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Neuroscience, Cognitive Science

Amelia Johnson, Michael Buice, Koosha Khalvati

Self-assessment of one’s choices, i.e., confidence, is the topic of many decision neuroscience studies. Computational models of confidence, however, are limited to specific scenarios such as between choices with the same value. Here we present a normative framework for modeling decision confidence that is generalizable to various tasks and experimental setups. We further drive the implications of our model from both theoretical and experimental points of view. Specifically, we show that our model maps to the planning as an inference framework where the objective function is maximizing the gained reward and information entropy of the policy. Moreover, we validate our model on two different psychophysics experiments and show its superiority over other approaches in explaining subjects' confidence reports.

Deep Learning · Theory

Chang hoon Song, Yesom Park, Myungjoo Kang

This paper analyzes the inverse relationship between the order of partial differential equations (PDEs) and the convergence of gradient descent in physics-informed neural networks (PINNs) with the power of ReLU activation. The integration of the PDE into a loss function endows PINNs with a distinctive feature to require computing derivatives of model up to the PDE order. Although it has been empirically observed that PINNs encounter difficulties in convergence when dealing with high-order or high-dimensional PDEs, a comprehensive theoretical understanding of this issue remains elusive. This paper offers theoretical support for this pathological behavior by demonstrating that the gradient flow converges in a lower probability when the PDE order is higher. In addition, we show that PINNs struggle to address high-dimensional problems because the influence of dimensionality on convergence is exacerbated with increasing PDE order. To address the pathology, we use the insights garnered to consider variable splitting that decomposes the high-order PDE into a system of lower-order PDEs. We prove that by reducing the differential order, the gradient flow of variable splitting is more likely to converge to the global optimum. Furthermore, we present numerical experiments in support of our theoretical claims.

Physical Models · Physics

Xiang Fu, Andrew Rosen, Kyle Bystrom, Rui Wang, Albert Musaelian, Boris Kozinsky, Tess Smidt, Tommi Jaakkola

In density functional theory, charge density is the core attribute of atomic systems from which all chemical properties can be derived. Machine learning methods are promising in significantly accelerating charge density prediction, yet existing approaches either lack accuracy or scalability. We propose a recipe that can achieve both. In particular, we identify three key ingredients: (1) representing the charge density with atomic and virtual orbitals (spherical fields centered at atom/virtual coordinates); (2) using expressive and learnable orbital basis sets (basis function for the spherical fields); and (3) using high-capacity equivariant neural network architecture. Our method achieves state-of-the-art accuracy while being more than an order of magnitude faster than existing methods. Furthermore, our method enables flexible efficiency-accuracy trade-offs by adjusting the model/basis sizes.

Reinforcement Learning · Multi-agent

Josh McClellan, Naveed Haghani, John Winder, Furong Huang, Pratap Tokekar

Multi-Agent Reinforcement Learning (MARL) struggles with sample inefficiency and poor generalization [1]. These challenges are partially due to a lack of structure or inductive bias in the neural networks typically used in learning the policy. One such form of structure that is commonly observed in multi-agent scenarios is symmetry. The field of Geometric Deep Learning has developed Equivariant Graph Neural Networks (EGNN) that are equivariant (or symmetric) to rotations, translations, and reflections of nodes. Incorporating equivariance has been shown to improve learning efficiency and decrease error [ 2 ]. In this paper, we demonstrate that EGNNs improve the sample efficiency and generalization in MARL. However, we also show that a naive application of EGNNs to MARL results in poor early exploration due to a bias in the EGNN structure. To mitigate this bias, we present Exploration-enhanced Equivariant Graph Neural Networks or E2GN2. We compare E2GN2 to other common function approximators using common MARL benchmarks MPE and SMACv2. E2GN2 demonstrates a significant improvement in sample efficiency, greater final reward convergence, and a 2x-5x gain in over standard GNNs in our generalization tests. These results pave the way for more reliable and effective solutions in complex multi-agent systems.

Physical Models · Physics

Jules Berman, Tobias Blickhan, Benjamin Peherstorfer

The aim of this work is to learn models of population dynamics of physical systems that feature stochastic and mean-field effects and that depend on physics parameters. The learned models can act as surrogates of classical numerical models to efficiently predict the system behavior over the physics parameters. Building on the Benamou-Brenier formula from optimal transport and action matching, we use a variational problem to infer parameter- and time-dependent gradient fields that represent approximations of the population dynamics. The inferred gradient fields can then be used to rapidly generate sample trajectories that mimic the dynamics of the physical system on a population level over varying physics parameters. We show that combining Monte Carlo sampling with higher-order quadrature rules is critical for accurately estimating the training objective from sample data and for stabilizing the training process. We demonstrate on Vlasov-Poisson instabilities as well as on high-dimensional particle and chaotic systems that our approach accurately predicts population dynamics over a wide range of parameters and outperforms state-of-the-art diffusion-based and flow-based modeling that simply condition on time and physics parameters.

Junhao Cai, Yuji Yang, Weihao Yuan, Yisheng HE, Zilong Dong, Liefeng Bo, Hui Cheng, Qifeng Chen

This paper studies the problem of estimating physical properties (system identification) through visual observations. To facilitate geometry-aware guidance in physical property estimation, we introduce a novel hybrid framework that leverages 3D Gaussian representation to not only capture explicit shapes but also enable the simulated continuum to render object masks as 2D shape surrogates during training. We propose a new dynamic 3D Gaussian framework based on motion factorization to recover the object as 3D Gaussian point sets across different time states. Furthermore, we develop a coarse-to-fine filling strategy to generate the density fields of the object from the Gaussian reconstruction, allowing for the extraction of object continuums along with their surfaces and the integration of Gaussian attributes into these continuum. In addition to the extracted object surfaces, the Gaussian-informed continuum also enables the rendering of object masks during simulations, serving as 2D-shape guidance for physical property estimation. Extensive experimental evaluations demonstrate that our pipeline achieves state-of-the-art performance across multiple benchmarks and metrics. Additionally, we illustrate the effectiveness of the proposed method through real-world demonstrations, showcasing its practical utility. Our project page is at https://jukgei.github.io/project/gic.

Generative Models · Diffusion models

Zhenzhi Wang, Jingbo Wang, Yixuan Li, Dahua Lin, Bo Dai

Text-conditioned motion synthesis has made remarkable progress with the emergence of diffusion models. However, the majority of these motion diffusion models are primarily designed for a single character and overlook multi-human interactions. In our approach, we strive to explore this problem by synthesizing human motion with interactions for a group of characters of any size in a zero-shot manner. The key aspect of our approach is the adaptation of human-wise interactions as pairs of human joints that can be either in contact or separated by a desired distance. In contrast to existing methods that necessitate training motion generation models on multi-human motion datasets with a fixed number of characters, our approach inherently possesses the flexibility to model human interactions involving an arbitrary number of individuals, thereby transcending the limitations imposed by the training data. We introduce a novel controllable motion generation method, InterControl, to encourage the synthesized motions maintaining the desired distance between joint pairs. It consists of a motion controller and an inverse kinematics guidance module that realistically and accurately aligns the joints of synthesized characters to the desired location. Furthermore, we demonstrate that the distance between joint pairs for human-wise interactions can be generated using an off-the-shelf Large Language Model (LLM). Experimental results highlight the capability of our framework to generate interactions with multiple human characters and its potential to work with off-the-shelf physics-based character simulators. Code is available at https://github.com/zhenzhiwang/intercontrol.

Trustworthy Machine Learning

Samuel Teuber, Stefan Mitsch, André Platzer

While neural networks (NNs) have a large potential as autonomous controllers for Cyber-Physical Systems, verifying the safety of neural network based control systems (NNCSs) poses significant challenges for the practical use of NNs— especially when safety is needed for unbounded time horizons. One reason for this is the intractability of analyzing NNs, ODEs and hybrid systems. To this end, we introduce VerSAILLE (Verifiably Safe AI via Logically Linked Envelopes): The first general approach that allows reusing control theory literature for NNCS verification. By joining forces, we can exploit the efficiency of NN verification tools while retaining the rigor of differential dynamic logic (dL). Based on a provably safe control envelope in dL, we derive a specification for the NN which is proven with NN verification tools. We show that a proof of the NN’s adherence to the specification is then mirrored by a dL proof on the infinite-time safety of the NNCS.The NN verification properties resulting from hybrid systems typically contain nonlinear arithmetic over formulas with arbitrary logical structure while efficient NN verification tools merely support linear constraints. To overcome this divide, we present Mosaic: An efficient, sound and complete verification approach for polynomial real arithmetic properties on piece-wise linear NNs. Mosaic partitions complex NN verification queries into simple queries and lifts off-the-shelf linear constraint tools to the nonlinear setting in a completeness-preserving manner by combining approximation with exact reasoning for counterexample regions. In our evaluation we demonstrate the versatility of VerSAILLE and Mosaic: We prove infinite-time safety on the classical Vertical Airborne Collision Avoidance NNCS verification benchmark for some scenarios while (exhaustively) enumerating counterexample regions in unsafe scenarios. We also show that our approach significantly outperforms the State-of-the-Art tools in closed-loop NNV

Generative Models · Diffusion models

Yiheng Li, Heyang Jiang, Akio Kodaira, Masayoshi TOMIZUKA, Kurt Keutzer, Chenfeng Xu

In this paper, we point out that suboptimal noise-data mapping leads to slow training of diffusion models. During diffusion training, current methods diffuse each image across the entire noise space, resulting in a mixture of all images at every point in the noise layer. We emphasize that this random mixture of noise-data mapping complicates the optimization of the denoising function in diffusion models. Drawing inspiration from the immiscibility phenomenon in physics, we propose *Immiscible Diffusion*, a simple and effective method to improve the random mixture of noise-data mapping. In physics, miscibility can vary according to various intermolecular forces. Thus, immiscibility means that the mixing of molecular sources is distinguishable. Inspired by this concept, we propose an assignment-then-diffusion training strategy to achieve *Immiscible Diffusion*. As one example, prior to diffusing the image data into noise, we assign diffusion target noise for the image data by minimizing the total image-noise pair distance in a mini-batch. The assignment functions analogously to external forces to expel the diffuse-able areas of images, thus mitigating the inherent difficulties in diffusion training. Our approach is remarkably simple, requiring only *one line of code* to restrict the diffuse-able area for each image while preserving the Gaussian distribution of noise. In this way, each image is preferably projected to nearby noise. To address the high complexity of the assignment algorithm, we employ a quantized assignment strategy, which significantly reduces the computational overhead to a negligible level (e.g. 22.8ms for a large batch size of 1024 on an A6000). Experiments demonstrate that our method can achieve up to 3x faster training for unconditional Consistency Models on the CIFAR dataset, as well as for DDIM and Stable Diffusion on CelebA and ImageNet dataset, and in class-conditional training and fine-tuning. In addition, we conducted a thorough analysis that sheds light on how it improves diffusion training speed while improving fidelity. The code is available at https://yhli123.github.io/immiscible-diffusion

Computer Vision

Cuong Le, John Viktor Johansson, Manon Kok, Bastian Wandt

Human motion capture from monocular videos has made significant progress in recent years. However, modern approaches often produce temporal artifacts, e.g. in form of jittery motion and struggle to achieve smooth and physically plausible motions. Explicitly integrating physics, in form of internal forces and exterior torques, helps alleviating these artifacts. Current state-of-the-art approaches make use of an automatic PD controller to predict torques and reaction forces in order to re-simulate the input kinematics, i.e. the joint angles of a predefined skeleton. However, due to imperfect physical models, these methods often require simplifying assumptions and extensive preprocessing of the input kinematics to achieve good performance. To this end, we propose a novel method to selectively incorporate the physics models with the kinematics observations in an online setting, inspired by a neural Kalman-filtering approach. We develop a control loop as a meta-PD controller to predict internal joint torques and external reaction forces, followed by a physics-based motion simulation. A recurrent neural network is introduced to realize a Kalman filter that attentively balances the kinematics input and simulated motion, resulting in an optimal-state dynamics prediction. We show that this filtering step is crucial to provide an online supervision that helps balancing the shortcoming of the respective input motions, thus being important for not only capturing accurate global motion trajectories but also producing physically plausible human poses. The proposed approach excels in the physics-based human pose estimation task and demonstrates the physical plausibility of the predictive dynamics, compared to state of the art. The code is available on https://github.com/cuongle1206/OSDCap.

Neuroscience, Cognitive Science

Yuchen Zhou, Emmy Liu, Graham Neubig, Michael Tarr, Leila Wehbe

Do machines and humans process language in similar ways? Recent research has hinted at the affirmative, showing that human neural activity can be effectively predicted using the internal representations of language models (LMs). Although such results are thought to reflect shared computational principles between LMs and human brains, there are also clear differences in how LMs and humans represent and use language. In this work, we systematically explore the divergences between human and machine language processing by examining the differences between LM representations and human brain responses to language as measured by Magnetoencephalography (MEG) across two datasets in which subjects read and listened to narrative stories. Using an LLM-based data-driven approach, we identify two domains that LMs do not capture well: social/emotional intelligence and physical commonsense. We validate these findings with human behavioral experiments and hypothesize that the gap is due to insufficient representations of social/emotional and physical knowledge in LMs. Our results show that fine-tuning LMs on these domains can improve their alignment with human brain responses.

Generative Models · Diffusion models

Jacob K Christopher, Stephen Baek, Nando Fioretto

This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative diffusion models as a constrained optimization problem, steering the generated data distribution to remain within a specified region to ensure adherence to the given constraints.These capabilities are validated on applications featuring both convex and challenging, non-convex, constraints as well as ordinary differential equations, in domains spanning from synthesizing new materials with precise morphometric properties, generating physics-informed motion, optimizing paths in planning scenarios, and human motion synthesis.

Generative Models

Minghao Guo, Bohan Wang, Pingchuan Ma, Tianyuan Zhang, Crystal Owens, Chuang Gan, Josh Tenenbaum, Kaiming He, Wojciech Matusik

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and rest-shape geometry. Existing single-view 3D reconstruction methods often overlook this underlying composition, presuming rigidity or neglecting external forces. Consequently, the reconstructed objects fail to withstand real-world physical forces, resulting in instability or undesirable deformation -- diverging from their intended designs as depicted in the image. Our optimization framework addresses this by embedding physical compatibility into the reconstruction process. We explicitly decompose the three physical attributes and link them through static equilibrium, which serves as a hard constraint, ensuring that the optimized physical shapes exhibit desired physical behaviors. Evaluations on a dataset collected from Objaverse demonstrate that our framework consistently enhances the physical realism of 3D models over existing methods. The utility of our framework extends to practical applications in dynamic simulations and 3D printing, where adherence to physical compatibility is paramount.

Online Learning

Skyler Wu, Fred Lu, Edward Raff, James Holt

Online learning methods, like the seminal Passive-Aggressive (PA) classifier, are still highly effective for high-dimensional streaming data, out-of-core processing, and other throughput-sensitive applications. Many such algorithms rely on fast adaptation to individual errors as a key to their convergence. While such algorithms enjoy low theoretical regret, in real-world deployment they can be sensitive to individual outliers that cause the algorithm to over-correct. When such outliers occur at the end of the data stream, this can cause the final solution to have unexpectedly low accuracy. We design a weighted reservoir sampling (WRS) approach to obtain a stable ensemble model from the sequence of solutions without requiring additional passes over the data, hold-out sets, or a growing amount of memory. Our key insight is that good solutions tend to be error-free for more iterations than bad solutions, and thus, the number of passive rounds provides an estimate of a solution's relative quality. Our reservoir thus contains $K$ previous intermediate weight vectors with high survival times. We demonstrate our WRS approach on the Passive-Aggressive Classifier (PAC) and First-Order Sparse Online Learning (FSOL), where our method consistently and significantly outperforms the unmodified approach. We show that the risk of the ensemble classifier is bounded with respect to the regret of the underlying online learning method.

Robotics

Siddhant Haldar, Zhuoran Peng, Lerrel Pinto

Training generalist agents capable of solving diverse tasks is challenging, often requiring large datasets of expert demonstrations. This is particularly problematic in robotics, where each data point requires physical execution of actions in the real world. Thus, there is a pressing need for architectures that can effectively leverage the available training data. In this work, we present BAKU, a simple transformer architecture that enables efficient learning of multi-task robot policies. BAKU builds upon recent advancements in offline imitation learning and meticulously combines observation trunks, action chunking, multi-sensory observations, and action heads to substantially improve upon prior work. Our experiments on 129 simulated tasks across LIBERO, Meta-World suite, and the Deepmind Control suite exhibit an overall 18% absolute improvement over RT-1 and MT-ACT, with a 36% improvement on the harder LIBERO benchmark. On 30 real-world manipulation tasks, given an average of just 17 demonstrations per task, BAKU achieves a 91% success rate. Videos of the robot are best viewed at baku-robot.github.io.

Physical Models · Physics

Yifei Li, Yuchen Sun, Pingchuan Ma, Eftychios Sifakis, Tao Du, Bo Zhu, Wojciech Matusik

We present NeuralFluid, a novel framework to explore neural control and design of complex fluidic systems with dynamic solid boundaries. Our system features a fast differentiable Navier-Stokes solver with solid-fluid interface handling, a low-dimensional differentiable parametric geometry representation, a control-shape co-design algorithm, and gym-like simulation environments to facilitate various fluidic control design applications. Additionally, we present a benchmark of design, control, and learning tasks on high-fidelity, high-resolution dynamic fluid environments that pose challenges for existing differentiable fluid simulators. These tasks include designing the control of artificial hearts, identifying robotic end-effector shapes, and controlling a fluid gate. By seamlessly incorporating our differentiable fluid simulator into a learning framework, we demonstrate successful design, control, and learning results that surpass gradient-free solutions in these benchmark tasks.

Physical Models · Climate

Robert Garrett, Trevor Harris, Zhuo Wang, Bo Li

The validation of global climate models is crucial to ensure the accuracy and efficacy of model output. We introduce the spherical convolutional Wasserstein distance to more comprehensively measure differences between climate models and reanalysis data. This new similarity measure accounts for spatial variability using convolutional projections and quantifies local differences in the distribution of climate variables. We apply this method to evaluate the historical model outputs of the Coupled Model Intercomparison Project (CMIP) members by comparing them to observational and reanalysis data products. Additionally, we investigate the progression from CMIP phase 5 to phase 6 and find modest improvements in the phase 6 models regarding their ability to produce realistic climatologies.

Physical Models · Physics

Jonas Spinner, Victor Breso, Pim de Haan, Tilman Plehn, Jesse Thaler, Johann Brehmer

Extracting scientific understanding from particle-physics experiments requires solving diverse learning problems with high precision and good data efficiency. We propose the Lorentz Geometric Algebra Transformer (L-GATr), a new multi-purpose architecture for high-energy physics. L-GATr represents high-energy data in a geometric algebra over four-dimensional space-time and is equivariant under Lorentz transformations, the symmetry group of relativistic kinematics. At the same time, the architecture is a Transformer, which makes it versatile and scalable to large systems. L-GATr is first demonstrated on regression and classification tasks from particle physics. We then construct the first Lorentz-equivariant generative model: a continuous normalizing flow based on an L-GATr network, trained with Riemannian flow matching. Across our experiments, L-GATr is on par with or outperforms strong domain-specific baselines.

Language · Speech

Nicholas Babaev, Kirill Tamogashev, Azat Saginbaev, Ivan Shchekotov, Hanbin Bae, Hosang Sung, WonJun Lee, Hoon-Young Cho, Pavel Andreev

In this paper, we address the challenge of speech enhancement in real-world recordings, which often contain various forms of distortion, such as background noise, reverberation, and microphone artifacts.We revisit the use of Generative Adversarial Networks (GANs) for speech enhancement and theoretically show that GANs are naturally inclined to seek the point of maximum density within the conditional clean speech distribution, which, as we argue, is essential for speech enhancement task.We study various feature extractors for perceptual loss to facilitate the stability of adversarial training, developing a methodology for probing the structure of the feature space.This leads us to integrate WavLM-based perceptual loss into MS-STFT adversarial training pipeline, creating an effective and stable training procedure for the speech enhancement model.The resulting speech enhancement model, which we refer to as FINALLY, builds upon the HiFi++ architecture, augmented with a WavLM encoder and a novel training pipeline.Empirical results on various datasets confirm our model's ability to produce clear, high-quality speech at 48 kHz, achieving state-of-the-art performance in the field of speech enhancement. Demo page: https://samsunglabs.github.io/FINALLY-page/

Reinforcement Learning · Multi-agent

Tao Jiang, Lei Yuan, Lihe Li, Cong Guan, Zongzhang Zhang, Yang Yu

The shift in dynamics results in significant performance degradation of policies trained in the source domain when deployed in a different target domain, posing a challenge for the practical application of reinforcement learning (RL) in real-world scenarios. Domain transfer methods aim to bridge this dynamics gap through techniques such as domain adaptation or domain calibration. While domain adaptation involves refining the policy through extensive interactions in the target domain, it may not be feasible for sensitive fields like healthcare and autonomous driving. On the other hand, offline domain calibration utilizes only static data from the target domain to adjust the physics parameters of the source domain (e.g., a simulator) to align with the target dynamics, enabling the direct deployment of the trained policy without sacrificing performance, which emerges as the most promising for policy deployment. However, existing techniques primarily rely on evolution algorithms for calibration, resulting in low sample efficiency.To tackle this issue, we propose a novel framework Madoc (\textbf{M}ulti-\textbf{a}gent \textbf{do}main \textbf{c}alibration). Firstly, we formulate a bandit RL objective to match the target trajectory distribution by learning a couple of classifiers. We then address the challenge of a large domain parameter space by modeling domain calibration as a cooperative multi-agent reinforcement learning (MARL) problem. Specifically, we utilize a Variational Autoencoder (VAE) to automatically cluster physics parameters with similar effects on the dynamics, grouping them into distinct agents. These grouped agents train calibration policies coordinately to adjust multiple parameters using MARL.Our empirical evaluation on 21 offline locomotion tasks in D4RL and NeoRL benchmarks showcases the superior performance of our method compared to strong existing offline model-based RL, offline domain calibration, and hybrid offline-and-online RL baselines.