LinSATNet: The Positive Linear Satisfiability Neural Networks

Encoding constraints into neural networks is attractive. This paper studies how to introduce the popular positive linear satisfiability to neural networks. We propose the first differentiable satisfiability layer based on an extension of the classic Sinkhorn algorithm for jointly encoding multiple sets of marginal distributions. We further theoretically characterize the convergence property of the Sinkhorn algorithm for multiple marginals. In contrast to the sequential decision e.g.\ reinforcement learning-based solvers, we showcase our technique in solving constrained (specifically satisfiability) problems by one-shot neural networks, including i) a neural routing solver learned without supervision of optimal solutions; ii) a partial graph matching network handling graphs with unmatchable outliers on both sides; iii) a predictive network for financial portfolios with continuous constraints. To our knowledge, there exists no one-shot neural solver for these scenarios when they are formulated as satisfiability problems. Source code is available at https://github.com/Thinklab-SJTU/LinSATNet

FORA: Fast-Forward Caching in Diffusion Transformer Acceleration

Diffusion transformers (DiT) have become the de facto choice for generating high-quality images and videos, largely due to their scalability, which enables the construction of larger models for enhanced performance. However, the increased size of these models leads to higher inference costs, making them less attractive for real-time applications. We present Fast-FORward CAching (FORA), a simple yet effective approach designed to accelerate DiT by exploiting the repetitive nature of the diffusion process. FORA implements a caching mechanism that stores and reuses intermediate outputs from the attention and MLP layers across denoising steps, thereby reducing computational overhead. This approach does not require model retraining and seamlessly integrates with existing transformer-based diffusion models. Experiments show that FORA can speed up diffusion transformers several times over while only minimally affecting performance metrics such as the IS Score and FID. By enabling faster processing with minimal trade-offs in quality, FORA represents a significant advancement in deploying diffusion transformers for real-time applications. Code will be made publicly available at: https://github.com/prathebaselva/FORA.

Towards Exact Gradient-based Training on Analog In-memory Computing

Given the high economic and environmental costs of using large vision or language models, analog in-memory accelerators present a promising solution for energy-efficient AI. While inference on analog accelerators has been studied recently, the training perspective is underexplored. Recent studies have shown that the "workhorse" of digital AI training - stochastic gradient descent (SGD) algorithm converges inexactly when applied to model training on non-ideal devices. This paper puts forth a theoretical foundation for gradient-based training on analog devices. We begin by characterizing the non-convergent issue of SGD, which is caused by the asymmetric updates on the analog devices. We then provide a lower bound of the asymptotic error to show that there is a fundamental performance limit of SGD-based analog training rather than an artifact of our analysis. To address this issue, we study a heuristic analog algorithm called Tiki-Taka that has recently exhibited superior empirical performance compared to SGD and rigorously show its ability to exactly converge to a critical point and hence eliminates the asymptotic error. The simulations verify the correctness of the analyses.

A Primal-Dual-Assisted Penalty Approach to Bilevel Optimization with Coupled Constraints

Interest in bilevel optimization has grown in recent years, partially due to its applications to tackle challenging machine-learning problems. Several exciting recent works have been centered around developing efficient gradient-based algorithms that can solve bilevel optimization problems with provable guarantees. However, the existing literature mainly focuses on bilevel problems either without constraints, or featuring only simple constraints that do not couple variables across the upper and lower levels, excluding a range of complex applications. Our paper studies this challenging but less explored scenario and develops a (fully) first-order algorithm, which we term BLOCC, to tackle BiLevel Optimization problems with Coupled Constraints. We establish rigorous convergence theory for the proposed algorithm and demonstrate its effectiveness on two well-known real-world applications - hyperparameter selection in support vector machine (SVM) and infrastructure planning in transportation networks using the real data from the city of Seville.

Exploring Key Factors for Long-Term Vessel Incident Risk Prediction

Factor analysis acts a pivotal role in enhancing maritime safety. Most previous studies conduct factor analysis within the framework of incident-related label prediction, where the developed models can be categorized into short-term and long-term prediction models. The long-term models offer a more strategic approach, enabling more proactive risk management, compared to the short-term ones. Nevertheless, few studies have devoted to rigorously identifying the key factors for the long-term prediction and undertaking comprehensive factor analysis. Hence, this study aims to delve into the key factors for predicting the incident risk levels in the subsequent year given a specific datestamp. The majority of candidate factors potentially contributing to the incident risk are collected from vessels' historical safety performance data spanning up to five years. An improved embedded feature selection, which integrates Random Forest classifier with a feature filtering process is proposed to identify key risk-contributing factors from the candidate pool. The results demonstrate superior performance of the proposed method in incident prediction and factor interpretability. Comprehensive analysis is conducted upon the key factors, which could help maritime stakeholders formulate management strategies for incident prevenion.

Assessing Image Inpainting via Re-Inpainting Self-Consistency Evaluation

Image inpainting, the task of reconstructing missing segments in corrupted images using available data, faces challenges in ensuring consistency and fidelity, especially under information-scarce conditions. Traditional evaluation methods, heavily dependent on the existence of unmasked reference images, inherently favor certain inpainting outcomes, introducing biases. Addressing this issue, we introduce an innovative evaluation paradigm that utilizes a self-supervised metric based on multiple re-inpainting passes. This approach, diverging from conventional reliance on direct comparisons in pixel or feature space with original images, emphasizes the principle of self-consistency to enable the exploration of various viable inpainting solutions, effectively reducing biases. Our extensive experiments across numerous benchmarks validate the alignment of our evaluation method with human judgment.

Analytic Federated Learning

In this paper, we introduce analytic federated learning (AFL), a new training paradigm that brings analytical (i.e., closed-form) solutions to the federated learning (FL) community. Our AFL draws inspiration from analytic learning -- a gradient-free technique that trains neural networks with analytical solutions in one epoch. In the local client training stage, the AFL facilitates a one-epoch training, eliminating the necessity for multi-epoch updates. In the aggregation stage, we derive an absolute aggregation (AA) law. This AA law allows a single-round aggregation, removing the need for multiple aggregation rounds. More importantly, the AFL exhibits a \textit{weight-invariant} property, meaning that regardless of how the full dataset is distributed among clients, the aggregated result remains identical. This could spawn various potentials, such as data heterogeneity invariance, client-number invariance, absolute convergence, and being hyperparameter-free (our AFL is the first hyperparameter-free method in FL history). We conduct experiments across various FL settings including extremely non-IID ones, and scenarios with a large number of clients (e.g., $\ge 1000$). In all these settings, our AFL constantly performs competitively while existing FL techniques encounter various obstacles. Code is available at \url{https://github.com/ZHUANGHP/Analytic-federated-learning}

SF-DQN: Provable Knowledge Transfer using Successor Feature for Deep Reinforcement Learning

This paper studies the transfer reinforcement learning (RL) problem where multiple RL problems have different reward functions but share the same underlying transition dynamics. In this setting, the Q-function of each RL problem (task) can be decomposed into a successor feature (SF) and a reward mapping: the former characterizes the transition dynamics, and the latter characterizes the task-specific reward function. This Q-function decomposition, coupled with a policy improvement operator known as generalized policy improvement (GPI), reduces the sample complexity of finding the optimal Q-function, and thus the SF \& GPI framework exhibits promising empirical performance compared to traditional RL methods like Q-learning. However, its theoretical foundations remain largely unestablished, especially when learning the successor features using deep neural networks (SF-DQN). This paper studies the provable knowledge transfer using SFs-DQN in transfer RL problems. We establish the first convergence analysis with provable generalization guarantees for SF-DQN with GPI. The theory reveals that SF-DQN with GPI outperforms conventional RL approaches, such as deep Q-network, in terms of both faster convergence rate and better generalization. Numerical experiments on real and synthetic RL tasks support the superior performance of SF-DQN \& GPI, aligning with our theoretical findings.

ManiFoundation Model for General-Purpose Robotic Manipulation of Contact Synthesis with Arbitrary Objects and Robots

To substantially enhance robot intelligence, there is a pressing need to develop a large model that enables general-purpose robots to proficiently undertake a broad spectrum of manipulation tasks, akin to the versatile task-planning ability exhibited by LLMs. The vast diversity in objects, robots, and manipulation tasks presents huge challenges. Our work introduces a comprehensive framework to develop a foundation model for general robotic manipulation that formalizes a manipulation task as contact synthesis. Specifically, our model takes as input object and robot manipulator point clouds, object physical attributes, target motions, and manipulation region masks. It outputs contact points on the object and associated contact forces or post-contact motions for robots to achieve the desired manipulation task. We perform extensive experiments both in the simulation and real-world settings, manipulating articulated rigid objects, rigid objects, and deformable objects that vary in dimensionality, ranging from one-dimensional objects like ropes to two-dimensional objects like cloth and extending to three-dimensional objects such as plasticine. Our model achieves average success rates of around 90\%. Supplementary materials and videos are available on our project website at https://manifoundationmodel.github.io/.

Efficient and Flexible Method for Reducing Moderate-size Deep Neural Networks with Condensation

Neural networks have been extensively applied to a variety of tasks, achieving astounding results. Applying neural networks in the scientific field is an important research direction that is gaining increasing attention. In scientific applications, the scale of neural networks is generally moderate-size, mainly to ensure the speed of inference during application. Additionally, comparing neural networks to traditional algorithms in scientific applications is inevitable. These applications often require rapid computations, making the reduction of neural network sizes increasingly important. Existing work has found that the powerful capabilities of neural networks are primarily due to their non-linearity. Theoretical work has discovered that under strong non-linearity, neurons in the same layer tend to behave similarly, a phenomenon known as condensation. Condensation offers an opportunity to reduce the scale of neural networks to a smaller subnetwork with similar performance. In this article, we propose a condensation reduction algorithm to verify the feasibility of this idea in practical problems. Our reduction method can currently be applied to both fully connected networks and convolutional networks, achieving positive results. In complex combustion acceleration tasks, we reduced the size of the neural network to 41.7% of its original scale while maintaining prediction accuracy. In the CIFAR10 image classification task, we reduced the network size to 11.5% of the original scale, still maintaining a satisfactory validation accuracy. Our method can be applied to most trained neural networks, reducing computational pressure and improving inference speed.