Automatic Gradient Descent: Deep Learning without HyperparametersJeremy Bernstein, Chris Mingard, Kevin Huang et al. · mit
The architecture of a deep neural network is defined explicitly in terms of the number of layers, the width of each layer and the general network topology. Existing optimisation frameworks neglect this information in favour of implicit architectural information (e.g. second-order methods) or architecture-agnostic distance functions (e.g. mirror descent). Meanwhile, the most popular optimiser in practice, Adam, is based on heuristics. This paper builds a new framework for deriving optimisation algorithms that explicitly leverage neural architecture. The theory extends mirror descent to non-convex composite objective functions: the idea is to transform a Bregman divergence to account for the non-linear structure of neural architecture. Working through the details for deep fully-connected networks yields automatic gradient descent: a first-order optimiser without any hyperparameters. Automatic gradient descent trains both fully-connected and convolutional networks out-of-the-box and at ImageNet scale. A PyTorch implementation is available at https://github.com/jxbz/agd and also in Appendix B. Overall, the paper supplies a rigorous theoretical foundation for a next-generation of architecture-dependent optimisers that work automatically and without hyperparameters.
16.0AIOct 10, 2022
Neurosymbolic Programming for ScienceJennifer J. Sun, Megan Tjandrasuwita, Atharva Sehgal et al. · mit
Neurosymbolic Programming (NP) techniques have the potential to accelerate scientific discovery. These models combine neural and symbolic components to learn complex patterns and representations from data, using high-level concepts or known constraints. NP techniques can interface with symbolic domain knowledge from scientists, such as prior knowledge and experimental context, to produce interpretable outputs. We identify opportunities and challenges between current NP models and scientific workflows, with real-world examples from behavior analysis in science: to enable the use of NP broadly for workflows across the natural and social sciences.
Neural-Fly Enables Rapid Learning for Agile Flight in Strong WindsMichael O'Connell, Guanya Shi, Xichen Shi et al.
Executing safe and precise flight maneuvers in dynamic high-speed winds is important for the ongoing commoditization of uninhabited aerial vehicles (UAVs). However, because the relationship between various wind conditions and its effect on aircraft maneuverability is not well understood, it is challenging to design effective robot controllers using traditional control design methods. We present Neural-Fly, a learning-based approach that allows rapid online adaptation by incorporating pretrained representations through deep learning. Neural-Fly builds on two key observations that aerodynamics in different wind conditions share a common representation and that the wind-specific part lies in a low-dimensional space. To that end, Neural-Fly uses a proposed learning algorithm, domain adversarially invariant meta-learning (DAIML), to learn the shared representation, only using 12 minutes of flight data. With the learned representation as a basis, Neural-Fly then uses a composite adaptation law to update a set of linear coefficients for mixing the basis elements. When evaluated under challenging wind conditions generated with the Caltech Real Weather Wind Tunnel, with wind speeds up to 43.6 kilometers/hour (12.1 meters/second), Neural-Fly achieves precise flight control with substantially smaller tracking error than state-of-the-art nonlinear and adaptive controllers. In addition to strong empirical performance, the exponential stability of Neural-Fly results in robustness guarantees. Last, our control design extrapolates to unseen wind conditions, is shown to be effective for outdoor flights with only onboard sensors, and can transfer across drones with minimal performance degradation.
6.9LGJun 16, 2022
Deep Neural Imputation: A Framework for Recovering Incomplete Brain RecordingsSabera Talukder, Jennifer J. Sun, Matthew Leonard et al. · uw
Neuroscientists and neuroengineers have long relied on multielectrode neural recordings to study the brain. However, in a typical experiment, many factors corrupt neural recordings from individual electrodes, including electrical noise, movement artifacts, and faulty manufacturing. Currently, common practice is to discard these corrupted recordings, reducing already limited data that is difficult to collect. To address this challenge, we propose Deep Neural Imputation (DNI), a framework to recover missing values from electrodes by learning from data collected across spatial locations, days, and participants. We explore our framework with a linear nearest-neighbor approach and two deep generative autoencoders, demonstrating DNI's flexibility. One deep autoencoder models participants individually, while the other extends this architecture to model many participants jointly. We evaluate our models across 12 human participants implanted with multielectrode intracranial electrocorticography arrays; participants had no explicit task and behaved naturally across hundreds of recording hours. We show that DNI recovers not only time series but also frequency content, and further establish DNI's practical value by recovering significant performance on a scientifically-relevant downstream neural decoding task.
17.5LGMar 3, 2023
Eventual Discounting Temporal Logic Counterfactual Experience ReplayCameron Voloshin, Abhinav Verma, Yisong Yue
Linear temporal logic (LTL) offers a simplified way of specifying tasks for policy optimization that may otherwise be difficult to describe with scalar reward functions. However, the standard RL framework can be too myopic to find maximally LTL satisfying policies. This paper makes two contributions. First, we develop a new value-function based proxy, using a technique we call eventual discounting, under which one can find policies that satisfy the LTL specification with highest achievable probability. Second, we develop a new experience replay method for generating off-policy data from on-policy rollouts via counterfactual reasoning on different ways of satisfying the LTL specification. Our experiments, conducted in both discrete and continuous state-action spaces, confirm the effectiveness of our counterfactual experience replay approach.
10.7LGJul 25, 2023
Learning Regions of Interest for Bayesian Optimization with Adaptive Level-Set EstimationFengxue Zhang, Jialin Song, James Bowden et al.
We study Bayesian optimization (BO) in high-dimensional and non-stationary scenarios. Existing algorithms for such scenarios typically require extensive hyperparameter tuning, which limits their practical effectiveness. We propose a framework, called BALLET, which adaptively filters for a high-confidence region of interest (ROI) as a superlevel-set of a nonparametric probabilistic model such as a Gaussian process (GP). Our approach is easy to tune, and is able to focus on local region of the optimization space that can be tackled by existing BO methods. The key idea is to use two probabilistic models: a coarse GP to identify the ROI, and a localized GP for optimization within the ROI. We show theoretically that BALLET can efficiently shrink the search space, and can exhibit a tighter regret bound than standard BO without ROI filtering. We demonstrate empirically the effectiveness of BALLET on both synthetic and real-world optimization tasks.
15.6LGJun 20, 2022
Policy Optimization with Linear Temporal Logic ConstraintsCameron Voloshin, Hoang M. Le, Swarat Chaudhuri et al.
We study the problem of policy optimization (PO) with linear temporal logic (LTL) constraints. The language of LTL allows flexible description of tasks that may be unnatural to encode as a scalar cost function. We consider LTL-constrained PO as a systematic framework, decoupling task specification from policy selection, and as an alternative to the standard of cost shaping. With access to a generative model, we develop a model-based approach that enjoys a sample complexity analysis for guaranteeing both task satisfaction and cost optimality (through a reduction to a reachability problem). Empirically, our algorithm can achieve strong performance even in low-sample regimes.
1.2SYAug 2, 2019
Barrier Certificates for Assured Machine TeachingMohamadreza Ahmadi, Bo Wu, Yuxin Chen et al.
Machine teaching can be viewed as optimal control for learning. Given a learner's model, machine teaching aims to determine the optimal training data to steer the learner towards a target hypothesis. In this paper, we are interested in providing assurances for machine teaching algorithms using control theory. In particular, we study a well-established learner's model in the machine teaching literature that is captured by the local preference over a version space. We interpret the problem of teaching a preference-based learner as solving a partially observable Markov decision process (POMDP). We then show that the POMDP formulation can be cast as a special hybrid system, i.e., a discrete-time switched system. Subsequently, we use barrier certificates to verify set-theoric properties of this special hybrid system. We show how the computation of the barrier certificate can be decomposed and numerically implemented as the solution to a sum-of-squares (SOS) program. For illustration, we show how the proposed framework based on control theory can be used to verify the teaching performance of two well-known machine teaching methods.
MABe22: A Multi-Species Multi-Task Benchmark for Learned Representations of BehaviorJennifer J. Sun, Markus Marks, Andrew Ulmer et al.
We introduce MABe22, a large-scale, multi-agent video and trajectory benchmark to assess the quality of learned behavior representations. This dataset is collected from a variety of biology experiments, and includes triplets of interacting mice (4.7 million frames video+pose tracking data, 10 million frames pose only), symbiotic beetle-ant interactions (10 million frames video data), and groups of interacting flies (4.4 million frames of pose tracking data). Accompanying these data, we introduce a panel of real-life downstream analysis tasks to assess the quality of learned representations by evaluating how well they preserve information about the experimental conditions (e.g. strain, time of day, optogenetic stimulation) and animal behavior. We test multiple state-of-the-art self-supervised video and trajectory representation learning methods to demonstrate the use of our benchmark, revealing that methods developed using human action datasets do not fully translate to animal datasets. We hope that our benchmark and dataset encourage a broader exploration of behavior representation learning methods across species and settings.
6.9ROMar 9, 2022
MLNav: Learning to Safely Navigate on Martian TerrainsShreyansh Daftry, Neil Abcouwer, Tyler Del Sesto et al.
We present MLNav, a learning-enhanced path planning framework for safety-critical and resource-limited systems operating in complex environments, such as rovers navigating on Mars. MLNav makes judicious use of machine learning to enhance the efficiency of path planning while fully respecting safety constraints. In particular, the dominant computational cost in such safety-critical settings is running a model-based safety checker on the proposed paths. Our learned search heuristic can simultaneously predict the feasibility for all path options in a single run, and the model-based safety checker is only invoked on the top-scoring paths. We validate in high-fidelity simulations using both real Martian terrain data collected by the Perseverance rover, as well as a suite of challenging synthetic terrains. Our experiments show that: (i) compared to the baseline ENav path planner on board the Perserverance rover, MLNav can provide a significant improvement in multiple key metrics, such as a 10x reduction in collision checks when navigating real Martian terrains, despite being trained with synthetic terrains; and (ii) MLNav can successfully navigate highly challenging terrains where the baseline ENav fails to find a feasible path before timing out.
Conformal Generative Modeling on Triangulated SurfacesVictor Dorobantu, Charlotte Borcherds, Yisong Yue
We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle mesh to a target triangle mesh of a simple manifold such as a sphere. After accounting for errors due to the mesh discretization, we can use any generative modeling approach developed for simple manifolds as a plug-and-play subroutine. We demonstrate our framework on multiple complicated manifolds and multiple generative modeling subroutines, where we show that our approach can learn good estimates of distributions on meshes from samples, and can also learn simultaneously from multiple distinct meshes of the same underlying manifold.
5.9ROMar 27
A Narwhal-Inspired Sensing-to-Control Framework for Small Fixed-Wing AircraftFengze Xie, Xiaozhou Fan, Jacob Schuster et al.
Fixed-wing unmanned aerial vehicles (UAVs) offer endurance and efficiency but lack low-speed agility due to highly coupled dynamics. We present an end-to-end sensing-to-control pipeline that combines bio-inspired hardware, physics-informed dynamics learning, and convex control allocation. Measuring airflow on a small airframe is difficult because near-body aerodynamics, propeller slipstream, control-surface actuation, and ambient gusts distort pressure signals. Inspired by the narwhal's protruding tusk, we mount in-house multi-hole probes far upstream and complement them with sparse, carefully placed wing pressure sensors for local flow measurement. A data-driven calibration maps probe pressures to airspeed and flow angles. We then learn a control-affine dynamics model using the estimated airspeed/angles and sparse sensors. A soft left/right symmetry regularizer improves identifiability under partial observability and limits confounding between wing pressures and flaperon inputs. Desired wrenches (forces and moments) are realized by a regularized least-squares allocator that yields smooth, trimmed actuation. Wind-tunnel studies across a wide operating range show that adding wing pressures reduces force-estimation error by 25-30%, the proposed model degrades less under distribution shift (about 12% versus 44% for an unstructured baseline), and force tracking improves with smoother inputs, including a 27% reduction in normal-force RMSE versus a plain affine model and 34% versus an unstructured baseline.
16.0AIAug 20, 2024
Strategist: Self-improvement of LLM Decision Making via Bi-Level Tree SearchJonathan Light, Min Cai, Weiqin Chen et al.
Traditional reinforcement learning and planning typically requires vast amounts of data and training to develop effective policies. In contrast, large language models (LLMs) exhibit strong generalization and zero-shot capabilities, but struggle with tasks that require detailed planning and decision-making in complex action spaces. We introduce STRATEGIST, a novel approach that integrates the strengths of both methods. Our approach leverages LLMs to search and update high-level strategies (as text), which are then refined and executed by low-level Monte Carlo Tree Search (MCTS). STRATEGIST is a generalizable framework to optimize the strategy through population-based self-play simulations without the need for any training data. We demonstrate the effectiveness of STRATEGIST in learning optimal strategies for competitive, multi-turn games with partial information, including Game of Pure Strategy (GOPS) and multi-agent, hidden-identity discussion games like The Resistance: Avalon. Our results show that agents equipped with STRATEGIST outperform those trained with traditional RL methods, other LLM-based skill acquisition techniques, pre-existing LLM agents across both game environments and achieves comparable performance against human players.
2.2OCJul 12, 2022
Compactly Restrictable Metric Policy Optimization ProblemsVictor D. Dorobantu, Kamyar Azizzadenesheli, Yisong Yue
We study policy optimization problems for deterministic Markov decision processes (MDPs) with metric state and action spaces, which we refer to as Metric Policy Optimization Problems (MPOPs). Our goal is to establish theoretical results on the well-posedness of MPOPs that can characterize practically relevant continuous control systems. To do so, we define a special class of MPOPs called Compactly Restrictable MPOPs (CR-MPOPs), which are flexible enough to capture the complex behavior of robotic systems but specific enough to admit solutions using dynamic programming methods such as value iteration. We show how to arrive at CR-MPOPs using forward-invariance. We further show that our theoretical results on CR-MPOPs can be used to characterize feedback linearizable control affine systems.
End-to-End Conformal Calibration for Optimization Under UncertaintyChristopher Yeh, Nicolas Christianson, Alan Wu et al.
Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to achieve with neural networks. Moreover, in high-dimensional settings, there may be many valid uncertainty estimates, each with its own performance profile - i.e., not all uncertainty is equally valuable for downstream decision-making. To address this problem, this paper develops an end-to-end framework to learn uncertainty sets for conditional robust optimization in a way that is informed by the downstream decision-making loss, with robustness and calibration guarantees provided by conformal prediction. In addition, we propose to represent general convex uncertainty sets with partially input-convex neural networks, which are learned as part of our framework. Our approach consistently improves upon two-stage estimate-then-optimize baselines on concrete applications in energy storage arbitrage and portfolio optimization.
FI-ODE: Certifiably Robust Forward Invariance in Neural ODEsYujia Huang, Ivan Dario Jimenez Rodriguez, Huan Zhang et al.
Forward invariance is a long-studied property in control theory that is used to certify that a dynamical system stays within some pre-specified set of states for all time, and also admits robustness guarantees (e.g., the certificate holds under perturbations). We propose a general framework for training and provably certifying robust forward invariance in Neural ODEs. We apply this framework to provide certified safety in robust continuous control. To our knowledge, this is the first instance of training Neural ODE policies with such non-vacuous certified guarantees. In addition, we explore the generality of our framework by using it to certify adversarial robustness for image classification.
CLEVER: A Curated Benchmark for Formally Verified Code GenerationAmitayush Thakur, Jasper Lee, George Tsoukalas et al.
We introduce ${\rm C{\small LEVER}}$, a high-quality, curated benchmark of 161 problems for end-to-end verified code generation in Lean. Each problem consists of (1) the task of generating a specification that matches a held-out ground-truth specification, and (2) the task of generating a Lean implementation that provably satisfies this specification. Unlike prior benchmarks, ${\rm C{\small LEVER}}$ avoids test-case supervision, LLM-generated annotations, and specifications that leak implementation logic or allow vacuous solutions. All outputs are verified post-hoc using Lean's type checker to ensure machine-checkable correctness. We use ${\rm C{\small LEVER}}$ to evaluate several few-shot and agentic approaches based on state-of-the-art language models. These methods all struggle to achieve full verification, establishing it as a challenging frontier benchmark for program synthesis and formal reasoning. Our benchmark can be found on GitHub(https://github.com/trishullab/clever) as well as HuggingFace(https://huggingface.co/datasets/amitayusht/clever). All our evaluation code is also available online(https://github.com/trishullab/clever-prover).
5.8AIDec 3, 2025
EnCompass: Enhancing Agent Programming with Search Over Program Execution PathsZhening Li, Armando Solar-Lezama, Yisong Yue et al.
We introduce a new approach to agent programming, the development of LLM-based agents. Current approaches to agent programming often entangle two aspects of agent design: the core workflow logic and the inference-time strategy (e.g., tree search). We introduce "probabilistic angelic nondeterminism" ("PAN"), a programming model that disentangles these two concerns, allowing the programmer to describe the agent workflow and independently experiment with different inference-time strategies by simply changing a few inputs. We provide an implementation of PAN in Python as the EnCompass framework, which uses a Python decorator to compile agent workflow programs into a search space. We present three case studies that demonstrate how the framework lets the programmer quickly improve the reliability of an agent and easily switch between different inference-time strategies, all with little additional coding.
13.1CVDec 15, 2025
Feedforward 3D Editing via Text-Steerable Image-to-3DZiqi Ma, Hongqiao Chen, Yisong Yue et al.
Recent progress in image-to-3D has opened up immense possibilities for design, AR/VR, and robotics. However, to use AI-generated 3D assets in real applications, a critical requirement is the capability to edit them easily. We present a feedforward method, Steer3D, to add text steerability to image-to-3D models, which enables editing of generated 3D assets with language. Our approach is inspired by ControlNet, which we adapt to image-to-3D generation to enable text steering directly in a forward pass. We build a scalable data engine for automatic data generation, and develop a two-stage training recipe based on flow-matching training and Direct Preference Optimization (DPO). Compared to competing methods, Steer3D more faithfully follows the language instruction and maintains better consistency with the original 3D asset, while being 2.4x to 28.5x faster. Steer3D demonstrates that it is possible to add a new modality (text) to steer the generation of pretrained image-to-3D generative models with 100k data. Project website: https://glab-caltech.github.io/steer3d/
CARE: a Benchmark Suite for the Classification and Retrieval of EnzymesJason Yang, Ariane Mora, Shengchao Liu et al.
Enzymes are important proteins that catalyze chemical reactions. In recent years, machine learning methods have emerged to predict enzyme function from sequence; however, there are no standardized benchmarks to evaluate these methods. We introduce CARE, a benchmark and dataset suite for the Classification And Retrieval of Enzymes (CARE). CARE centers on two tasks: (1) classification of a protein sequence by its enzyme commission (EC) number and (2) retrieval of an EC number given a chemical reaction. For each task, we design train-test splits to evaluate different kinds of out-of-distribution generalization that are relevant to real use cases. For the classification task, we provide baselines for state-of-the-art methods. Because the retrieval task has not been previously formalized, we propose a method called Contrastive Reaction-EnzymE Pretraining (CREEP) as one of the first baselines for this task and compare it to the recent method, CLIPZyme. CARE is available at https://github.com/jsunn-y/CARE/.
ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree SearchDan Zhang, Sining Zhoubian, Ziniu Hu et al.
Recent methodologies in LLM self-training mostly rely on LLM generating responses and filtering those with correct output answers as training data. This approach often yields a low-quality fine-tuning training set (e.g., incorrect plans or intermediate reasoning). In this paper, we develop a reinforced self-training approach, called ReST-MCTS*, based on integrating process reward guidance with tree search MCTS* for collecting higher-quality reasoning traces as well as per-step value to train policy and reward models. ReST-MCTS* circumvents the per-step manual annotation typically used to train process rewards by tree-search-based reinforcement learning: Given oracle final correct answers, ReST-MCTS* is able to infer the correct process rewards by estimating the probability this step can help lead to the correct answer. These inferred rewards serve dual purposes: they act as value targets for further refining the process reward model and also facilitate the selection of high-quality traces for policy model self-training. We first show that the tree-search policy in ReST-MCTS* achieves higher accuracy compared with prior LLM reasoning baselines such as Best-of-N and Tree-of-Thought, within the same search budget. We then show that by using traces searched by this tree-search policy as training data, we can continuously enhance the three language models for multiple iterations, and outperform other self-training algorithms such as ReST$^\text{EM}$ and Self-Rewarding LM. We release all code at https://github.com/THUDM/ReST-MCTS.
Population Transformer: Learning Population-level Representations of Neural ActivityGeeling Chau, Christopher Wang, Sabera Talukder et al.
We present a self-supervised framework that learns population-level codes for arbitrary ensembles of neural recordings at scale. We address key challenges in scaling models with neural time-series data, namely, sparse and variable electrode distribution across subjects and datasets. The Population Transformer (PopT) stacks on top of pretrained temporal embeddings and enhances downstream decoding by enabling learned aggregation of multiple spatially-sparse data channels. The pretrained PopT lowers the amount of data required for downstream decoding experiments, while increasing accuracy, even on held-out subjects and tasks. Compared to end-to-end methods, this approach is computationally lightweight, while achieving similar or better decoding performance. We further show how our framework is generalizable to multiple time-series embeddings and neural data modalities. Beyond decoding, we interpret the pretrained and fine-tuned PopT models to show how they can be used to extract neuroscience insights from large amounts of data. We release our code as well as a pretrained PopT to enable off-the-shelf improvements in multi-channel intracranial data decoding and interpretability. Code is available at https://github.com/czlwang/PopulationTransformer.
LyaNet: A Lyapunov Framework for Training Neural ODEsIvan Dario Jimenez Rodriguez, Aaron D. Ames, Yisong Yue
We propose a method for training ordinary differential equations by using a control-theoretic Lyapunov condition for stability. Our approach, called LyaNet, is based on a novel Lyapunov loss formulation that encourages the inference dynamics to converge quickly to the correct prediction. Theoretically, we show that minimizing Lyapunov loss guarantees exponential convergence to the correct solution and enables a novel robustness guarantee. We also provide practical algorithms, including one that avoids the cost of backpropagating through a solver or using the adjoint method. Relative to standard Neural ODE training, we empirically find that LyaNet can offer improved prediction performance, faster convergence of inference dynamics, and improved adversarial robustness. Our code available at https://github.com/ivandariojr/LyapunovLearning .
Learning to Control an Unstable System with One Minute of Data: Leveraging Gaussian Process Differentiation in Predictive ControlIvan D. Jimenez Rodriguez, Ugo Rosolia, Aaron D. Ames et al.
We present a straightforward and efficient way to control unstable robotic systems using an estimated dynamics model. Specifically, we show how to exploit the differentiability of Gaussian Processes to create a state-dependent linearized approximation of the true continuous dynamics that can be integrated with model predictive control. Our approach is compatible with most Gaussian process approaches for system identification, and can learn an accurate model using modest amounts of training data. We validate our approach by learning the dynamics of an unstable system such as a segway with a 7-D state space and 2-D input space (using only one minute of data), and we show that the resulting controller is robust to unmodelled dynamics and disturbances, while state-of-the-art control methods based on nominal models can fail under small perturbations. Code is open sourced at https://github.com/learning-and-control/core .
Empirical Study of Off-Policy Policy Evaluation for Reinforcement LearningCameron Voloshin, Hoang M. Le, Nan Jiang et al.
We offer an experimental benchmark and empirical study for off-policy policy evaluation (OPE) in reinforcement learning, which is a key problem in many safety critical applications. Given the increasing interest in deploying learning-based methods, there has been a flurry of recent proposals for OPE method, leading to a need for standardized empirical analyses. Our work takes a strong focus on diversity of experimental design to enable stress testing of OPE methods. We provide a comprehensive benchmarking suite to study the interplay of different attributes on method performance. We distill the results into a summarized set of guidelines for OPE in practice. Our software package, the Caltech OPE Benchmarking Suite (COBS), is open-sourced and we invite interested researchers to further contribute to the benchmark.
Symbolic Music Generation with Non-Differentiable Rule Guided DiffusionYujia Huang, Adishree Ghatare, Yuanzhe Liu et al.
We study the problem of symbolic music generation (e.g., generating piano rolls), with a technical focus on non-differentiable rule guidance. Musical rules are often expressed in symbolic form on note characteristics, such as note density or chord progression, many of which are non-differentiable which pose a challenge when using them for guided diffusion. We propose Stochastic Control Guidance (SCG), a novel guidance method that only requires forward evaluation of rule functions that can work with pre-trained diffusion models in a plug-and-play way, thus achieving training-free guidance for non-differentiable rules for the first time. Additionally, we introduce a latent diffusion architecture for symbolic music generation with high time resolution, which can be composed with SCG in a plug-and-play fashion. Compared to standard strong baselines in symbolic music generation, this framework demonstrates marked advancements in music quality and rule-based controllability, outperforming current state-of-the-art generators in a variety of settings. For detailed demonstrations, code and model checkpoints, please visit our project website: https://scg-rule-guided-music.github.io/.
19.8CVNov 20, 2024
Find Any Part in 3DZiqi Ma, Yisong Yue, Georgia Gkioxari
Why don't we have foundation models in 3D yet? A key limitation is data scarcity. For 3D object part segmentation, existing datasets are small in size and lack diversity. We show that it is possible to break this data barrier by building a data engine powered by 2D foundation models. Our data engine automatically annotates any number of object parts: 1755x more unique part types than existing datasets combined. By training on our annotated data with a simple contrastive objective, we obtain an open-world model that generalizes to any part in any object based on any text query. Even when evaluated zero-shot, we outperform existing methods on the datasets they train on. We achieve 260% improvement in mIoU and boost speed by 6x to 300x. Our scaling analysis confirms that this generalization stems from the data scale, which underscores the impact of our data engine. Finally, to advance general-category open-world 3D part segmentation, we release a benchmark covering a wide range of objects and parts. Project website: https://ziqi-ma.github.io/find3dsite/
19.7LGFeb 23, 2025
DISC: Dynamic Decomposition Improves LLM Inference ScalingJonathan Light, Wei Cheng, Benjamin Riviere et al.
Inference scaling methods for LLMs often rely on decomposing problems into steps (or groups of tokens), followed by sampling and selecting the best next steps. However, these steps and their sizes are often predetermined or manually designed based on domain knowledge. We propose dynamic decomposition, a method that adaptively and automatically partitions solution and reasoning traces into manageable steps during inference. By more effectively allocating compute -- particularly through subdividing challenging steps and prioritizing their sampling -- dynamic decomposition significantly improves inference efficiency. Experiments on benchmarks such as APPS, MATH, and LiveCodeBench demonstrate that dynamic decomposition outperforms static approaches, including token-level, sentence-level, and single-step decompositions, reducing the pass@10 error rate by 5.0%, 6.7%, and 10.5% respectively. These findings highlight the potential of dynamic decomposition to improve a wide range of inference scaling techniques.
10.2CVMar 31, 2025
Self-Evolving Visual Concept Library using Vision-Language CriticsAtharva Sehgal, Patrick Yuan, Ziniu Hu et al.
We study the problem of building a visual concept library for visual recognition. Building effective visual concept libraries is challenging, as manual definition is labor-intensive, while relying solely on LLMs for concept generation can result in concepts that lack discriminative power or fail to account for the complex interactions between them. Our approach, ESCHER, takes a library learning perspective to iteratively discover and improve visual concepts. ESCHER uses a vision-language model (VLM) as a critic to iteratively refine the concept library, including accounting for interactions between concepts and how they affect downstream classifiers. By leveraging the in-context learning abilities of LLMs and the history of performance using various concepts, ESCHER dynamically improves its concept generation strategy based on the VLM critic's feedback. Finally, ESCHER does not require any human annotations, and is thus an automated plug-and-play framework. We empirically demonstrate the ability of ESCHER to learn a concept library for zero-shot, few-shot, and fine-tuning visual classification tasks. This work represents, to our knowledge, the first application of concept library learning to real-world visual tasks.
15.7LGOct 9, 2025
Conformal Risk Training: End-to-End Optimization of Conformal Risk ControlChristopher Yeh, Nicolas Christianson, Adam Wierman et al.
While deep learning models often achieve high predictive accuracy, their predictions typically do not come with any provable guarantees on risk or reliability, which are critical for deployment in high-stakes applications. The framework of conformal risk control (CRC) provides a distribution-free, finite-sample method for controlling the expected value of any bounded monotone loss function and can be conveniently applied post-hoc to any pre-trained deep learning model. However, many real-world applications are sensitive to tail risks, as opposed to just expected loss. In this work, we develop a method for controlling the general class of Optimized Certainty-Equivalent (OCE) risks, a broad class of risk measures which includes as special cases the expected loss (generalizing the original CRC method) and common tail risks like the conditional value-at-risk (CVaR). Furthermore, standard post-hoc CRC can degrade average-case performance due to its lack of feedback to the model. To address this, we introduce "conformal risk training," an end-to-end approach that differentiates through conformal OCE risk control during model training or fine-tuning. Our method achieves provable risk guarantees while demonstrating significantly improved average-case performance over post-hoc approaches on applications to controlling classifiers' false negative rate and controlling financial risk in battery storage operation.
5.8AINov 24, 2024
PIANIST: Learning Partially Observable World Models with LLMs for Multi-Agent Decision MakingJonathan Light, Sixue Xing, Yuanzhe Liu et al.
Effective extraction of the world knowledge in LLMs for complex decision-making tasks remains a challenge. We propose a framework PIANIST for decomposing the world model into seven intuitive components conducive to zero-shot LLM generation. Given only the natural language description of the game and how input observations are formatted, our method can generate a working world model for fast and efficient MCTS simulation. We show that our method works well on two different games that challenge the planning and decision making skills of the agent for both language and non-language based action taking, without any training on domain-specific training data or explicitly defined world model.
4.1LGNov 17, 2025
Learning Time-Scale Invariant Population-Level Neural RepresentationsEshani Patel, Yisong Yue, Geeling Chau
General-purpose foundation models for neural time series can help accelerate neuroscientific discoveries and enable applications such as brain computer interfaces (BCIs). A key component in scaling these models is population-level representation learning, which leverages information across channels to capture spatial as well as temporal structure. Population-level approaches have recently shown that such representations can be both efficient to learn on top of pretrained temporal encoders and produce useful representations for decoding a variety of downstream tasks. However, these models remain sensitive to mismatches in preprocessing, particularly on time-scales, between pretraining and downstream settings. We systematically examine how time-scale mismatches affects generalization and find that existing representations lack invariance. To address this, we introduce Time-scale Augmented Pretraining (TSAP), which consistently improves robustness to different time-scales across decoding tasks and builds invariance in the representation space. These results highlight handling preprocessing diversity as a key step toward building generalizable neural foundation models.
13.0LGSep 18, 2025
Kuramoto Orientation Diffusion ModelsYue Song, T. Anderson Keller, Sevan Brodjian et al.
Orientation-rich images, such as fingerprints and textures, often exhibit coherent angular directional patterns that are challenging to model using standard generative approaches based on isotropic Euclidean diffusion. Motivated by the role of phase synchronization in biological systems, we propose a score-based generative model built on periodic domains by leveraging stochastic Kuramoto dynamics in the diffusion process. In neural and physical systems, Kuramoto models capture synchronization phenomena across coupled oscillators -- a behavior that we re-purpose here as an inductive bias for structured image generation. In our framework, the forward process performs \textit{synchronization} among phase variables through globally or locally coupled oscillator interactions and attraction to a global reference phase, gradually collapsing the data into a low-entropy von Mises distribution. The reverse process then performs \textit{desynchronization}, generating diverse patterns by reversing the dynamics with a learned score function. This approach enables structured destruction during forward diffusion and a hierarchical generation process that progressively refines global coherence into fine-scale details. We implement wrapped Gaussian transition kernels and periodicity-aware networks to account for the circular geometry. Our method achieves competitive results on general image benchmarks and significantly improves generation quality on orientation-dense datasets like fingerprints and textures. Ultimately, this work demonstrates the promise of biologically inspired synchronization dynamics as structured priors in generative modeling.
Langevin Flows for Modeling Neural Latent DynamicsYue Song, T. Anderson Keller, Yisong Yue et al.
Neural populations exhibit latent dynamical structures that drive time-evolving spiking activities, motivating the search for models that capture both intrinsic network dynamics and external unobserved influences. In this work, we introduce LangevinFlow, a sequential Variational Auto-Encoder where the time evolution of latent variables is governed by the underdamped Langevin equation. Our approach incorporates physical priors -- such as inertia, damping, a learned potential function, and stochastic forces -- to represent both autonomous and non-autonomous processes in neural systems. Crucially, the potential function is parameterized as a network of locally coupled oscillators, biasing the model toward oscillatory and flow-like behaviors observed in biological neural populations. Our model features a recurrent encoder, a one-layer Transformer decoder, and Langevin dynamics in the latent space. Empirically, our method outperforms state-of-the-art baselines on synthetic neural populations generated by a Lorenz attractor, closely matching ground-truth firing rates. On the Neural Latents Benchmark (NLB), the model achieves superior held-out neuron likelihoods (bits per spike) and forward prediction accuracy across four challenging datasets. It also matches or surpasses alternative methods in decoding behavioral metrics such as hand velocity. Overall, this work introduces a flexible, physics-inspired, high-performing framework for modeling complex neural population dynamics and their unobserved influences.
Practical Bayesian Algorithm Execution via Posterior SamplingChu Xin Cheng, Raul Astudillo, Thomas Desautels et al.
We consider Bayesian algorithm execution (BAX), a framework for efficiently selecting evaluation points of an expensive function to infer a property of interest encoded as the output of a base algorithm. Since the base algorithm typically requires more evaluations than are feasible, it cannot be directly applied. Instead, BAX methods sequentially select evaluation points using a probabilistic numerical approach. Current BAX methods use expected information gain to guide this selection. However, this approach is computationally intensive. Observing that, in many tasks, the property of interest corresponds to a target set of points defined by the function, we introduce PS-BAX, a simple, effective, and scalable BAX method based on posterior sampling. PS-BAX is applicable to a wide range of problems, including many optimization variants and level set estimation. Experiments across diverse tasks demonstrate that PS-BAX performs competitively with existing baselines while being significantly faster, simpler to implement, and easily parallelizable, setting a strong baseline for future research. Additionally, we establish conditions under which PS-BAX is asymptotically convergent, offering new insights into posterior sampling as an algorithm design paradigm.
17.6LGJun 22, 2024
Distributionally Robust Constrained Reinforcement Learning under Strong DualityZhengfei Zhang, Kishan Panaganti, Laixi Shi et al.
We study the problem of Distributionally Robust Constrained RL (DRC-RL), where the goal is to maximize the expected reward subject to environmental distribution shifts and constraints. This setting captures situations where training and testing environments differ, and policies must satisfy constraints motivated by safety or limited budgets. Despite significant progress toward algorithm design for the separate problems of distributionally robust RL and constrained RL, there do not yet exist algorithms with end-to-end convergence guarantees for DRC-RL. We develop an algorithmic framework based on strong duality that enables the first efficient and provable solution in a class of environmental uncertainties. Further, our framework exposes an inherent structure of DRC-RL that arises from the combination of distributional robustness and constraints, which prevents a popular class of iterative methods from tractably solving DRC-RL, despite such frameworks being applicable for each of distributionally robust RL and constrained RL individually. Finally, we conduct experiments on a car racing benchmark to evaluate the effectiveness of the proposed algorithm.
Self-Control of LLM Behaviors by Compressing Suffix Gradient into Prefix ControllerMin Cai, Yuchen Zhang, Shichang Zhang et al.
We propose SelfControl, an inference-time model control method utilizing gradients to control the behavior of large language models (LLMs) without explicit human annotations. Given a desired behavior expressed in a natural language suffix string concatenated to the input prompt, SelfControl computes gradients of the LLM's self-evaluation of the suffix with respect to its latent representations. The gradients are used to directly control the auto-regressive generation process towards desired behaviors, which eliminates human supervision, achieves precise and transparent control, and offers on-the-fly adaptability. To further enhance efficiency, we introduce SelfControl_{Prefix}, a compact module that encapsulates the learned representations from gradients into a SelfControl_{Prefix}, facilitating efficient inference-time control with no latency compared to the original model and allowing control for multiple behaviors simultaneously. Our experiments demonstrate SelfControl's efficacy across multiple domains, where it improves over SOTA for 8.3% in detoxification, 3.1% in truthfulness enhancement, 4%~10% in controlling on emotion tones, and 48.2% in privacy protection, i.e., completely remove privacy leakage issue. Additionally, we demonstrate that SelfControl can be used for data synthesis and to improve reasoning abilities.
Distributionally Robust Policy Evaluation under General Covariate Shift in Contextual BanditsYihong Guo, Hao Liu, Yisong Yue et al.
We introduce a distributionally robust approach that enhances the reliability of offline policy evaluation in contextual bandits under general covariate shifts. Our method aims to deliver robust policy evaluation results in the presence of discrepancies in both context and policy distribution between logging and target data. Central to our methodology is the application of robust regression, a distributionally robust technique tailored here to improve the estimation of conditional reward distribution from logging data. Utilizing the reward model obtained from robust regression, we develop a comprehensive suite of policy value estimators, by integrating our reward model into established evaluation frameworks, namely direct methods and doubly robust methods. Through theoretical analysis, we further establish that the proposed policy value estimators offer a finite sample upper bound for the bias, providing a clear advantage over traditional methods, especially when the shift is large. Finally, we designed an extensive range of policy evaluation scenarios, covering diverse magnitudes of shifts and a spectrum of logging and target policies. Our empirical results indicate that our approach significantly outperforms baseline methods, most notably in 90% of the cases under the policy shift-only settings and 72% of the scenarios under the general covariate shift settings.
14.7RODec 15, 2021
Safety-Aware Preference-Based Learning for Safety-Critical ControlRyan K. Cosner, Maegan Tucker, Andrew J. Taylor et al.
Bringing dynamic robots into the wild requires a tenuous balance between performance and safety. Yet controllers designed to provide robust safety guarantees often result in conservative behavior, and tuning these controllers to find the ideal trade-off between performance and safety typically requires domain expertise or a carefully constructed reward function. This work presents a design paradigm for systematically achieving behaviors that balance performance and robust safety by integrating safety-aware Preference-Based Learning (PBL) with Control Barrier Functions (CBFs). Fusing these concepts -- safety-aware learning and safety-critical control -- gives a robust means to achieve safe behaviors on complex robotic systems in practice. We demonstrate the capability of this design paradigm to achieve safe and performant perception-based autonomous operation of a quadrupedal robot both in simulation and experimentally on hardware.
Self-Supervised Keypoint Discovery in Behavioral VideosJennifer J. Sun, Serim Ryou, Roni Goldshmid et al.
We propose a method for learning the posture and structure of agents from unlabelled behavioral videos. Starting from the observation that behaving agents are generally the main sources of movement in behavioral videos, our method, Behavioral Keypoint Discovery (B-KinD), uses an encoder-decoder architecture with a geometric bottleneck to reconstruct the spatiotemporal difference between video frames. By focusing only on regions of movement, our approach works directly on input videos without requiring manual annotations. Experiments on a variety of agent types (mouse, fly, human, jellyfish, and trees) demonstrate the generality of our approach and reveal that our discovered keypoints represent semantically meaningful body parts, which achieve state-of-the-art performance on keypoint regression among self-supervised methods. Additionally, B-KinD achieve comparable performance to supervised keypoints on downstream tasks, such as behavior classification, suggesting that our method can dramatically reduce model training costs vis-a-vis supervised methods.
Automatic Synthesis of Diverse Weak Supervision Sources for Behavior AnalysisAlbert Tseng, Jennifer J. Sun, Yisong Yue
Obtaining annotations for large training sets is expensive, especially in settings where domain knowledge is required, such as behavior analysis. Weak supervision has been studied to reduce annotation costs by using weak labels from task-specific labeling functions (LFs) to augment ground truth labels. However, domain experts still need to hand-craft different LFs for different tasks, limiting scalability. To reduce expert effort, we present AutoSWAP: a framework for automatically synthesizing data-efficient task-level LFs. The key to our approach is to efficiently represent expert knowledge in a reusable domain-specific language and more general domain-level LFs, with which we use state-of-the-art program synthesis techniques and a small labeled dataset to generate task-level LFs. Additionally, we propose a novel structural diversity cost that allows for efficient synthesis of diverse sets of LFs, further improving AutoSWAP's performance. We evaluate AutoSWAP in three behavior analysis domains and demonstrate that AutoSWAP outperforms existing approaches using only a fraction of the data. Our results suggest that AutoSWAP is an effective way to automatically generate LFs that can significantly reduce expert effort for behavior analysis.
5.3ROSep 10, 2021
Natural Multicontact Walking for Robotic Assistive Devices via Musculoskeletal Models and Hybrid Zero DynamicsKejun Li, Maegan Tucker, Rachel Gehlhar et al.
Generating stable walking gaits that yield natural locomotion when executed on robotic-assistive devices is a challenging task that often requires hand-tuning by domain experts. This paper presents an alternative methodology, where we propose the addition of musculoskeletal models directly into the gait generation process to intuitively shape the resulting behavior. In particular, we construct a multi-domain hybrid system model that combines the system dynamics with muscle models to represent natural multicontact walking. Provably stable walking gaits can then be generated for this model via the hybrid zero dynamics (HZD) method. We experimentally apply our integrated framework towards achieving multicontact locomotion on a dual-actuated transfemoral prosthesis, AMPRO3, for two subjects. The results demonstrate that enforcing muscle model constraints produces gaits that yield natural locomotion (as analyzed via comparison to motion capture data and electromyography). Moreover, gaits generated with our framework were strongly preferred by the non-disabled prosthetic users as compared to gaits generated with the nominal HZD method, even with the use of systematic tuning methods. We conclude that the novel approach of combining robotic walking methods (specifically HZD) with muscle models successfully generates anthropomorphic robotic-assisted locomotion.
Unsupervised Learning of Neurosymbolic EncodersEric Zhan, Jennifer J. Sun, Ann Kennedy et al.
We present a framework for the unsupervised learning of neurosymbolic encoders, which are encoders obtained by composing neural networks with symbolic programs from a domain-specific language. Our framework naturally incorporates symbolic expert knowledge into the learning process, which leads to more interpretable and factorized latent representations compared to fully neural encoders. We integrate modern program synthesis techniques with the variational autoencoding (VAE) framework, in order to learn a neurosymbolic encoder in conjunction with a standard decoder. The programmatic descriptions from our encoders can benefit many analysis workflows, such as in behavior modeling where interpreting agent actions and movements is important. We evaluate our method on learning latent representations for real-world trajectory data from animal biology and sports analytics. We show that our approach offers significantly better separation of meaningful categories than standard VAEs and leads to practical gains on downstream analysis tasks, such as for behavior classification.
3.1LGJun 11, 2021
Interpreting Expert Annotation Differences in Animal BehaviorMegan Tjandrasuwita, Jennifer J. Sun, Ann Kennedy et al.
Hand-annotated data can vary due to factors such as subjective differences, intra-rater variability, and differing annotator expertise. We study annotations from different experts who labelled the same behavior classes on a set of animal behavior videos, and observe a variation in annotation styles. We propose a new method using program synthesis to help interpret annotation differences for behavior analysis. Our model selects relevant trajectory features and learns a temporal filter as part of a program, which corresponds to estimated importance an annotator places on that feature at each timestamp. Our experiments on a dataset from behavioral neuroscience demonstrate that compared to baseline approaches, our method is more accurate at capturing annotator labels and learns interpretable temporal filters. We believe that our method can lead to greater reproducibility of behavior annotations used in scientific studies. We plan to release our code.
Meta-Adaptive Nonlinear Control: Theory and AlgorithmsGuanya Shi, Kamyar Azizzadenesheli, Michael O'Connell et al.
We present an online multi-task learning approach for adaptive nonlinear control, which we call Online Meta-Adaptive Control (OMAC). The goal is to control a nonlinear system subject to adversarial disturbance and unknown $\textit{environment-dependent}$ nonlinear dynamics, under the assumption that the environment-dependent dynamics can be well captured with some shared representation. Our approach is motivated by robot control, where a robotic system encounters a sequence of new environmental conditions that it must quickly adapt to. A key emphasis is to integrate online representation learning with established methods from control theory, in order to arrive at a unified framework that yields both control-theoretic and learning-theoretic guarantees. We provide instantiations of our approach under varying conditions, leading to the first non-asymptotic end-to-end convergence guarantee for multi-task nonlinear control. OMAC can also be integrated with deep representation learning. Experiments show that OMAC significantly outperforms conventional adaptive control approaches which do not learn the shared representation, in inverted pendulum and 6-DoF drone control tasks under varying wind conditions.
6.5LGJun 9, 2021
Learning Pseudo-Backdoors for Mixed Integer ProgramsAaron Ferber, Jialin Song, Bistra Dilkina et al.
We propose a machine learning approach for quickly solving Mixed Integer Programs (MIP) by learning to prioritize a set of decision variables, which we call pseudo-backdoors, for branching that results in faster solution times. Learning-based approaches have seen success in the area of solving combinatorial optimization problems by being able to flexibly leverage common structures in a given distribution of problems. Our approach takes inspiration from the concept of strong backdoors, which corresponds to a small set of variables such that only branching on these variables yields an optimal integral solution and a proof of optimality. Our notion of pseudo-backdoors corresponds to a small set of variables such that only branching on them leads to faster solve time (which can be solver dependent). A key advantage of pseudo-backdoors over strong backdoors is that they are much amenable to data-driven identification or prediction. Our proposed method learns to estimate the solver performance of a proposed pseudo-backdoor, using a labeled dataset collected on a set of training MIP instances. This model can then be used to identify high-quality pseudo-backdoors on new MIP instances from the same distribution. We evaluate our method on the generalized independent set problems and find that our approach can efficiently identify high-quality pseudo-backdoors. In addition, we compare our learned approach against Gurobi, a state-of-the-art MIP solver, demonstrating that our method can be used to improve solver performance.
End-to-End Sequential Sampling and Reconstruction for MRITianwei Yin, Zihui Wu, He Sun et al.
Accelerated MRI shortens acquisition time by subsampling in the measurement $κ$-space. Recovering a high-fidelity anatomical image from subsampled measurements requires close cooperation between two components: (1) a sampler that chooses the subsampling pattern and (2) a reconstructor that recovers images from incomplete measurements. In this paper, we leverage the sequential nature of MRI measurements, and propose a fully differentiable framework that jointly learns a sequential sampling policy simultaneously with a reconstruction strategy. This co-designed framework is able to adapt during acquisition in order to capture the most informative measurements for a particular target. Experimental results on the fastMRI knee dataset demonstrate that the proposed approach successfully utilizes intermediate information during the sampling process to boost reconstruction performance. In particular, our proposed method can outperform the current state-of-the-art learned $κ$-space sampling baseline on over 96% of test samples. We also investigate the individual and collective benefits of the sequential sampling and co-design strategies.
The Multi-Agent Behavior Dataset: Mouse Dyadic Social InteractionsJennifer J. Sun, Tomomi Karigo, Dipam Chakraborty et al.
Multi-agent behavior modeling aims to understand the interactions that occur between agents. We present a multi-agent dataset from behavioral neuroscience, the Caltech Mouse Social Interactions (CalMS21) Dataset. Our dataset consists of trajectory data of social interactions, recorded from videos of freely behaving mice in a standard resident-intruder assay. To help accelerate behavioral studies, the CalMS21 dataset provides benchmarks to evaluate the performance of automated behavior classification methods in three settings: (1) for training on large behavioral datasets all annotated by a single annotator, (2) for style transfer to learn inter-annotator differences in behavior definitions, and (3) for learning of new behaviors of interest given limited training data. The dataset consists of 6 million frames of unlabeled tracked poses of interacting mice, as well as over 1 million frames with tracked poses and corresponding frame-level behavior annotations. The challenge of our dataset is to be able to classify behaviors accurately using both labeled and unlabeled tracking data, as well as being able to generalize to new settings.
14.6LGMar 2, 2021
Minimax Model LearningCameron Voloshin, Nan Jiang, Yisong Yue
We present a novel off-policy loss function for learning a transition model in model-based reinforcement learning. Notably, our loss is derived from the off-policy policy evaluation objective with an emphasis on correcting distribution shift. Compared to previous model-based techniques, our approach allows for greater robustness under model misspecification or distribution shift induced by learning/evaluating policies that are distinct from the data-generating policy. We provide a theoretical analysis and show empirical improvements over existing model-based off-policy evaluation methods. We provide further analysis showing our loss can be used for off-policy optimization (OPO) and demonstrate its integration with more recent improvements in OPO.
Computing the Information Content of Trained Neural NetworksJeremy Bernstein, Yisong Yue
How much information does a learning algorithm extract from the training data and store in a neural network's weights? Too much, and the network would overfit to the training data. Too little, and the network would not fit to anything at all. Naïvely, the amount of information the network stores should scale in proportion to the number of trainable weights. This raises the question: how can neural networks with vastly more weights than training data still generalise? A simple resolution to this conundrum is that the number of weights is usually a bad proxy for the actual amount of information stored. For instance, typical weight vectors may be highly compressible. Then another question occurs: is it possible to compute the actual amount of information stored? This paper derives both a consistent estimator and a closed-form upper bound on the information content of infinitely wide neural networks. The derivation is based on an identification between neural information content and the negative log probability of a Gaussian orthant. This identification yields bounds that analytically control the generalisation behaviour of the entire solution space of infinitely wide networks. The bounds have a simple dependence on both the network architecture and the training data. Corroborating the findings of Valle-Pérez et al. (2019), who conducted a similar analysis using approximate Gaussian integration techniques, the bounds are found to be both non-vacuous and correlated with the empirical generalisation behaviour at finite width.