Neural networks are emerging as a tool for scalable data-driven simulation of high-dimensional dynamical systems, especially in settings where numerical methods are infeasible or computationally expensive. Notably, it has been shown that incorporating domain symmetries in deterministic neural simulators can substantially improve their accuracy, sample efficiency, and parameter efficiency. However, to incorporate symmetries in probabilistic neural simulators that can simulate stochastic phenomena, we need a model that produces equivariant distributions over trajectories, rather than equivariant function approximations. In this paper, we propose Equivariant Probabilistic Neural Simulation (EPNS), a framework for autoregressive probabilistic modeling of equivariant distributions over system evolutions. We use EPNS to design models for a stochastic n-body system and stochastic cellular dynamics. Our results show that EPNS considerably outperforms existing neural network-based methods for probabilistic simulation. More specifically, we demonstrate that incorporating equivariance in EPNS improves simulation quality, data efficiency, rollout stability, and uncertainty quantification. We conclude that EPNS is a promising method for efficient and effective data-driven probabilistic simulation in a diverse range of domains.
相關內容
We develop and analyze stochastic approximation algorithms for solving nested compositional bi-level optimization problems. These problems involve a nested composition of $T$ potentially non-convex smooth functions in the upper-level, and a smooth and strongly convex function in the lower-level. Our proposed algorithm does not rely on matrix inversions or mini-batches and can achieve an $\epsilon$-stationary solution with an oracle complexity of approximately $\tilde{O}_T(1/\epsilon^{2})$, assuming the availability of stochastic first-order oracles for the individual functions in the composition and the lower-level, which are unbiased and have bounded moments. Here, $\tilde{O}_T$ hides polylog factors and constants that depend on $T$. The key challenge we address in establishing this result relates to handling three distinct sources of bias in the stochastic gradients. The first source arises from the compositional nature of the upper-level, the second stems from the bi-level structure, and the third emerges due to the utilization of Neumann series approximations to avoid matrix inversion. To demonstrate the effectiveness of our approach, we apply it to the problem of robust feature learning for deep neural networks under covariate shift, showcasing the benefits and advantages of our methodology in that context.
We report a flexible language-model based deep learning strategy, applied here to solve complex forward and inverse problems in protein modeling, based on an attention neural network that integrates transformer and graph convolutional architectures in a causal multi-headed graph mechanism, to realize a generative pretrained model. The model is applied to predict secondary structure content (per-residue level and overall content), protein solubility, and sequencing tasks. Further trained on inverse tasks, the model is rendered capable of designing proteins with these properties as target features. The model is formulated as a general framework, completely prompt-based, and can be adapted for a variety of downstream tasks. We find that adding additional tasks yields emergent synergies that the model exploits in improving overall performance, beyond what would be possible by training a model on each dataset alone. Case studies are presented to validate the method, yielding protein designs specifically focused on structural proteins, but also exploring the applicability in the design of soluble, antimicrobial biomaterials. While our model is trained to ultimately perform 8 distinct tasks, with available datasets it can be extended to solve additional problems. In a broader sense, this work illustrates a form of multiscale modeling that relates a set of ultimate building blocks (here, byte-level utf8 characters that define the nature of the physical system at hand) to complex output. This materiomic scheme captures complex emergent relationships between universal building block and resulting properties via a synergizing learning capacity to express a set of potentialities embedded in the knowledge used in training, via the interplay of universality and diversity.
Movement primitives are trainable parametric models that reproduce robotic movements starting from a limited set of demonstrations. Previous works proposed simple linear models that exhibited high sample efficiency and generalization power by allowing temporal modulation of movements (reproducing movements faster or slower), blending (merging two movements into one), via-point conditioning (constraining a movement to meet some particular via-points) and context conditioning (generation of movements based on an observed variable, e.g., position of an object). Previous works have proposed neural network-based motor primitive models, having demonstrated their capacity to perform tasks with some forms of input conditioning or time-modulation representations. However, there has not been a single unified deep motor primitive's model proposed that is capable of all previous operations, limiting neural motor primitive's potential applications. This paper proposes a deep movement primitive architecture that encodes all the operations above and uses a Bayesian context aggregator that allows a more sound context conditioning and blending. Our results demonstrate our approach can scale to reproduce complex motions on a larger variety of input choices compared to baselines while maintaining operations of linear movement primitives provide.
Rendering photorealistic and dynamically moving human heads is crucial for ensuring a pleasant and immersive experience in AR/VR and video conferencing applications. However, existing methods often struggle to model challenging facial regions (e.g., mouth interior, eyes, hair/beard), resulting in unrealistic and blurry results. In this paper, we propose {\fullname} ({\name}), a method that adopts the neural point representation as well as the neural volume rendering process and discards the predefined connectivity and hard correspondence imposed by mesh-based approaches. Specifically, the neural points are strategically constrained around the surface of the target expression via a high-resolution UV displacement map, achieving increased modeling capacity and more accurate control. We introduce three technical innovations to improve the rendering and training efficiency: a patch-wise depth-guided (shading point) sampling strategy, a lightweight radiance decoding process, and a Grid-Error-Patch (GEP) ray sampling strategy during training. By design, our {\name} is better equipped to handle topologically changing regions and thin structures while also ensuring accurate expression control when animating avatars. Experiments conducted on three subjects from the Multiface dataset demonstrate the effectiveness of our designs, outperforming previous state-of-the-art methods, especially in handling challenging facial regions.
Safe exploration aims at addressing the limitations of Reinforcement Learning (RL) in safety-critical scenarios, where failures during trial-and-error learning may incur high costs. Several methods exist to incorporate external knowledge or to use proximal sensor data to limit the exploration of unsafe states. However, reducing exploration risks in unknown environments, where an agent must discover safety threats during exploration, remains challenging. In this paper, we target the problem of safe exploration by guiding the training with counterexamples of the safety requirement. Our method abstracts both continuous and discrete state-space systems into compact abstract models representing the safety-relevant knowledge acquired by the agent during exploration. We then exploit probabilistic counterexample generation to construct minimal simulation submodels eliciting safety requirement violations, where the agent can efficiently train offline to refine its policy towards minimising the risk of safety violations during the subsequent online exploration. We demonstrate our method's effectiveness in reducing safety violations during online exploration in preliminary experiments by an average of 40.3% compared with QL and DQN standard algorithms and 29.1% compared with previous related work, while achieving comparable cumulative rewards with respect to unrestricted exploration and alternative approaches.
Reinforcement learning has been successful across several applications in which agents have to learn to act in environments with sparse feedback. However, despite this empirical success there is still a lack of theoretical understanding of how the parameters of reinforcement learning models and the features used to represent states interact to control the dynamics of learning. In this work, we use concepts from statistical physics, to study the typical case learning curves for temporal difference learning of a value function with linear function approximators. Our theory is derived under a Gaussian equivalence hypothesis where averages over the random trajectories are replaced with temporally correlated Gaussian feature averages and we validate our assumptions on small scale Markov Decision Processes. We find that the stochastic semi-gradient noise due to subsampling the space of possible episodes leads to significant plateaus in the value error, unlike in traditional gradient descent dynamics. We study how learning dynamics and plateaus depend on feature structure, learning rate, discount factor, and reward function. We then analyze how strategies like learning rate annealing and reward shaping can favorably alter learning dynamics and plateaus. To conclude, our work introduces new tools to open a new direction towards developing a theory of learning dynamics in reinforcement learning.
Temporal Point Processes (TPPs) serve as the standard mathematical framework for modeling asynchronous event sequences in continuous time. However, classical TPP models are often constrained by strong assumptions, limiting their ability to capture complex real-world event dynamics. To overcome this limitation, researchers have proposed Neural TPPs, which leverage neural network parametrizations to offer more flexible and efficient modeling. While recent studies demonstrate the effectiveness of Neural TPPs, they often lack a unified setup, relying on different baselines, datasets, and experimental configurations. This makes it challenging to identify the key factors driving improvements in predictive accuracy, hindering research progress. To bridge this gap, we present a comprehensive large-scale experimental study that systematically evaluates the predictive accuracy of state-of-the-art neural TPP models. Our study encompasses multiple real-world and synthetic event sequence datasets, following a carefully designed unified setup. We thoroughly investigate the influence of major architectural components such as event encoding, history encoder, and decoder parametrization on both time and mark prediction tasks. Additionally, we delve into the less explored area of probabilistic calibration for neural TPP models. By analyzing our results, we draw insightful conclusions regarding the significance of history size and the impact of architectural components on predictive accuracy. Furthermore, we shed light on the miscalibration of mark distributions in neural TPP models. Our study aims to provide valuable insights into the performance and characteristics of neural TPP models, contributing to a better understanding of their strengths and limitations.
This paper addresses the challenges of optimally placing a finite number of sensors to detect Poisson-distributed targets in a bounded domain. We seek to rigorously account for uncertainty in the target arrival model throughout the problem. Sensor locations are selected to maximize the probability that no targets are missed. While this objective function is well-suited to applications where failure to detect targets is highly undesirable, it does not lead to a computationally efficient optimization problem. We propose an approximation of the objective function that is non-negative, submodular, and monotone and for which greedy selection of sensor locations works well. We also characterize the gap between the desired objective function and our approximation. For numerical illustrations, we consider the case of the detection of ship traffic using sensors mounted on the seafloor.
We study how to release summary statistics on a data stream subject to the constraint of differential privacy. In particular, we focus on releasing the family of symmetric norms, which are invariant under sign-flips and coordinate-wise permutations on an input data stream and include $L_p$ norms, $k$-support norms, top-$k$ norms, and the box norm as special cases. Although it may be possible to design and analyze a separate mechanism for each symmetric norm, we propose a general parametrizable framework that differentially privately releases a number of sufficient statistics from which the approximation of all symmetric norms can be simultaneously computed. Our framework partitions the coordinates of the underlying frequency vector into different levels based on their magnitude and releases approximate frequencies for the "heavy" coordinates in important levels and releases approximate level sizes for the "light" coordinates in important levels. Surprisingly, our mechanism allows for the release of an arbitrary number of symmetric norm approximations without any overhead or additional loss in privacy. Moreover, our mechanism permits $(1+\alpha)$-approximation to each of the symmetric norms and can be implemented using sublinear space in the streaming model for many regimes of the accuracy and privacy parameters.
Deep Ensembles, as a type of Bayesian Neural Networks, can be used to estimate uncertainty on the prediction of multiple neural networks by collecting votes from each network and computing the difference in those predictions. In this paper, we introduce a method for uncertainty estimation that considers a set of independent categorical distributions for each layer of the network, giving many more possible samples with overlapped layers than in the regular Deep Ensembles. We further introduce an optimized inference procedure that reuses common layer outputs, achieving up to 19x speed up and reducing memory usage quadratically. We also show that the method can be further improved by ranking samples, resulting in models that require less memory and time to run while achieving higher uncertainty quality than Deep Ensembles.
小貼士
登錄享
相關主題
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191