to personalize a learning curriculum for different learners (embodiments), their robustness to the ratio of learnable/unlearnable environments, and their scalability to non-linear and high-dimensional parameter spaces. Videos and code are available at https://github.com/flowersteam/teachDeepRL.

Coordinated path following in multi-agent systems is a key challenge in robotics, with applications in automated logistics, surveillance, and collaborative exploration. Traditional formation control techniques often rely on time-parameterized trajectories and path integrals, which can result in synchronization issues and rigid behavior. In this work, we address the problem of sequential path following, where agents maintain fixed spatial separation along a common trajectory, guided by a leader under centralized control. We introduce Robot Conga, a leader-follower control strategy that updates each agent's desired state based on the leader's spatial displacement rather than time, assuming access to a global position reference, an assumption valid in indoor environments equipped with motion capture, vision-based tracking, or UWB localization systems. The algorithm was validated in simulation using both TurtleBot3 and quadruped (Laikago) robots. Results demonstrate accurate trajectory tracking, stable inter-agent spacing, and fast convergence, with all agents aligning within 250 time steps (approx. 0.25 seconds) in the quadruped case, and almost instantaneously in the TurtleBot3 implementation.

Multimodal agents have demonstrated strong performance in general GUI interactions, but their application in automotive systems has been largely unexplored. In-vehicle GUIs present distinct challenges: drivers' limited attention, strict safety requirements, and complex location-based interaction patterns. To address these challenges, we introduce Automotive-ENV, the first high-fidelity benchmark and interaction environment tailored for vehicle GUIs. This platform defines 185 parameterized tasks spanning explicit control, implicit intent understanding, and safety-aware tasks, and provides structured multimodal observations with precise programmatic checks for reproducible evaluation. Building on this benchmark, we propose ASURADA, a geo-aware multimodal agent that integrates GPS-informed context to dynamically adjust actions based on location, environmental conditions, and regional driving norms. Experiments show that geo-aware information significantly improves success on safety-aware tasks, highlighting the importance of location-based context in automotive environments. We will release Automotive-ENV, complete with all tasks and benchmarking tools, to further the development of safe and adaptive in-vehicle agents.

Relighting radiance fields is severely underconstrained for multi-view data, which is most often captured under a single illumination condition; It is especially hard for full scenes containing multiple objects. We introduce a method to create relightable radiance fields using such single-illumination data by exploiting priors extracted from 2D image diffusion models. We first fine-tune a 2D diffusion model on a multi-illumination dataset conditioned by light direction, allowing us to augment a single-illumination capture into a realistic -- but possibly inconsistent -- multi-illumination dataset from directly defined light directions. We use this augmented data to create a relightable radiance field represented by 3D Gaussian splats. To allow direct control of light direction for low-frequency lighting, we represent appearance with a multi-layer perceptron parameterized on light direction. To enforce multi-view consistency and overcome inaccuracies we optimize a per-image auxiliary feature vector. We show results on synthetic and real multi-view data under single illumination, demonstrating that our method successfully exploits 2D diffusion model priors to allow realistic 3D relighting for complete scenes. Project site https://repo-sam.inria.fr/fungraph/generative-radiance-field-relighting/

This work presents HeadArtist for 3D head generation from text descriptions. With a landmark-guided ControlNet serving as the generative prior, we come up with an efficient pipeline that optimizes a parameterized 3D head model under the supervision of the prior distillation itself. We call such a process self score distillation (SSD). In detail, given a sampled camera pose, we first render an image and its corresponding landmarks from the head model, and add some particular level of noise onto the image. The noisy image, landmarks, and text condition are then fed into the frozen ControlNet twice for noise prediction. Two different classifier-free guidance (CFG) weights are applied during these two predictions, and the prediction difference offers a direction on how the rendered image can better match the text of interest. Experimental results suggest that our approach delivers high-quality 3D head sculptures with adequate geometry and photorealistic appearance, significantly outperforming state-ofthe-art methods. We also show that the same pipeline well supports editing the generated heads, including both geometry deformation and appearance change.

Modern large language models (LLMs) employ various forms of logical inference, both implicitly and explicitly, when addressing reasoning tasks. Understanding how to optimally leverage these inference paradigms is critical for advancing LLMs' reasoning capabilities. This paper adopts an exploratory approach by introducing a controlled evaluation environment for analogical reasoning -- a fundamental cognitive task -- that is systematically parameterized across three dimensions: modality (textual, visual, symbolic), difficulty (easy, medium, hard), and task format (multiple-choice or free-text generation). We analyze the comparative dynamics of inductive, abductive, and deductive inference pipelines across these dimensions, and demonstrate that our findings generalize to broader in-context learning tasks. Additionally, we investigate advanced paradigms such as hypothesis selection, verification, and refinement, revealing their potential to scale up logical inference in LLM reasoning. This exploratory study provides a foundation for future research in enhancing LLM reasoning through systematic logical inference strategies.

In recent years, lightweight large language models (LLMs) have garnered significant attention in the robotics field due to their low computational resource requirements and suitability for edge deployment. However, in task planning -- particularly for complex tasks that involve dynamic semantic logic reasoning -- lightweight LLMs have underperformed. To address this limitation, we propose a novel task planner, LightPlanner, which enhances the performance of lightweight LLMs in complex task planning by fully leveraging their reasoning capabilities. Unlike conventional planners that use fixed skill templates, LightPlanner controls robot actions via parameterized function calls, dynamically generating parameter values. This approach allows for fine-grained skill control and improves task planning success rates in complex scenarios. Furthermore, we introduce hierarchical deep reasoning. Before generating each action decision step, LightPlanner thoroughly considers three levels: action execution (feedback verification), semantic parsing (goal consistency verification), and parameter generation (parameter validity verification). This ensures the correctness of subsequent action controls. Additionally, we incorporate a memory module to store historical actions, thereby reducing context length and enhancing planning efficiency for long-term tasks. We train the LightPlanner-1.5B model on our LightPlan-40k dataset, which comprises 40,000 action controls across tasks with 2 to 13 action steps. Experiments demonstrate that our model achieves the highest task success rate despite having the smallest number of parameters. In tasks involving spatial semantic reasoning, the success rate exceeds that of ReAct by 14.9 percent. Moreover, we demonstrate LightPlanner's potential to operate on edge devices.

We describe a mobile manipulation hardware and software system capable of autonomously performing complex human-level tasks in real homes, after being taught the task with a single demonstration from a person in virtual reality. This is enabled by a highly capable mobile manipulation robot, whole-body task space hybrid position/force control, teaching of parameterized primitives linked to a robust learned dense visual embeddings representation of the scene, and a task graph of the taught behaviors. We demonstrate the robustness of the approach by presenting results for performing a variety of tasks, under different environmental conditions, in multiple real homes. Our approach achieves 85% overall success rate on three tasks that consist of an average of 45 behaviors each.

Generative Adversarial Imitation Learning (GAIL) is a powerful and practical approach for learning sequential decision-making policies. Different from Reinforcement Learning (RL), GAIL takes advantage of demonstration data by experts (e.g., human), and learns both the policy and reward function of the unknown environment. Despite the significant empirical progresses, the theory behind GAIL is still largely unknown. The major difficulty comes from the underlying temporal dependency of the demonstration data and the minimax computational formulation of GAIL without convex-concave structure. To bridge such a gap between theory and practice, this paper investigates the theoretical properties of GAIL. Specifically, we show: (1) For GAIL with general reward parameterization, the generalization can be guaranteed as long as the class of the reward functions is properly controlled; (2) For GAIL, where the reward is parameterized as a reproducing kernel function, GAIL can be efficiently solved by stochastic first order optimization algorithms, which attain sublinear convergence to a stationary solution. To the best of our knowledge, these are the first results on statistical and computational guarantees of imitation learning with reward/policy function approximation. Numerical experiments are provided to support our analysis.

Large language models (LLMs) trained on code completion have been shown to be capable of synthesizing simple Python programs from docstrings [1]. We find that these code-writing LLMs can be re-purposed to write robot policy code, given natural language commands. Specifically, policy code can express functions or feedback loops that process perception outputs (e.g.,from object detectors [2], [3]) and parameterize control primitive APIs. When provided as input several example language commands (formatted as comments) followed by corresponding policy code (via few-shot prompting), LLMs can take in new commands and autonomously re-compose API calls to generate new policy code respectively. By chaining classic logic structures and referencing third-party libraries (e.g., NumPy, Shapely) to perform arithmetic, LLMs used in this way can write robot policies that (i) exhibit spatial-geometric reasoning, (ii) generalize to new instructions, and (iii) prescribe precise values (e.g., velocities) to ambiguous descriptions ("faster") depending on context (i.e., behavioral commonsense). This paper presents code as policies: a robot-centric formulation of language model generated programs (LMPs) that can represent reactive policies (e.g., impedance controllers), as well as waypoint-based policies (vision-based pick and place, trajectory-based control), demonstrated across multiple real robot platforms. Central to our approach is prompting hierarchical code-gen (recursively defining undefined functions), which can write more complex code and also improves state-of-the-art to solve 39.8% of problems on the HumanEval [1] benchmark. Code and videos are available at https://code-as-policies.github.io

Both biological and artificial neural networks inherently balance their performance with their operational cost, which balances their computational abilities. Typically, an efficient neuromorphic neural network is one that learns representations that reduce the redundancies and dimensionality of its input. This is for instance achieved in sparse coding, and sparse representations derived from natural images yield representations that are heterogeneous, both in their sampling of input features and in the variance of those features. Here, we investigated the connection between natural images' structure, particularly oriented features, and their corresponding sparse codes. We showed that representations of input features scattered across multiple levels of variance substantially improve the sparseness and resilience of sparse codes, at the cost of reconstruction performance. This echoes the structure of the model's input, allowing to account for the heterogeneously aleatoric structures of natural images. We demonstrate that learning kernel from natural images produces heterogeneity by balancing between approximate and dense representations, which improves all reconstruction metrics. Using a parametrized control of the kernels' heterogeneity used by a convolutional sparse coding algorithm, we show that heterogeneity emphasizes sparseness, while homogeneity improves representation granularity. In a broader context, these encoding strategy can serve as inputs to deep convolutional neural networks. We prove that such variance-encoded sparse image datasets enhance computational efficiency, emphasizing the benefits of kernel heterogeneity to leverage naturalistic and variant input structures and possible applications to improve the throughput of neuromorphic hardware.

People employ expressive behaviors to effectively communicate and coordinate their actions with others, such as nodding to acknowledge a person glancing at them or saying "excuse me" to pass people in a busy corridor. We would like robots to also demonstrate expressive behaviors in human-robot interaction. Prior work proposes rule-based methods that struggle to scale to new communication modalities or social situations, while data-driven methods require specialized datasets for each social situation the robot is used in. We propose to leverage the rich social context available from large language models (LLMs) and their ability to generate motion based on instructions or user preferences, to generate expressive robot motion that is adaptable and composable, building upon each other. Our approach utilizes few-shot chain-of-thought prompting to translate human language instructions into parametrized control code using the robot's available and learned skills. Through user studies and simulation experiments, we demonstrate that our approach produces behaviors that users found to be competent and easy to understand. Supplementary material can be found at https://generative-expressive-motion.github.io/.

In open-ended continuous environments, robots need to learn multiple parameterised control tasks in hierarchical reinforcement learning. We hypothesise that the most complex tasks can be learned more easily by transferring knowledge from simpler tasks, and faster by adapting the complexity of the actions to the task. We propose a task-oriented representation of complex actions, called procedures, to learn online task relationships and unbounded sequences of action primitives to control the different observables of the environment. Combining both goal-babbling with imitation learning, and active learning with transfer of knowledge based on intrinsic motivation, our algorithm self-organises its learning process. It chooses at any given time a task to focus on; and what, how, when and from whom to transfer knowledge. We show with a simulation and a real industrial robot arm, in cross-task and cross-learner transfer settings, that task composition is key to tackle highly complex tasks. Task decomposition is also efficiently transferred across different embodied learners and by active imitation, where the robot requests just a small amount of demonstrations and the adequate type of information. The robot learns and exploits task dependencies so as to learn tasks of every complexity.

We propose a novel parameterized skill-learning algorithm that aims to learn transferable parameterized skills and synthesize them into a new action space that supports efficient learning in long-horizon tasks. We propose to leverage off-policy Meta-RL combined with a trajectory-centric smoothness term to learn a set of parameterized skills. Our agent can use these learned skills to construct a three-level hierarchical framework that models a Temporally-extended Parameterized Action Markov Decision Process. We empirically demonstrate that the proposed algorithms enable an agent to solve a set of difficult long-horizon (obstacle-course and robot manipulation) tasks.

Sequential learning paradigms pose challenges for gradient-based deep learning due to difficulties incorporating new data and retaining prior knowledge. While Gaussian processes elegantly tackle these problems, they struggle with scalability and handling rich inputs, such as images. To address these issues, we introduce a technique that converts neural networks from weight space to function space, through a dual parameterization. Our parameterization offers: (i) a way to scale function-space methods to large data sets via sparsification, (ii) retention of prior knowledge when access to past data is limited, and (iii) a mechanism to incorporate new data without retraining. Our experiments demonstrate that we can retain knowledge in continual learning and incorporate new data efficiently. We further show its strengths in uncertainty quantification and guiding exploration in model-based RL. Further information and code is available on the project website.

Synthesizing optimal controllers for dynamical systems often involves solving optimization problems with hard real-time constraints. These constraints determine the class of numerical methods that can be applied: computationally expensive but accurate numerical routines are replaced by fast and inaccurate methods, trading inference time for solution accuracy. This paper provides techniques to improve the quality of optimized control policies given a fixed computational budget. We achieve the above via a hypersolvers approach, which hybridizes a differential equation solver and a neural network. The performance is evaluated in direct and receding-horizon optimal control tasks in both low and high dimensions, where the proposed approach shows consistent Pareto improvements in solution accuracy and control performance.

This paper introduces a new parameterization of deep neural networks (both fully-connected and convolutional) with guaranteed ell^2 Lipschitz bounds, i.e. limited sensitivity to input perturbations. The Lipschitz guarantees are equivalent to the tightest-known bounds based on certification via a semidefinite program (SDP). We provide a ``direct'' parameterization, i.e., a smooth mapping from mathbb R^N onto the set of weights satisfying the SDP-based bound. Moreover, our parameterization is complete, i.e. a neural network satisfies the SDP bound if and only if it can be represented via our parameterization. This enables training using standard gradient methods, without any inner approximation or computationally intensive tasks (e.g. projections or barrier terms) for the SDP constraint. The new parameterization can equivalently be thought of as either a new layer type (the sandwich layer), or a novel parameterization of standard feedforward networks with parameter sharing between neighbouring layers. A comprehensive set of experiments on image classification shows that sandwich layers outperform previous approaches on both empirical and certified robust accuracy. Code is available at https://github.com/acfr/LBDN.

Even for known nonlinear dynamical systems, feedback controller synthesis is a difficult problem that often requires leveraging the particular structure of the dynamics to induce a stable closed-loop system. For general nonlinear models, including those fit to data, there may not be enough known structure to reliably synthesize a stabilizing feedback controller. In this paper, we discuss a state-dependent nonlinear tracking controller formulation based on a state-dependent Riccati equation for general nonlinear control-affine systems. This formulation depends on a nonlinear factorization of the system of vector fields defining the control-affine dynamics, which always exists under mild smoothness assumptions. We propose a method for learning this factorization from a finite set of data. On a variety of simulated nonlinear dynamical systems, we empirically demonstrate the efficacy of learned versions of this controller in stable trajectory tracking. Alongside our learning method, we evaluate recent ideas in jointly learning a controller and stabilizability certificate for known dynamical systems; we show experimentally that such methods can be frail in comparison.

The cost of hyperparameter tuning in deep learning has been rising with model sizes, prompting practitioners to find new tuning methods using a proxy of smaller networks. One such proposal uses muP parameterized networks, where the optimal hyperparameters for small width networks transfer to networks with arbitrarily large width. However, in this scheme, hyperparameters do not transfer across depths. As a remedy, we study residual networks with a residual branch scale of 1/text{depth} in combination with the muP parameterization. We provide experiments demonstrating that residual architectures including convolutional ResNets and Vision Transformers trained with this parameterization exhibit transfer of optimal hyperparameters across width and depth on CIFAR-10 and ImageNet. Furthermore, our empirical findings are supported and motivated by theory. Using recent developments in the dynamical mean field theory (DMFT) description of neural network learning dynamics, we show that this parameterization of ResNets admits a well-defined feature learning joint infinite-width and infinite-depth limit and show convergence of finite-size network dynamics towards this limit.

We consider funnel control for linear infinite-dimensional systems that are impedance passive, meaning that they satisfy an energy balance in which the stored energy equals the squared norm of the state and the supplied power is the inner product of input and output. For the analysis we employ the system node approach, which offers a unified framework for infinite-dimensional systems with boundary and distributed control and observation. The resulting closed-loop dynamics are governed by a nonlinear evolution equation; we establish its solvability and hence the applicability of funnel control to this class. The applicability is illustrated by an Euler-Bernoulli beam, which is studied in two distinct scenarios: once with boundary control and once with distributed control.

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.

A common pipeline in learning-based control is to iteratively estimate a model of system dynamics, and apply a trajectory optimization algorithm - e.g.~iLQR - on the learned model to minimize a target cost. This paper conducts a rigorous analysis of a simplified variant of this strategy for general nonlinear systems. We analyze an algorithm which iterates between estimating local linear models of nonlinear system dynamics and performing iLQR-like policy updates. We demonstrate that this algorithm attains sample complexity polynomial in relevant problem parameters, and, by synthesizing locally stabilizing gains, overcomes exponential dependence in problem horizon. Experimental results validate the performance of our algorithm, and compare to natural deep-learning baselines.

We investigate model predictive control (MPC) formulations for linear systems subject to i.i.d. stochastic disturbances with bounded support and chance constraints. Existing stochastic MPC formulations with closed-loop guarantees can be broadly classified in two separate frameworks: i) using robust techniques; ii) feasibility preserving algorithms. We investigate two particular MPC formulations representative for these two frameworks called robust-stochastic MPC and indirect feedback stochastic MPC. We provide a qualitative analysis, highlighting intrinsic limitations of both approaches in different edge cases. Then, we derive a unifying stochastic MPC framework that naturally includes these two formulations as limit cases. This qualitative analysis is complemented with numerical results, showcasing the advantages and limitations of each method.

Numerical simulations in climate, chemistry, or astrophysics are computationally too expensive for uncertainty quantification or parameter-exploration at high-resolution. Reduced-order or surrogate models are multiple orders of magnitude faster, but traditional surrogates are inflexible or inaccurate and pure machine learning (ML)-based surrogates too data-hungry. We propose a hybrid, flexible surrogate model that exploits known physics for simulating large-scale dynamics and limits learning to the hard-to-model term, which is called parametrization or closure and captures the effect of fine- onto large-scale dynamics. Leveraging neural operators, we are the first to learn grid-independent, non-local, and flexible parametrizations. Our multiscale neural operator is motivated by a rich literature in multiscale modeling, has quasilinear runtime complexity, is more accurate or flexible than state-of-the-art parametrizations and demonstrated on the chaotic equation multiscale Lorenz96.

While recent AI-for-math has made strides in pure mathematics, areas of applied mathematics, particularly PDEs, remain underexplored despite their significant real-world applications. We present PDE-Controller, a framework that enables large language models (LLMs) to control systems governed by partial differential equations (PDEs). Our approach enables LLMs to transform informal natural language instructions into formal specifications, and then execute reasoning and planning steps to improve the utility of PDE control. We build a holistic solution comprising datasets (both human-written cases and 2 million synthetic samples), math-reasoning models, and novel evaluation metrics, all of which require significant effort. Our PDE-Controller significantly outperforms prompting the latest open-source and GPT models in reasoning, autoformalization, and program synthesis, achieving up to a 62% improvement in utility gain for PDE control. By bridging the gap between language generation and PDE systems, we demonstrate the potential of LLMs in addressing complex scientific and engineering challenges. We will release all data, model checkpoints, and code at https://pde-controller.github.io/.

Control variates are variance reduction tools for Monte Carlo estimators. They can provide significant variance reduction, but usually require a large number of samples, which can be prohibitive when sampling or evaluating the integrand is computationally expensive. Furthermore, there are many scenarios where we need to compute multiple related integrals simultaneously or sequentially, which can further exacerbate computational costs. In this paper, we propose vector-valued control variates, an extension of control variates which can be used to reduce the variance of multiple Monte Carlo estimators jointly. This allows for the transfer of information across integration tasks, and hence reduces the need for a large number of samples. We focus on control variates based on kernel interpolants and our novel construction is obtained through a generalised Stein identity and the development of novel matrix-valued Stein reproducing kernels. We demonstrate our methodology on a range of problems including multifidelity modelling, Bayesian inference for dynamical systems, and model evidence computation through thermodynamic integration.

In this work, we consider the problem of deriving and incorporating accurate dynamic models for model predictive control (MPC) with an application to quadrotor control. MPC relies on precise dynamic models to achieve the desired closed-loop performance. However, the presence of uncertainties in complex systems and the environments they operate in poses a challenge in obtaining sufficiently accurate representations of the system dynamics. In this work, we make use of a deep learning tool, knowledge-based neural ordinary differential equations (KNODE), to augment a model obtained from first principles. The resulting hybrid model encompasses both a nominal first-principle model and a neural network learnt from simulated or real-world experimental data. Using a quadrotor, we benchmark our hybrid model against a state-of-the-art Gaussian Process (GP) model and show that the hybrid model provides more accurate predictions of the quadrotor dynamics and is able to generalize beyond the training data. To improve closed-loop performance, the hybrid model is integrated into a novel MPC framework, known as KNODE-MPC. Results show that the integrated framework achieves 60.2% improvement in simulations and more than 21% in physical experiments, in terms of trajectory tracking performance.

We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a general framework for first-order optimization of these processes, that performs jointly, in a single loop, optimization and sampling steps. This approach is inspired by recent advances in bilevel optimization and automatic implicit differentiation, leveraging the point of view of sampling as optimization over the space of probability distributions. We provide theoretical guarantees on the performance of our method, as well as experimental results demonstrating its effectiveness in real-world settings.

Structural optimization is a popular method for designing objects such as bridge trusses, airplane wings, and optical devices. Unfortunately, the quality of solutions depends heavily on how the problem is parameterized. In this paper, we propose using the implicit bias over functions induced by neural networks to improve the parameterization of structural optimization. Rather than directly optimizing densities on a grid, we instead optimize the parameters of a neural network which outputs those densities. This reparameterization leads to different and often better solutions. On a selection of 116 structural optimization tasks, our approach produces the best design 50% more often than the best baseline method.

Policy optimization methods are powerful algorithms in Reinforcement Learning (RL) for their flexibility to deal with policy parameterization and ability to handle model misspecification. However, these methods usually suffer from slow convergence rates and poor sample complexity. Hence it is important to design provably sample efficient algorithms for policy optimization. Yet, recent advances for this problems have only been successful in tabular and linear setting, whose benign structures cannot be generalized to non-linearly parameterized policies. In this paper, we address this problem by leveraging recent advances in value-based algorithms, including bounded eluder-dimension and online sensitivity sampling, to design a low-switching sample-efficient policy optimization algorithm, LPO, with general non-linear function approximation. We show that, our algorithm obtains an varepsilon-optimal policy with only O(text{poly(d)}{varepsilon^3}) samples, where varepsilon is the suboptimality gap and d is a complexity measure of the function class approximating the policy. This drastically improves previously best-known sample bound for policy optimization algorithms, O(text{poly(d)}{varepsilon^8}). Moreover, we empirically test our theory with deep neural nets to show the benefits of the theoretical inspiration.

Existing methods for optimal control struggle to deal with the complexity commonly encountered in real-world systems, including dimensionality, process error, model bias and data heterogeneity. Instead of tackling these system complexities directly, researchers have typically sought to simplify models to fit optimal control methods. But when is the optimal solution to an approximate, stylized model better than an approximate solution to a more accurate model? While this question has largely gone unanswered owing to the difficulty of finding even approximate solutions for complex models, recent algorithmic and computational advances in deep reinforcement learning (DRL) might finally allow us to address these questions. DRL methods have to date been applied primarily in the context of games or robotic mechanics, which operate under precisely known rules. Here, we demonstrate the ability for DRL algorithms using deep neural networks to successfully approximate solutions (the "policy function" or control rule) in a non-linear three-variable model for a fishery without knowing or ever attempting to infer a model for the process itself. We find that the reinforcement learning agent discovers an effective simplification of the problem to obtain an interpretable control rule. We show that the policy obtained with DRL is both more profitable and more sustainable than any constant mortality policy -- the standard family of policies considered in fishery management.

Model-based reinforcement learning is a powerful tool, but collecting data to fit an accurate model of the system can be costly. Exploring an unknown environment in a sample-efficient manner is hence of great importance. However, the complexity of dynamics and the computational limitations of real systems make this task challenging. In this work, we introduce FLEX, an exploration algorithm for nonlinear dynamics based on optimal experimental design. Our policy maximizes the information of the next step and results in an adaptive exploration algorithm, compatible with generic parametric learning models and requiring minimal resources. We test our method on a number of nonlinear environments covering different settings, including time-varying dynamics. Keeping in mind that exploration is intended to serve an exploitation objective, we also test our algorithm on downstream model-based classical control tasks and compare it to other state-of-the-art model-based and model-free approaches. The performance achieved by FLEX is competitive and its computational cost is low.

The performance of an algorithm often critically depends on its parameter configuration. While a variety of automated algorithm configuration methods have been proposed to relieve users from the tedious and error-prone task of manually tuning parameters, there is still a lot of untapped potential as the learned configuration is static, i.e., parameter settings remain fixed throughout the run. However, it has been shown that some algorithm parameters are best adjusted dynamically during execution, e.g., to adapt to the current part of the optimization landscape. Thus far, this is most commonly achieved through hand-crafted heuristics. A promising recent alternative is to automatically learn such dynamic parameter adaptation policies from data. In this article, we give the first comprehensive account of this new field of automated dynamic algorithm configuration (DAC), present a series of recent advances, and provide a solid foundation for future research in this field. Specifically, we (i) situate DAC in the broader historical context of AI research; (ii) formalize DAC as a computational problem; (iii) identify the methods used in prior-art to tackle this problem; (iv) conduct empirical case studies for using DAC in evolutionary optimization, AI planning, and machine learning.

Second-order optimization has been developed to accelerate the training of deep neural networks and it is being applied to increasingly larger-scale models. In this study, towards training on further larger scales, we identify a specific parameterization for second-order optimization that promotes feature learning in a stable manner even if the network width increases significantly. Inspired by a maximal update parameterization, we consider a one-step update of the gradient and reveal the appropriate scales of hyperparameters including random initialization, learning rates, and damping terms. Our approach covers two major second-order optimization algorithms, K-FAC and Shampoo, and we demonstrate that our parameterization achieves higher generalization performance in feature learning. In particular, it enables us to transfer the hyperparameters across models with different widths.

Ensuring safety is of paramount importance in physical human-robot interaction applications. This requires both adherence to safety constraints defined on the system state, as well as guaranteeing compliant behavior of the robot. If the underlying dynamical system is known exactly, the former can be addressed with the help of control barrier functions. The incorporation of elastic actuators in the robot's mechanical design can address the latter requirement. However, this elasticity can increase the complexity of the resulting system, leading to unmodeled dynamics, such that control barrier functions cannot directly ensure safety. In this paper, we mitigate this issue by learning the unknown dynamics using Gaussian process regression. By employing the model in a feedback linearizing control law, the safety conditions resulting from control barrier functions can be robustified to take into account model errors, while remaining feasible. In order to enforce them on-line, we formulate the derived safety conditions in the form of a second-order cone program. We demonstrate our proposed approach with simulations on a two-degree-of-freedom planar robot with elastic joints.

Robust and effective scaling of models from small to large width typically requires the precise adjustment of many algorithmic and architectural details, such as parameterization and optimizer choices. In this work, we propose a new perspective on parameterization by investigating a key assumption in prior work about the alignment between parameters and data and derive new theoretical results under weaker assumptions and a broader set of optimizers. Our extensive empirical investigation includes tens of thousands of models trained with all combinations of three optimizers, four parameterizations, several alignment assumptions, more than a dozen learning rates, and fourteen model sizes up to 26.8B parameters. We find that the best learning rate scaling prescription would often have been excluded by the assumptions in prior work. Our results show that all parameterizations, not just maximal update parameterization (muP), can achieve hyperparameter transfer; moreover, our novel per-layer learning rate prescription for standard parameterization outperforms muP. Finally, we demonstrate that an overlooked aspect of parameterization, the epsilon parameter in Adam, must be scaled correctly to avoid gradient underflow and propose Adam-atan2, a new numerically stable, scale-invariant version of Adam that eliminates the epsilon hyperparameter entirely.

The technique of data augmentation (DA) is often used in machine learning for regularization purposes to better generalize under i.i.d. settings. In this work, we present a unifying framework with topics in causal inference to make a case for the use of DA beyond just the i.i.d. setting, but for generalization across interventions as well. Specifically, we argue that when the outcome generating mechanism is invariant to our choice of DA, then such augmentations can effectively be thought of as interventions on the treatment generating mechanism itself. This can potentially help to reduce bias in causal effect estimation arising from hidden confounders. In the presence of such unobserved confounding we typically make use of instrumental variables (IVs) -- sources of treatment randomization that are conditionally independent of the outcome. However, IVs may not be as readily available as DA for many applications, which is the main motivation behind this work. By appropriately regularizing IV based estimators, we introduce the concept of IV-like (IVL) regression for mitigating confounding bias and improving predictive performance across interventions even when certain IV properties are relaxed. Finally, we cast parameterized DA as an IVL regression problem and show that when used in composition can simulate a worst-case application of such DA, further improving performance on causal estimation and generalization tasks beyond what simple DA may offer. This is shown both theoretically for the population case and via simulation experiments for the finite sample case using a simple linear example. We also present real data experiments to support our case.

Straight line equation y=mx with slope m, when singularly perturbed as ay^3+y=mx with a positive parameter a, results in S-shaped curves or S-curves on a real plane. As arightarrow 0, we get back y=mx which is a cumulative distribution function of a continuous uniform distribution that describes the occurrence of every event in an interval to be equally probable. As arightarrowinfty, the derivative of y has finite support only at y=0 resembling a degenerate distribution. Based on these arguments, in this work, we propose that these S-curves can represent maximum entropy uniform distribution to a zero entropy single value. We also argue that these S-curves are superposable as they are only parametrically nonlinear but fundamentally linear. So far, the superposed forms have been used to capture the patterns of natural systems such as nonlinear dynamics of biological growth and kinetics of enzyme reactions. Here, we attempt to use the S-curve and its superposed form as statistical models. We fit the models on a classical dataset containing flower measurements of iris plants and analyze their usefulness in pattern recognition. Based on these models, we claim that any non-uniform pattern can be represented as a singular perturbation to uniform distribution. However, our parametric estimation procedure have some limitations such as sensitivity to initial conditions depending on the data at hand.

This paper investigates the global convergence of stepsized Newton methods for convex functions. We propose several simple stepsize schedules with fast global convergence guarantees, up to O (k^{-3}), nearly matching lower complexity bounds Omega (k^{-3.5}) of second-order methods. For cases with multiple plausible smoothness parameterizations or an unknown smoothness constant, we introduce a stepsize backtracking procedure that ensures convergence as if the optimal smoothness parameters were known.

We tackle the challenge of large-scale network intervention for guiding excitatory point processes, such as infectious disease spread or traffic congestion control. Our model-based reinforcement learning utilizes neural ODEs to capture how the networked excitatory point processes will evolve subject to the time-varying changes in network topology. Our approach incorporates Gradient-Descent based Model Predictive Control (GD-MPC), offering policy flexibility to accommodate prior knowledge and constraints. To address the intricacies of planning and overcome the high dimensionality inherent to such decision-making problems, we design an Amortize Network Interventions (ANI) framework, allowing for the pooling of optimal policies from history and other contexts, while ensuring a permutation equivalent property. This property enables efficient knowledge transfer and sharing across diverse contexts. Our approach has broad applications, from curbing infectious disease spread to reducing carbon emissions through traffic light optimization, and thus has the potential to address critical societal and environmental challenges.

We introduce Diffusion Policy Policy Optimization, DPPO, an algorithmic framework including best practices for fine-tuning diffusion-based policies (e.g. Diffusion Policy) in continuous control and robot learning tasks using the policy gradient (PG) method from reinforcement learning (RL). PG methods are ubiquitous in training RL policies with other policy parameterizations; nevertheless, they had been conjectured to be less efficient for diffusion-based policies. Surprisingly, we show that DPPO achieves the strongest overall performance and efficiency for fine-tuning in common benchmarks compared to other RL methods for diffusion-based policies and also compared to PG fine-tuning of other policy parameterizations. Through experimental investigation, we find that DPPO takes advantage of unique synergies between RL fine-tuning and the diffusion parameterization, leading to structured and on-manifold exploration, stable training, and strong policy robustness. We further demonstrate the strengths of DPPO in a range of realistic settings, including simulated robotic tasks with pixel observations, and via zero-shot deployment of simulation-trained policies on robot hardware in a long-horizon, multi-stage manipulation task. Website with code: diffusion-ppo.github.io

We introduce a novel approach for analyzing the training dynamics of ReLU networks by examining the characteristic activation boundaries of individual ReLU neurons. Our proposed analysis reveals a critical instability in common neural network parameterizations and normalizations during stochastic optimization, which impedes fast convergence and hurts generalization performance. Addressing this, we propose Geometric Parameterization (GmP), a novel neural network parameterization technique that effectively separates the radial and angular components of weights in the hyperspherical coordinate system. We show theoretically that GmP resolves the aforementioned instability issue. We report empirical results on various models and benchmarks to verify GmP's theoretical advantages of optimization stability, convergence speed and generalization performance.

The enduring challenge in the field of artificial intelligence has been the control of systems to achieve desired behaviours. While for systems governed by straightforward dynamics equations, methods like Linear Quadratic Regulation (LQR) have historically proven highly effective, most real-world tasks, which require a general problem-solver, demand world models with dynamics that cannot be easily described by simple equations. Consequently, these models must be learned from data using neural networks. Most model predictive control (MPC) algorithms designed for visual world models have traditionally explored gradient-free population-based optimisation methods, such as Cross Entropy and Model Predictive Path Integral (MPPI) for planning. However, we present an exploration of a gradient-based alternative that fully leverages the differentiability of the world model. In our study, we conduct a comparative analysis between our method and other MPC-based alternatives, as well as policy-based algorithms. In a sample-efficient setting, our method achieves on par or superior performance compared to the alternative approaches in most tasks. Additionally, we introduce a hybrid model that combines policy networks and gradient-based MPC, which outperforms pure policy based methods thereby holding promise for Gradient-based planning with world models in complex real-world tasks.

We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constant memory cost, adapt their evaluation strategy to each input, and can explicitly trade numerical precision for speed. We demonstrate these properties in continuous-depth residual networks and continuous-time latent variable models. We also construct continuous normalizing flows, a generative model that can train by maximum likelihood, without partitioning or ordering the data dimensions. For training, we show how to scalably backpropagate through any ODE solver, without access to its internal operations. This allows end-to-end training of ODEs within larger models.

We consider the reinforcement learning (RL) problem with general utilities which consists in maximizing a function of the state-action occupancy measure. Beyond the standard cumulative reward RL setting, this problem includes as particular cases constrained RL, pure exploration and learning from demonstrations among others. For this problem, we propose a simpler single-loop parameter-free normalized policy gradient algorithm. Implementing a recursive momentum variance reduction mechanism, our algorithm achieves mathcal{O}(epsilon^{-3}) and mathcal{O}(epsilon^{-2}) sample complexities for epsilon-first-order stationarity and epsilon-global optimality respectively, under adequate assumptions. We further address the setting of large finite state action spaces via linear function approximation of the occupancy measure and show a mathcal{O}(epsilon^{-4}) sample complexity for a simple policy gradient method with a linear regression subroutine.

Model Predictive Controllers (MPC) require a good model for the controlled process. In this paper I infer inductive biases about a physical system. I use these biases to derive a new neural network architecture that can model this real system that has noise and inertia. The main inductive biases exploited here are: the delayed impact of some inputs on the system and the separability between the temporal component and how the inputs interact to produce the output of a system. The inputs are independently delayed using shifted convolutional kernels. Feature interactions are modelled using a fully connected network that does not have access to temporal information. The available data and the problem setup allow the usage of Self Supervised Learning in order to train the models. The baseline architecture is an Attention based Reccurent network adapted to work with MPC like inputs. The proposed networks are faster, better at exploiting larger data volumes and are almost as good as baseline networks in terms of prediction performance. The proposed architecture family called Delay can be used in a real scenario to control systems with delayed responses with respect to its controls or inputs. Ablation studies show that the presence of delay kernels are vital to obtain any learning in proposed architecture. Code and some experimental data are available online.

Ever since the original algorithm by Nesterov (1983), the true nature of the acceleration phenomenon has remained elusive, with various interpretations of why the method is actually faster. The diagnosis of the algorithm through the lens of Ordinary Differential Equations (ODEs) and the corresponding dynamical system formulation to explain the underlying dynamics has a rich history. In the literature, the ODEs that explain algorithms are typically derived by considering the limiting case of the algorithm maps themselves, that is, an ODE formulation follows the development of an algorithm. This obfuscates the underlying higher order principles and thus provides little evidence of the working of the algorithm. Such has been the case with Nesterov algorithm and the various analogies used to describe the acceleration phenomena, viz, momentum associated with the rolling of a Heavy-Ball down a slope, Hessian damping etc. The main focus of our work is to ideate the genesis of the Nesterov algorithm from the viewpoint of dynamical systems leading to demystifying the mathematical rigour behind the algorithm. Instead of reverse engineering ODEs from discrete algorithms, this work explores tools from the recently developed control paradigm titled Passivity and Immersion approach and the Geometric Singular Perturbation theory which are applied to arrive at the formulation of a dynamical system that explains and models the acceleration phenomena. This perspective helps to gain insights into the various terms present and the sequence of steps used in Nesterovs accelerated algorithm for the smooth strongly convex and the convex case. The framework can also be extended to derive the acceleration achieved using the triple momentum method and provides justifications for the non-convergence to the optimal solution in the Heavy-Ball method.

Model-free control strategies such as reinforcement learning have shown the ability to learn control strategies without requiring an accurate model or simulator of the world. While this is appealing due to the lack of modeling requirements, such methods can be sample inefficient, making them impractical in many real-world domains. On the other hand, model-based control techniques leveraging accurate simulators can circumvent these challenges and use a large amount of cheap simulation data to learn controllers that can effectively transfer to the real world. The challenge with such model-based techniques is the requirement for an extremely accurate simulation, requiring both the specification of appropriate simulation assets and physical parameters. This requires considerable human effort to design for every environment being considered. In this work, we propose a learning system that can leverage a small amount of real-world data to autonomously refine a simulation model and then plan an accurate control strategy that can be deployed in the real world. Our approach critically relies on utilizing an initial (possibly inaccurate) simulator to design effective exploration policies that, when deployed in the real world, collect high-quality data. We demonstrate the efficacy of this paradigm in identifying articulation, mass, and other physical parameters in several challenging robotic manipulation tasks, and illustrate that only a small amount of real-world data can allow for effective sim-to-real transfer. Project website at https://weirdlabuw.github.io/asid

In this paper, a safe and learning-based control framework for model predictive control (MPC) is proposed to optimize nonlinear systems with a non-differentiable objective function under uncertain environmental disturbances. The control framework integrates a learning-based MPC with an auxiliary controller in a way of minimal intervention. The learning-based MPC augments the prior nominal model with incremental Gaussian Processes to learn the uncertain disturbances. The cross-entropy method (CEM) is utilized as the sampling-based optimizer for the MPC with a non-differentiable objective function. A minimal intervention controller is devised with a control Lyapunov function and a control barrier function to guide the sampling process and endow the system with high probabilistic safety. The proposed algorithm shows a safe and adaptive control performance on a simulated quadrotor in the tasks of trajectory tracking and obstacle avoidance under uncertain wind disturbances.

This work explores the in-context learning capabilities of State Space Models (SSMs) and presents, to the best of our knowledge, the first theoretical explanation of a possible underlying mechanism. We introduce a novel weight construction for SSMs, enabling them to predict the next state of any dynamical system after observing previous states without parameter fine-tuning. This is accomplished by extending the HiPPO framework to demonstrate that continuous SSMs can approximate the derivative of any input signal. Specifically, we find an explicit weight construction for continuous SSMs and provide an asymptotic error bound on the derivative approximation. The discretization of this continuous SSM subsequently yields a discrete SSM that predicts the next state. Finally, we demonstrate the effectiveness of our parameterization empirically. This work should be an initial step toward understanding how sequence models based on SSMs learn in context.

It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal is to recover a low-rank ground-truth matrix from near-isotropic linear measurements. It is shown that GD with small initialization behaves similarly to the greedy low-rank learning heuristics (Li et al., 2020) and follows an incremental learning procedure (Gissin et al., 2019): GD sequentially learns solutions with increasing ranks until it recovers the ground truth matrix. Compared to existing works which only analyze the first learning phase for rank-1 solutions, our result provides characterizations for the whole learning process. Moreover, besides the over-parameterized regime that many prior works focused on, our analysis of the incremental learning procedure also applies to the under-parameterized regime. Finally, we conduct numerical experiments to confirm our theoretical findings.

The objective of personalized medicine is to tailor interventions to an individual patient's unique characteristics. A key technology for this purpose involves medical digital twins, computational models of human biology that can be personalized and dynamically updated to incorporate patient-specific data collected over time. Certain aspects of human biology, such as the immune system, are not easily captured with physics-based models, such as differential equations. Instead, they are often multi-scale, stochastic, and hybrid. This poses a challenge to existing model-based control and optimization approaches that cannot be readily applied to such models. Recent advances in automatic differentiation and neural-network control methods hold promise in addressing complex control problems. However, the application of these approaches to biomedical systems is still in its early stages. This work introduces dynamics-informed neural-network controllers as an alternative approach to control of medical digital twins. As a first use case for this method, the focus is on agent-based models, a versatile and increasingly common modeling platform in biomedicine. The effectiveness of the proposed neural-network control method is illustrated and benchmarked against other methods with two widely-used agent-based model types. The relevance of the method introduced here extends beyond medical digital twins to other complex dynamical systems.

Automatic analysis of the enormous sets of images is a critical task in life sciences. This faces many challenges such as: algorithms are highly parameterized, significant human input is intertwined, and lacking a standard meta-visualization approach. This paper proposes an alternative iterative approach for optimizing input parameters, saving time by minimizing the user involvement, and allowing for understanding the workflow of algorithms and discovering new ones. The main focus is on developing an interactive visualization technique that enables users to analyze the relationships between sampled input parameters and corresponding output. This technique is implemented as a prototype called Veni Vidi Vici, or "I came, I saw, I conquered." This strategy is inspired by the mathematical formulas of numbering computable functions and is developed atop ImageJ, a scientific image processing program. A case study is presented to investigate the proposed framework. Finally, the paper explores some potential future issues in the application of the proposed approach in parameter space analysis in visualization.

Generative methods for 3D assets have recently achieved remarkable progress, yet providing intuitive and precise control over the object geometry remains a key challenge. Existing approaches predominantly rely on text or image prompts, which often fall short in geometric specificity: language can be ambiguous, and images are cumbersome to edit. In this work, we introduce SpaceControl, a training-free test-time method for explicit spatial control of 3D generation. Our approach accepts a wide range of geometric inputs, from coarse primitives to detailed meshes, and integrates seamlessly with modern pre-trained generative models without requiring any additional training. A controllable parameter lets users trade off between geometric fidelity and output realism. Extensive quantitative evaluation and user studies demonstrate that SpaceControl outperforms both training-based and optimization-based baselines in geometric faithfulness while preserving high visual quality. Finally, we present an interactive user interface that enables online editing of superquadrics for direct conversion into textured 3D assets, facilitating practical deployment in creative workflows. Find our project page at https://spacecontrol3d.github.io/

This paper presents a concrete and a symbolic rewriting logic semantics for parametric time Petri nets with inhibitor arcs (PITPNs), a flexible model of timed systems where parameters are allowed in firing bounds. We prove that our semantics is bisimilar to the "standard" semantics of PITPNs. This allows us to use the rewriting logic tool Maude, combined with SMT solving, to provide sound and complete formal analyses for PITPNs. We develop and implement a new general folding approach for symbolic reachability, so that Maude-with-SMT reachability analysis terminates whenever the parametric state-class graph of the PITPN is finite. Our work opens up the possibility of using the many formal analysis capabilities of Maude -- including full LTL model checking, analysis with user-defined analysis strategies, and even statistical model checking -- for such nets. We illustrate this by explaining how almost all formal analysis and parameter synthesis methods supported by the state-of-the-art PITPN tool Romeo can be performed using Maude with SMT. In addition, we also support analysis and parameter synthesis from parametric initial markings, as well as full LTL model checking and analysis with user-defined execution strategies. Experiments show that our methods outperform Romeo in many cases.

We address the computational challenges of solving parametric PDEs with non parametrized geometric variations and non-reducible problems, such as those involving shocks and discontinuities of variable positions. Traditional dimensionality reduction methods like POD struggle with these scenarios due to slowly decaying Kolmogorov widths. To overcome this, we propose a novel non-linear dimensionality reduction technique to reduce the required modes for representation. The non-linear reduction is obtained through a POD after applying a transformation on the fields, which we call optimal mappings, and is a solution to an optimization problem in infinite dimension. The proposed learning framework combines morphing techniques, non-linear dimensionality reduction, and Gaussian Process Regression (GPR). The problem is reformulated on a reference geometry before applying the dimensionality reduction. Our method learns both the optimal mapping, and the solution fields, using a series of GPR models, enabling efficient and accurate modeling of complex parametric PDEs with geometrical variability. The results obtained concur with current state-of-the-art models. We mainly compare our method with the winning solution of the ML4CFD NeurIPS 2024 competition.

In this work, we introduce a single parameter omega, to effectively control granularity in diffusion-based synthesis. This parameter is incorporated during the denoising steps of the diffusion model's reverse process. Our approach does not require model retraining, architectural modifications, or additional computational overhead during inference, yet enables precise control over the level of details in the generated outputs. Moreover, spatial masks or denoising schedules with varying omega values can be applied to achieve region-specific or timestep-specific granularity control. Prior knowledge of image composition from control signals or reference images further facilitates the creation of precise omega masks for granularity control on specific objects. To highlight the parameter's role in controlling subtle detail variations, the technique is named Omegance, combining "omega" and "nuance". Our method demonstrates impressive performance across various image and video synthesis tasks and is adaptable to advanced diffusion models. The code is available at https://github.com/itsmag11/Omegance.

Empirical scaling laws prescribe how to allocate parameters, data, and compute, while maximal-update parameterization (muP) enables learning-rate transfer across widths by equalizing early-time update magnitudes. However, in modern scale-invariant architectures, training quickly enters an optimizer-governed steady state where normalization layers create backward scale sensitivity and the effective learning rate becomes width dependent, degrading muP transfer. We address this by introducing a weight-decay scaling rule for AdamW that preserves sublayer gain across widths. Empirically, the singular-value spectrum of each matrix parameter scales in norm as eta/lambda with an approximately invariant shape; under width scaling d, we observe that the top singular value scales approximately as eta/lambdacdot d^{0.75}. Combining this observation with the muP learning-rate rule eta_2propto d^{-1} for matrix-like parameters implies an empirical weight-decay scaling rule lambda_2propto d that approximately keeps sublayer gains width invariant. Together with vector-like parameters trained at eta_1=Theta_d(1) and lambda_1=0, this yields zero-shot transfer of both learning rate and weight decay from proxy to target widths, removing per-width sweeps. We validate the rule on LLaMA-style Transformers and in a minimal synthetic setting, and we provide a simple diagnostic, matching top singular values, to check sublayer-gain invariance. Our results extend muP beyond the near-init regime by explicitly controlling steady-state scales set by the optimizer, offering a practical recipe for width-robust hyperparameter transfer under AdamW.

We study compute efficiency of LLM training when using different parameterizations, i.e., rules for adjusting model and optimizer hyperparameters (HPs) as model size changes. Some parameterizations fail to transfer optimal base HPs (such as learning rate) across changes in model depth, requiring practitioners to either re-tune these HPs as they scale up (expensive), or accept sub-optimal training when re-tuning is prohibitive. Even when they achieve HP transfer, we develop theory to show parameterizations may still exist in the lazy learning regime where layers learn only features close to their linearization, preventing effective use of depth and nonlinearity. Finally, we identify and adopt the parameterization we call CompleteP that achieves both depth-wise HP transfer and non-lazy learning in all layers. CompleteP enables a wider range of model width/depth ratios to remain compute-efficient, unlocking shapes better suited for different hardware settings and operational contexts. Moreover, CompleteP enables 12-34% compute efficiency improvements over the prior state-of-the-art.

In this paper we provide a new method to certify that a nearby polynomial system has a singular isolated root with a prescribed multiplicity structure. More precisely, given a polynomial system f =(f_1, ldots, f_N)in C[x_1, ldots, x_n]^N, we present a Newton iteration on an extended deflated system that locally converges, under regularity conditions, to a small deformation of f such that this deformed system has an exact singular root. The iteration simultaneously converges to the coordinates of the singular root and the coefficients of the so called inverse system that describes the multiplicity structure at the root. We use $alpha$-theory test to certify the quadratic convergence, and togive bounds on the size of the deformation and on the approximation error. The approach relies on an analysis of the punctual Hilbert scheme, for which we provide a new description. We show in particular that some of its strata can be rationally parametrized and exploit these parametrizations in the certification. We show in numerical experimentation how the approximate inverse system can be computed as a starting point of the Newton iterations and the fast numerical convergence to the singular root with its multiplicity structure, certified by our criteria.

We consider the problem of global optimization with noisy zeroth order oracles - a well-motivated problem useful for various applications ranging from hyper-parameter tuning for deep learning to new material design. Existing work relies on Gaussian processes or other non-parametric family, which suffers from the curse of dimensionality. In this paper, we propose a new algorithm GO-UCB that leverages a parametric family of functions (e.g., neural networks) instead. Under a realizable assumption and a few other mild geometric conditions, we show that GO-UCB achieves a cumulative regret of O(T) where T is the time horizon. At the core of GO-UCB is a carefully designed uncertainty set over parameters based on gradients that allows optimistic exploration. Synthetic and real-world experiments illustrate GO-UCB works better than Bayesian optimization approaches in high dimensional cases, even if the model is misspecified.

We propose iterative inversion -- an algorithm for learning an inverse function without input-output pairs, but only with samples from the desired output distribution and access to the forward function. The key challenge is a distribution shift between the desired outputs and the outputs of an initial random guess, and we prove that iterative inversion can steer the learning correctly, under rather strict conditions on the function. We apply iterative inversion to learn control. Our input is a set of demonstrations of desired behavior, given as video embeddings of trajectories (without actions), and our method iteratively learns to imitate trajectories generated by the current policy, perturbed by random exploration noise. Our approach does not require rewards, and only employs supervised learning, which can be easily scaled to use state-of-the-art trajectory embedding techniques and policy representations. Indeed, with a VQ-VAE embedding, and a transformer-based policy, we demonstrate non-trivial continuous control on several tasks. Further, we report an improved performance on imitating diverse behaviors compared to reward based methods.

This paper reinterprets the Synthetic Control (SC) framework through the lens of weighting philosophy, arguing that the contrast between traditional SC and Difference-in-Differences (DID) reflects two distinct modeling mindsets: sparse versus dense weighting schemes. Rather than viewing sparsity as inherently superior, we treat it as a modeling choice simple but potentially fragile. We propose an L-infinity-regularized SC method that combines the strengths of both approaches. Like DID, it employs a denser weighting scheme that distributes weights more evenly across control units, enhancing robustness and reducing overreliance on a few control units. Like traditional SC, it remains flexible and data-driven, increasing the likelihood of satisfying the parallel trends assumption while preserving interpretability. We develop an interior point algorithm for efficient computation, derive asymptotic theory under weak dependence, and demonstrate strong finite-sample performance through simulations and real-world applications.

Late-lumping feedback design for infinite-dimensional linear systems with unbounded input operators is considered. The proposed scheme is suitable for the approximation of backstepping and flatness-based designs and relies on a decomposition of the feedback into a bounded and an unbounded part. Approximation applies to the bounded part only, while the unbounded part is assumed to allow for an exact realization. Based on spectral results, the convergence of the closed-loop dynamics to the desired dynamics is established. By duality, similar results apply to the approximation of the observer output-injection gains for systems with boundary observation. The proposed design and approximation steps are demonstrated and illustrated based on a hyperbolic infinite-dimensional system.

Large artificial neural networks have become a mainstay of language, vision, and audio processing and synthesis, yet their initializations and learning rates are often set in an unsophisticated fashion, due to the high cost of hyperparameter sweeps at scale. The mu-Parameterization (muP) offers a potential solution to this challenge, yielding scaling rules for model initialization and learning rates while reportedly enabling zero-shot hyperparameter transfer from small to large models. Despite its evident promise, the muP method is not yet widely adopted, perhaps due to higher implementation complexity, many variations, or complex theoretical background. This work investigates muP empirically, focusing on the ubiquitous transformer architecture, and aims to answer a simple question: does mu-Transfer yield optimal learning rates in practice? Studying models of up to 10B parameters and training budgets of up to 190B tokens, we find mu-Transfer works as intended for the majority of important cases, yet also identify a few cases where it may not.

Over the past three decades, numerous controllers have been developed to regulate complex chemical processes, but they have certain limitations. Traditional PI/PID controllers often require customized tuning for various set-point scenarios. On the other hand, MPC frameworks involve resource-intensive steps, and the utilization of black-box machine learning (ML) models can lead to issues such as local minima and infeasibility. Thus, there is a need for an alternative controller paradigm that combines the simplicity of a PI controller with the grade-to-grade (G2G) transferability of an MPC approach. To this end, we developed a novel LSTM controller (LSTMc) as a model-free data-driven controller framework. The LSTMc considers an augmented input tensor that incorporates information on state evolution and error dynamics for the current and previous W time steps, to predict the manipulated input at the next step (u_{t+1}). To demonstrate LSTMc, batch crystallization of dextrose was taken as a representative case study. The desired output for set-point tracking was the mean crystal size (L), with the manipulated input being the jacket temperature (T_j). Extensive training data, encompassing 7000+ different operating conditions, was compiled to ensure comprehensive training of LSTMc across a wide state space region. For comparison, we also designed a PI controller and an LSTM-MPC for different set-point tracking cases. The results consistently showed that LSTMc achieved the lowest set-point deviation (<2\%), three times lower than the MPC. Remarkably, LSTMc maintained this superior performance across all set points, even when sensor measurements contained noise levels of 10\% to 15\%. In summary, by effectively leveraging process data and utilizing sequential ML models, LSTMc offers a superior controller design approach.

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

Continuous control tasks often involve high-dimensional, dynamic, and non-linear environments. State-of-the-art performance in these tasks is achieved through complex closed-box policies that are effective, but suffer from an inherent opacity. Interpretable policies, while generally underperforming compared to their closed-box counterparts, advantageously facilitate transparent decision-making within automated systems. Hence, their usage is often essential for diagnosing and mitigating errors, supporting ethical and legal accountability, and fostering trust among stakeholders. In this paper, we propose SMOSE, a novel method to train sparsely activated interpretable controllers, based on a top-1 Mixture-of-Experts architecture. SMOSE combines a set of interpretable decisionmakers, trained to be experts in different basic skills, and an interpretable router that assigns tasks among the experts. The training is carried out via state-of-the-art Reinforcement Learning algorithms, exploiting load-balancing techniques to ensure fair expert usage. We then distill decision trees from the weights of the router, significantly improving the ease of interpretation. We evaluate SMOSE on six benchmark environments from MuJoCo: our method outperforms recent interpretable baselines and narrows the gap with noninterpretable state-of-the-art algorithms

This paper rigorously shows how over-parameterization changes the convergence behaviors of gradient descent (GD) for the matrix sensing problem, where the goal is to recover an unknown low-rank ground-truth matrix from near-isotropic linear measurements. First, we consider the symmetric setting with the symmetric parameterization where M^* in R^{n times n} is a positive semi-definite unknown matrix of rank r ll n, and one uses a symmetric parameterization XX^top to learn M^*. Here X in R^{n times k} with k > r is the factor matrix. We give a novel Omega (1/T^2) lower bound of randomly initialized GD for the over-parameterized case (k >r) where T is the number of iterations. This is in stark contrast to the exact-parameterization scenario (k=r) where the convergence rate is exp (-Omega (T)). Next, we study asymmetric setting where M^* in R^{n_1 times n_2} is the unknown matrix of rank r ll min{n_1,n_2}, and one uses an asymmetric parameterization FG^top to learn M^* where F in R^{n_1 times k} and G in R^{n_2 times k}. Building on prior work, we give a global exact convergence result of randomly initialized GD for the exact-parameterization case (k=r) with an exp (-Omega(T)) rate. Furthermore, we give the first global exact convergence result for the over-parameterization case (k>r) with an exp(-Omega(alpha^2 T)) rate where alpha is the initialization scale. This linear convergence result in the over-parameterization case is especially significant because one can apply the asymmetric parameterization to the symmetric setting to speed up from Omega (1/T^2) to linear convergence. On the other hand, we propose a novel method that only modifies one step of GD and obtains a convergence rate independent of alpha, recovering the rate in the exact-parameterization case.

We investigate the challenge of parametrizing policies for reinforcement learning (RL) in high-dimensional continuous action spaces. Our objective is to develop a multimodal policy that overcomes limitations inherent in the commonly-used Gaussian parameterization. To achieve this, we propose a principled framework that models the continuous RL policy as a generative model of optimal trajectories. By conditioning the policy on a latent variable, we derive a novel variational bound as the optimization objective, which promotes exploration of the environment. We then present a practical model-based RL method, called Reparameterized Policy Gradient (RPG), which leverages the multimodal policy parameterization and learned world model to achieve strong exploration capabilities and high data efficiency. Empirical results demonstrate that our method can help agents evade local optima in tasks with dense rewards and solve challenging sparse-reward environments by incorporating an object-centric intrinsic reward. Our method consistently outperforms previous approaches across a range of tasks. Code and supplementary materials are available on the project page https://haosulab.github.io/RPG/

Solving time-dependent parametric partial differential equations (PDEs) is challenging, as models must adapt to variations in parameters such as coefficients, forcing terms, and boundary conditions. Data-driven neural solvers either train on data sampled from the PDE parameters distribution in the hope that the model generalizes to new instances or rely on gradient-based adaptation and meta-learning to implicitly encode the dynamics from observations. This often comes with increased inference complexity. Inspired by the in-context learning capabilities of large language models (LLMs), we introduce Zebra, a novel generative auto-regressive transformer designed to solve parametric PDEs without requiring gradient adaptation at inference. By leveraging in-context information during both pre-training and inference, Zebra dynamically adapts to new tasks by conditioning on input sequences that incorporate context trajectories or preceding states. This approach enables Zebra to flexibly handle arbitrarily sized context inputs and supports uncertainty quantification through the sampling of multiple solution trajectories. We evaluate Zebra across a variety of challenging PDE scenarios, demonstrating its adaptability, robustness, and superior performance compared to existing approaches.

We address the problem of finite-horizon control of a discrete-time linear system, where the initial state distribution follows a Gaussian mixture model, the terminal state must follow a specified Gaussian distribution, and the state and control inputs must obey chance constraints. We show that, throughout the time horizon, the state and control distributions are fully characterized by Gaussian mixtures. We then formulate the cost, distributional terminal constraint, and affine/2-norm chance constraints on the state and control, as convex functions of the decision variables. This is leveraged to formulate the chance-constrained path planning problem as a single convex optimization problem. A numerical example demonstrates the effectiveness of the proposed method.

Large language models deliver strong reasoning and tool-use skills, yet their computational demands make them impractical for edge or cost-sensitive deployments. We present Xmodel-2.5, a 1.3-billion-parameter small language model designed as a drop-in agent core. Training with maximal-update parameterization (μP) allows hyper-parameters tuned on a 20M-parameter proxy to transfer directly to the full model, even under the parameter-tied tie-word-embedding architecture. A 1.4T-token Warmup--Stable--Decay curriculum is used, and we further show that switching from AdamW to Muon during the decay phase improves the 13-task reasoning average by 4.58\,\% while keeping every other hyper-parameter fixed, verifying that early AdamW stability can be paired with late Muon sharpening for better downstream performance. FP8-mixed-precision training balances accuracy and throughput. All checkpoints, recipes, and evaluation code are released under the Apache-2.0 license.https://huggingface.co/XiaoduoAILab/Xmodel-2.5 and https://huggingface.co/XiaoduoAILab/Xmodel-2.5-history (training checkpoints). Training code and evaluation harness: https://github.com/XiaoduoAILab/Xmodel-2.5.

We propose a new method to ensure neural ordinary differential equations (ODEs) satisfy output specifications by using invariance set propagation. Our approach uses a class of control barrier functions to transform output specifications into constraints on the parameters and inputs of the learning system. This setup allows us to achieve output specification guarantees simply by changing the constrained parameters/inputs both during training and inference. Moreover, we demonstrate that our invariance set propagation through data-controlled neural ODEs not only maintains generalization performance but also creates an additional degree of robustness by enabling causal manipulation of the system's parameters/inputs. We test our method on a series of representation learning tasks, including modeling physical dynamics and convexity portraits, as well as safe collision avoidance for autonomous vehicles.

In this work, we investigate the data-driven safe control synthesis problem for unknown dynamic systems. We first formulate the safety synthesis problem as a robust convex program (RCP) based on notion of control barrier function. To resolve the issue of unknown system dynamic, we follow the existing approach by converting the RCP to a scenario convex program (SCP) by randomly collecting finite samples of system trajectory. However, to improve the sample efficiency to achieve a desired confidence bound, we provide a new posteriori method with validation tests. Specifically, after collecting a set of data for the SCP, we further collect another set of independent validate data as posterior information to test the obtained solution. We derive a new overall confidence bound for the safety of the controller that connects the original sample data, the support constraints, and the validation data. The efficiency of the proposed approach is illustrated by a case study of room temperature control. We show that, compared with existing methods, the proposed approach can significantly reduce the required number of sample data to achieve a desired confidence bound.

Temporal Difference (TD) algorithms are widely used in Deep Reinforcement Learning (RL). Their performance is heavily influenced by the size of the neural network. While in supervised learning, the regime of over-parameterization and its benefits are well understood, the situation in RL is much less clear. In this paper, we present a theoretical analysis of the influence of network size and l_2-regularization on performance. We identify the ratio between the number of parameters and the number of visited states as a crucial factor and define over-parameterization as the regime when it is larger than one. Furthermore, we observe a double descent phenomenon, i.e., a sudden drop in performance around the parameter/state ratio of one. Leveraging random features and the lazy training regime, we study the regularized Least-Square Temporal Difference (LSTD) algorithm in an asymptotic regime, as both the number of parameters and states go to infinity, maintaining a constant ratio. We derive deterministic limits of both the empirical and the true Mean-Squared Bellman Error (MSBE) that feature correction terms responsible for the double descent. Correction terms vanish when the l_2-regularization is increased or the number of unvisited states goes to zero. Numerical experiments with synthetic and small real-world environments closely match the theoretical predictions.

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.

Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz bound in neural networks has emerged as an essential area of research for enhancing adversarial robustness and network certifiability. This paper uses a rigorous approach to design L-Lipschitz deep residual networks using a Linear Matrix Inequality (LMI) framework. The ResNet architecture was reformulated as a pseudo-tri-diagonal LMI with off-diagonal elements and derived closed-form constraints on network parameters to ensure L-Lipschitz continuity. To address the lack of explicit eigenvalue computations for such matrix structures, the Gershgorin circle theorem was employed to approximate eigenvalue locations, guaranteeing the LMI's negative semi-definiteness. Our contributions include a provable parameterization methodology for constructing Lipschitz-constrained networks and a compositional framework for managing recursive systems within hierarchical architectures. These findings enable robust network designs applicable to adversarial robustness, certified training, and control systems. However, a limitation was identified in the Gershgorin-based approximations, which over-constrain the system, suppressing non-linear dynamics and diminishing the network's expressive capacity.

Integral reinforcement learning (IntRL) demands the precise computation of the utility function's integral at its policy evaluation (PEV) stage. This is achieved through quadrature rules, which are weighted sums of utility functions evaluated from state samples obtained in discrete time. Our research reveals a critical yet underexplored phenomenon: the choice of the computational method -- in this case, the quadrature rule -- can significantly impact control performance. This impact is traced back to the fact that computational errors introduced in the PEV stage can affect the policy iteration's convergence behavior, which in turn affects the learned controller. To elucidate how computation impacts control, we draw a parallel between IntRL's policy iteration and Newton's method applied to the Hamilton-Jacobi-Bellman equation. In this light, computational error in PEV manifests as an extra error term in each iteration of Newton's method, with its upper bound proportional to the computational error. Further, we demonstrate that when the utility function resides in a reproducing kernel Hilbert space (RKHS), the optimal quadrature is achievable by employing Bayesian quadrature with the RKHS-inducing kernel function. We prove that the local convergence rates for IntRL using the trapezoidal rule and Bayesian quadrature with a Mat\'ern kernel to be O(N^{-2}) and O(N^{-b}), where N is the number of evenly-spaced samples and b is the Mat\'ern kernel's smoothness parameter. These theoretical findings are finally validated by two canonical control tasks.

Global climate models typically operate at a grid resolution of hundreds of kilometers and fail to resolve atmospheric mesoscale processes, e.g., clouds, precipitation, and gravity waves (GWs). Model representation of these processes and their sources is essential to the global circulation and planetary energy budget, but subgrid scale contributions from these processes are often only approximately represented in models using parameterizations. These parameterizations are subject to approximations and idealizations, which limit their capability and accuracy. The most drastic of these approximations is the "single-column approximation" which completely neglects the horizontal evolution of these processes, resulting in key biases in current climate models. With a focus on atmospheric GWs, we present the first-ever global simulation of atmospheric GW fluxes using machine learning (ML) models trained on the WINDSET dataset to emulate global GW emulation in the atmosphere, as an alternative to traditional single-column parameterizations. Using an Attention U-Net-based architecture trained on globally resolved GW momentum fluxes, we illustrate the importance and effectiveness of global nonlocality, when simulating GWs using data-driven schemes.

Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks, and (2) the design of good heuristics or approximation algorithms often requires significant manual trial-and-error. In this work, we argue that data-driven strategies can automate this process and learn efficient algorithms without compromising optimality. To do so, we present network control problems through the lens of reinforcement learning and propose a graph network-based framework to handle a broad class of problems. Instead of naively computing actions over high-dimensional graph elements, e.g., edges, we propose a bi-level formulation where we (1) specify a desired next state via RL, and (2) solve a convex program to best achieve it, leading to drastically improved scalability and performance. We further highlight a collection of desirable features to system designers, investigate design decisions, and present experiments on real-world control problems showing the utility, scalability, and flexibility of our framework.

The field of image synthesis has made tremendous strides forward in the last years. Besides defining the desired output image with text-prompts, an intuitive approach is to additionally use spatial guidance in form of an image, such as a depth map. For this, a recent and highly popular approach is to use a controlling network, such as ControlNet, in combination with a pre-trained image generation model, such as Stable Diffusion. When evaluating the design of existing controlling networks, we observe that they all suffer from the same problem of a delay in information flowing between the generation and controlling process. This, in turn, means that the controlling network must have generative capabilities. In this work we propose a new controlling architecture, called ControlNet-XS, which does not suffer from this problem, and hence can focus on the given task of learning to control. In contrast to ControlNet, our model needs only a fraction of parameters, and hence is about twice as fast during inference and training time. Furthermore, the generated images are of higher quality and the control is of higher fidelity. All code and pre-trained models will be made publicly available.

Policy constraint methods to offline reinforcement learning (RL) typically utilize parameterization or regularization that constrains the policy to perform actions within the support set of the behavior policy. The elaborative designs of parameterization methods usually intrude into the policy networks, which may bring extra inference cost and cannot take full advantage of well-established online methods. Regularization methods reduce the divergence between the learned policy and the behavior policy, which may mismatch the inherent density-based definition of support set thereby failing to avoid the out-of-distribution actions effectively. This paper presents Supported Policy OpTimization (SPOT), which is directly derived from the theoretical formalization of the density-based support constraint. SPOT adopts a VAE-based density estimator to explicitly model the support set of behavior policy and presents a simple but effective density-based regularization term, which can be plugged non-intrusively into off-the-shelf off-policy RL algorithms. SPOT achieves the state-of-the-art performance on standard benchmarks for offline RL. Benefiting from the pluggable design, offline pretrained models from SPOT can also be applied to perform online fine-tuning seamlessly.

Recent years have seen a growing interest and adoption of LLMs, with muTransfer becoming a key technique for tuning hyperparameters in large-scale training. Meanwhile, Mixture-of-Experts (MoE) has emerged as a leading architecture in extremely large models. However, the intersection of these two advancements has remained unexplored. In this work, we derive a mu-Parameterization (muP) for MoE, providing theoretical guarantees for feature learning across model widths in both the router and experts. We empirically validate our parameterization and further investigate how scaling the number of experts and granularity affects the optimal learning rate.

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.

We consider an improper reinforcement learning setting where a learner is given M base controllers for an unknown Markov decision process, and wishes to combine them optimally to produce a potentially new controller that can outperform each of the base ones. This can be useful in tuning across controllers, learnt possibly in mismatched or simulated environments, to obtain a good controller for a given target environment with relatively few trials. Towards this, we propose two algorithms: (1) a Policy Gradient-based approach; and (2) an algorithm that can switch between a simple Actor-Critic (AC) based scheme and a Natural Actor-Critic (NAC) scheme depending on the available information. Both algorithms operate over a class of improper mixtures of the given controllers. For the first case, we derive convergence rate guarantees assuming access to a gradient oracle. For the AC-based approach we provide convergence rate guarantees to a stationary point in the basic AC case and to a global optimum in the NAC case. Numerical results on (i) the standard control theoretic benchmark of stabilizing an cartpole; and (ii) a constrained queueing task show that our improper policy optimization algorithm can stabilize the system even when the base policies at its disposal are unstable.

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control - potentially with non-smoothness both on the level of the objectives or in the system dynamics. This results in new challenges such as dealing with expensive models (e.g., governed by partial differential equations (PDEs)) and developing dedicated algorithms handling the non-smoothness. Since in contrast to single-objective optimization, the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in the field of multiobjective optimization of non-smooth PDE-constrained problems. In particular we report on the advances achieved within Project 2 "Multiobjective Optimization of Non-Smooth PDE-Constrained Problems - Switches, State Constraints and Model Order Reduction" of the DFG Priority Programm 1962 "Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization".

Model Predictive Control (MPC) has been demonstrated to be effective in continuous control tasks. When a world model and a value function are available, planning a sequence of actions ahead of time leads to a better policy. Existing methods typically obtain the value function and the corresponding policy in a model-free manner. However, we find that such an approach struggles with complex tasks, resulting in poor policy learning and inaccurate value estimation. To address this problem, we leverage the strengths of MPC itself. In this work, we introduce Bootstrapped Model Predictive Control (BMPC), a novel algorithm that performs policy learning in a bootstrapped manner. BMPC learns a network policy by imitating an MPC expert, and in turn, uses this policy to guide the MPC process. Combined with model-based TD-learning, our policy learning yields better value estimation and further boosts the efficiency of MPC. We also introduce a lazy reanalyze mechanism, which enables computationally efficient imitation learning. Our method achieves superior performance over prior works on diverse continuous control tasks. In particular, on challenging high-dimensional locomotion tasks, BMPC significantly improves data efficiency while also enhancing asymptotic performance and training stability, with comparable training time and smaller network sizes. Code is available at https://github.com/wertyuilife2/bmpc.

Recently, the impressive empirical success of policy gradient (PG) methods has catalyzed the development of their theoretical foundations. Despite the huge efforts directed at the design of efficient stochastic PG-type algorithms, the understanding of their convergence to a globally optimal policy is still limited. In this work, we develop improved global convergence guarantees for a general class of Fisher-non-degenerate parameterized policies which allows to address the case of continuous state action spaces. First, we propose a Normalized Policy Gradient method with Implicit Gradient Transport (N-PG-IGT) and derive a mathcal{O}(varepsilon^{-2.5}) sample complexity of this method for finding a global varepsilon-optimal policy. Improving over the previously known mathcal{O}(varepsilon^{-3}) complexity, this algorithm does not require the use of importance sampling or second-order information and samples only one trajectory per iteration. Second, we further improve this complexity to mathcal{mathcal{O} }(varepsilon^{-2}) by considering a Hessian-Aided Recursive Policy Gradient ((N)-HARPG) algorithm enhanced with a correction based on a Hessian-vector product. Interestingly, both algorithms are (i) simple and easy to implement: single-loop, do not require large batches of trajectories and sample at most two trajectories per iteration; (ii) computationally and memory efficient: they do not require expensive subroutines at each iteration and can be implemented with memory linear in the dimension of parameters.

We study the robust interpolation problem of arbitrary data distributions supported on a bounded space and propose a two-fold law of robustness. Robust interpolation refers to the problem of interpolating n noisy training data points in R^d by a Lipschitz function. Although this problem has been well understood when the samples are drawn from an isoperimetry distribution, much remains unknown concerning its performance under generic or even the worst-case distributions. We prove a Lipschitzness lower bound Omega(n/p) of the interpolating neural network with p parameters on arbitrary data distributions. With this result, we validate the law of robustness conjecture in prior work by Bubeck, Li, and Nagaraj on two-layer neural networks with polynomial weights. We then extend our result to arbitrary interpolating approximators and prove a Lipschitzness lower bound Omega(n^{1/d}) for robust interpolation. Our results demonstrate a two-fold law of robustness: i) we show the potential benefit of overparametrization for smooth data interpolation when n=poly(d), and ii) we disprove the potential existence of an O(1)-Lipschitz robust interpolating function when n=exp(omega(d)).

Motion trajectories offer reliable references for physics-based motion learning but suffer from sparsity, particularly in regions that lack sufficient data coverage. To address this challenge, we introduce a self-supervised, structured representation and generation method that extracts spatial-temporal relationships in periodic or quasi-periodic motions. The motion dynamics in a continuously parameterized latent space enable our method to enhance the interpolation and generalization capabilities of motion learning algorithms. The motion learning controller, informed by the motion parameterization, operates online tracking of a wide range of motions, including targets unseen during training. With a fallback mechanism, the controller dynamically adapts its tracking strategy and automatically resorts to safe action execution when a potentially risky target is proposed. By leveraging the identified spatial-temporal structure, our work opens new possibilities for future advancements in general motion representation and learning algorithms.

Varying dynamics parameters in simulation is a popular Domain Randomization (DR) approach for overcoming the reality gap in Reinforcement Learning (RL). Nevertheless, DR heavily hinges on the choice of the sampling distribution of the dynamics parameters, since high variability is crucial to regularize the agent's behavior but notoriously leads to overly conservative policies when randomizing excessively. In this paper, we propose a novel approach to address sim-to-real transfer, which automatically shapes dynamics distributions during training in simulation without requiring real-world data. We introduce DOmain RAndomization via Entropy MaximizatiON (DORAEMON), a constrained optimization problem that directly maximizes the entropy of the training distribution while retaining generalization capabilities. In achieving this, DORAEMON gradually increases the diversity of sampled dynamics parameters as long as the probability of success of the current policy is sufficiently high. We empirically validate the consistent benefits of DORAEMON in obtaining highly adaptive and generalizable policies, i.e. solving the task at hand across the widest range of dynamics parameters, as opposed to representative baselines from the DR literature. Notably, we also demonstrate the Sim2Real applicability of DORAEMON through its successful zero-shot transfer in a robotic manipulation setup under unknown real-world parameters.

The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural implicit surfaces to simple parametric domains like spheres and polycubes. Our method allows users to specify the number of cubes in the parametric domain, learning a configuration that closely resembles the target 3D object's geometry. It computes bi-directional deformation between the object and the domain using a forward mapping from the object's zero level set and an inverse deformation for backward mapping. We ensure nearly bijective mapping with a cycle loss and optimize deformation smoothness. The parameterization quality, assessed by angle and area distortions, is guaranteed using a Laplacian regularizer and an optimized learned parametric domain. Our framework integrates with existing neural rendering pipelines, using multi-view images of a single object or multiple objects of similar geometries to reconstruct 3D geometry and compute texture maps automatically, eliminating the need for any prior information. We demonstrate the method's effectiveness on images of human heads and man-made objects.

Diffusion Policies have demonstrated impressive performance in robotic manipulation tasks. However, their long inference time, resulting from an extensive iterative denoising process, and the need to execute an action chunk before the next prediction to maintain consistent actions limit their applicability to latency-critical tasks or simple tasks with a short cycle time. While recent methods explored distillation or alternative policy structures to accelerate inference, these often demand additional training, which can be resource-intensive for large robotic models. In this paper, we introduce a novel approach inspired by the Real-Time Iteration (RTI) Scheme, a method from optimal control that accelerates optimization by leveraging solutions from previous time steps as initial guesses for subsequent iterations. We explore the application of this scheme in diffusion inference and propose a scaling-based method to effectively handle discrete actions, such as grasping, in robotic manipulation. The proposed scheme significantly reduces runtime computational costs without the need for distillation or policy redesign. This enables a seamless integration into many pre-trained diffusion-based models, in particular, to resource-demanding large models. We also provide theoretical conditions for the contractivity which could be useful for estimating the initial denoising step. Quantitative results from extensive simulation experiments show a substantial reduction in inference time, with comparable overall performance compared with Diffusion Policy using full-step denoising. Our project page with additional resources is available at: https://rti-dp.github.io/.

As hyperparameter tuning becomes increasingly costly at scale, efficient tuning methods are essential. Yet principles for guiding hyperparameter tuning remain limited. In this work, we seek to establish such principles by considering a broad range of hyperparameters, including batch size, learning rate, and weight decay. We identify a phenomenon we call trajectory invariance, where pre-training loss curves, gradient noise, and gradient norm exhibit invariance--closely overlapping--with respect to a quantity that combines learning rate and weight decay. This phenomenon effectively reduces the original two-dimensional hyperparameter space to one dimension, yielding an efficient tuning rule: follow the salient direction revealed by trajectory invariance. Furthermore, we refine previous scaling laws and challenge several existing viewpoints. Overall, our work proposes new principles for efficient tuning and inspires future research on scaling laws.

Models with fewer parameters are necessary for the neural control of memory-limited, performant robots. Finding these smaller neural network architectures can be time-consuming. We propose HyperPPO, an on-policy reinforcement learning algorithm that utilizes graph hypernetworks to estimate the weights of multiple neural architectures simultaneously. Our method estimates weights for networks that are much smaller than those in common-use networks yet encode highly performant policies. We obtain multiple trained policies at the same time while maintaining sample efficiency and provide the user the choice of picking a network architecture that satisfies their computational constraints. We show that our method scales well - more training resources produce faster convergence to higher-performing architectures. We demonstrate that the neural policies estimated by HyperPPO are capable of decentralized control of a Crazyflie2.1 quadrotor. Website: https://sites.google.com/usc.edu/hyperppo

Diffusion models are powerful generative models that allow for precise control over the characteristics of the generated samples. While these diffusion models trained on large datasets have achieved success, there is often a need to introduce additional controls in downstream fine-tuning processes, treating these powerful models as pre-trained diffusion models. This work presents a novel method based on reinforcement learning (RL) to add such controls using an offline dataset comprising inputs and labels. We formulate this task as an RL problem, with the classifier learned from the offline dataset and the KL divergence against pre-trained models serving as the reward functions. Our method, CTRL (Conditioning pre-Trained diffusion models with Reinforcement Learning), produces soft-optimal policies that maximize the abovementioned reward functions. We formally demonstrate that our method enables sampling from the conditional distribution with additional controls during inference. Our RL-based approach offers several advantages over existing methods. Compared to classifier-free guidance, it improves sample efficiency and can greatly simplify dataset construction by leveraging conditional independence between the inputs and additional controls. Additionally, unlike classifier guidance, it eliminates the need to train classifiers from intermediate states to additional controls. The code is available at https://github.com/zhaoyl18/CTRL.

Dynamics models learned from visual observations have shown to be effective in various robotic manipulation tasks. One of the key questions for learning such dynamics models is what scene representation to use. Prior works typically assume representation at a fixed dimension or resolution, which may be inefficient for simple tasks and ineffective for more complicated tasks. In this work, we investigate how to learn dynamic and adaptive representations at different levels of abstraction to achieve the optimal trade-off between efficiency and effectiveness. Specifically, we construct dynamic-resolution particle representations of the environment and learn a unified dynamics model using graph neural networks (GNNs) that allows continuous selection of the abstraction level. During test time, the agent can adaptively determine the optimal resolution at each model-predictive control (MPC) step. We evaluate our method in object pile manipulation, a task we commonly encounter in cooking, agriculture, manufacturing, and pharmaceutical applications. Through comprehensive evaluations both in the simulation and the real world, we show that our method achieves significantly better performance than state-of-the-art fixed-resolution baselines at the gathering, sorting, and redistribution of granular object piles made with various instances like coffee beans, almonds, corn, etc.

Risk-sensitive reinforcement learning (RL) has become a popular tool to control the risk of uncertain outcomes and ensure reliable performance in various sequential decision-making problems. While policy gradient methods have been developed for risk-sensitive RL, it remains unclear if these methods enjoy the same global convergence guarantees as in the risk-neutral case. In this paper, we consider a class of dynamic time-consistent risk measures, called Expected Conditional Risk Measures (ECRMs), and derive policy gradient updates for ECRM-based objective functions. Under both constrained direct parameterization and unconstrained softmax parameterization, we provide global convergence and iteration complexities of the corresponding risk-averse policy gradient algorithms. We further test risk-averse variants of REINFORCE and actor-critic algorithms to demonstrate the efficacy of our method and the importance of risk control.

Spatial conditioning in pretrained text-to-image diffusion models has significantly improved fine-grained control over the structure of generated images. However, existing control adapters exhibit limited adaptability and incur high training costs when encountering novel spatial control conditions that differ substantially from the training tasks. To address this limitation, we propose Universal Few-Shot Control (UFC), a versatile few-shot control adapter capable of generalizing to novel spatial conditions. Given a few image-condition pairs of an unseen task and a query condition, UFC leverages the analogy between query and support conditions to construct task-specific control features, instantiated by a matching mechanism and an update on a small set of task-specific parameters. Experiments on six novel spatial control tasks show that UFC, fine-tuned with only 30 annotated examples of novel tasks, achieves fine-grained control consistent with the spatial conditions. Notably, when fine-tuned with 0.1% of the full training data, UFC achieves competitive performance with the fully supervised baselines in various control tasks. We also show that UFC is applicable agnostically to various diffusion backbones and demonstrate its effectiveness on both UNet and DiT architectures. Code is available at https://github.com/kietngt00/UFC.

In this work, we propose a communication-efficient parameterization, FedPara, for federated learning (FL) to overcome the burdens on frequent model uploads and downloads. Our method re-parameterizes weight parameters of layers using low-rank weights followed by the Hadamard product. Compared to the conventional low-rank parameterization, our FedPara method is not restricted to low-rank constraints, and thereby it has a far larger capacity. This property enables to achieve comparable performance while requiring 3 to 10 times lower communication costs than the model with the original layers, which is not achievable by the traditional low-rank methods. The efficiency of our method can be further improved by combining with other efficient FL optimizers. In addition, we extend our method to a personalized FL application, pFedPara, which separates parameters into global and local ones. We show that pFedPara outperforms competing personalized FL methods with more than three times fewer parameters.