ZKP systems have surged attention and held a fundamental role in contemporary cryptography. Zk-SNARK protocols dominate the ZKP usage, often implemented through arithmetic circuit programming paradigm. However, underconstrained or overconstrained circuits may lead to bugs. Underconstrained circuits refer to circuits that lack the necessary constraints, resulting in unexpected solutions in the circuit and causing the verifier to accept a bogus witness. Overconstrained circuits refer to circuits that are constrained excessively, resulting in the circuit lacking necessary solutions and causing the verifier to accept no witness, rendering the circuit meaningless. This paper introduces a novel approach for pinpointing two distinct types of bugs in ZKP circuits. The method involves encoding the arithmetic circuit constraints to polynomial equation systems and solving polynomial equation systems over a finite field by algebraic computation. The classification of verification results is refined, greatly enhancing the expressive power of the system. We proposed a tool, AC4, to represent the implementation of this method. Experiments demonstrate that AC4 represents a substantial 29% increase in the checked ratio compared to prior work. Within a solvable range, the checking time of AC4 has also exhibited noticeable improvement, demonstrating a magnitude increase compared to previous efforts.

This paper considers a Min-Max Multiple Traveling Salesman Problem (MTSP), where the goal is to find a set of tours, one for each agent, to collectively visit all the cities while minimizing the length of the longest tour. Though MTSP has been widely studied, obtaining near-optimal solutions for large-scale problems is still challenging due to its NP-hardness. Recent efforts in data-driven methods face challenges of the need for hard-to-obtain supervision and issues with high variance in gradient estimations, leading to slow convergence and highly suboptimal solutions. We address these issues by reformulating MTSP as a bilevel optimization problem, using the concept of imperative learning (IL). This involves introducing an allocation network that decomposes the MTSP into multiple single-agent traveling salesman problems (TSPs). The longest tour from these TSP solutions is then used to self-supervise the allocation network, resulting in a new self-supervised, bilevel, end-to-end learning framework, which we refer to as imperative MTSP (iMTSP). Additionally, to tackle the high-variance gradient issues during the optimization, we introduce a control variate-based gradient estimation algorithm. Our experiments showed that these innovative designs enable our gradient estimator to converge 20% faster than the advanced reinforcement learning baseline and find up to 80% shorter tour length compared with Google OR-Tools MTSP solver, especially in large-scale problems (e.g. 1000 cities and 15 agents).

Learning from Demonstration allows robots to mimic human actions. However, these methods do not model constraints crucial to ensure safety of the learned skill. Moreover, even when explicitly modelling constraints, they rely on the assumption of a known cost function, which limits their practical usability for task with unknown cost. In this work we propose a two-step optimization process that allow to estimate cost and constraints by decoupling the learning of cost functions from the identification of unknown constraints within the demonstrated trajectories. Initially, we identify the cost function by isolating the effect of constraints on parts of the demonstrations. Subsequently, a constraint leaning method is used to identify the unknown constraints. Our approach is validated both on simulated trajectories and a real robotic manipulation task. Our experiments show the impact that incorrect cost estimation has on the learned constraints and illustrate how the proposed method is able to infer unknown constraints, such as obstacles, from demonstrated trajectories without any initial knowledge of the cost.

Semi-supervised symmetric non-negative matrix factorization (SNMF) utilizes the available supervisory information (usually in the form of pairwise constraints) to improve the clustering ability of SNMF. The previous methods introduce the pairwise constraints from the local perspective, i.e., they either directly refine the similarity matrix element-wisely or restrain the distance of the decomposed vectors in pairs according to the pairwise constraints, which overlook the global perspective, i.e., in the ideal case, the pairwise constraint matrix and the ideal similarity matrix possess the same low-rank structure. To this end, we first propose a novel semi-supervised SNMF model by seeking low-rank representation for the tensor synthesized by the pairwise constraint matrix and a similarity matrix obtained by the product of the embedding matrix and its transpose, which could strengthen those two matrices simultaneously from a global perspective. We then propose an enhanced SNMF model, making the embedding matrix tailored to the above tensor low-rank representation. We finally refine the similarity matrix by the strengthened pairwise constraints. We repeat the above steps to continuously boost the similarity matrix and pairwise constraint matrix, leading to a high-quality embedding matrix. Extensive experiments substantiate the superiority of our method. The code is available at https://github.com/JinaLeejnl/TSNMF.

Issues of safety, explainability, and efficiency are of increasing concern in learning systems deployed with hard and soft constraints. Symbolic Constrained Learning and Knowledge Distillation techniques have shown promising results in this area, by embedding and extracting knowledge, as well as providing logical constraints during neural network training. Although many frameworks exist to date, through an integration of logic and information geometry, we provide a construction and theoretical framework for these tasks that generalize many approaches. We propose a loss-based method that embeds knowledge--enforces logical constraints--into a machine learning model that outputs probability distributions. This is done by constructing a distribution from the external knowledge/logic formula, and constructing a loss function as a linear combination of the original loss function with the Fisher-Rao distance or Kullback-Leibler divergence to the constraint distribution. This construction includes logical constraints in the form of propositional formulas (Boolean variables), formulas of a first-order language with finite variables over a model with compact domain (categorical and continuous variables), and in general,likely applicable to any statistical model that was pretrained with semantic information. We evaluate our method on a variety of learning tasks, including classification tasks with logic constraints, transferring knowledge from logic formulas, and knowledge distillation from general distributions.

Probabilistic Circuits (PCs) have emerged as an efficient framework for representing and learning complex probability distributions. Nevertheless, the existing body of research on PCs predominantly concentrates on data-driven parameter learning, often neglecting the potential of knowledge-intensive learning, a particular issue in data-scarce/knowledge-rich domains such as healthcare. To bridge this gap, we propose a novel unified framework that can systematically integrate diverse domain knowledge into the parameter learning process of PCs. Experiments on several benchmarks as well as real world datasets show that our proposed framework can both effectively and efficiently leverage domain knowledge to achieve superior performance compared to purely data-driven learning approaches.

Motivated by information sharing in online platforms, we study repeated persuasion between a sender and a stream of receivers where at each time, the sender observes a payoff-relevant state drawn independently and identically from an unknown distribution, and shares state information with the receivers who each choose an action. The sender seeks to persuade the receivers into taking actions aligned with the sender's preference by selectively sharing state information. However, in contrast to the standard models, neither the sender nor the receivers know the distribution, and the sender has to persuade while learning the distribution on the fly. We study the sender's learning problem of making persuasive action recommendations to achieve low regret against the optimal persuasion mechanism with the knowledge of the distribution. To do this, we first propose and motivate a persuasiveness criterion for the unknown distribution setting that centers robustness as a requirement in the face of uncertainty. Our main result is an algorithm that, with high probability, is robustly-persuasive and achieves $O(\sqrt{T\log T})$ regret, where $T$ is the horizon length. Intuitively, at each time our algorithm maintains a set of candidate distributions, and chooses a signaling mechanism that is simultaneously persuasive for all of them. Core to our proof is a tight analysis about the cost of robust persuasion, which may be of independent interest. We further prove that this regret order is optimal (up to logarithmic terms) by showing that no algorithm can achieve regret better than $\Omega(\sqrt{T})$.

This letter proposes a few-shot physics-guided spatial temporal graph convolutional network (FPG-STGCN) to fast solve unit commitment (UC). Firstly, STGCN is tailored to parameterize UC. Then, few-shot physics-guided learning scheme is proposed. It exploits few typical UC solutions yielded via commercial optimizer to escape from local minimum, and leverages the augmented Lagrangian method for constraint satisfaction. To further enable both feasibility and continuous relaxation for integers in learning process, straight-through estimator for Tanh-Sign composition is proposed to fully differentiate the mixed integer solution space. Case study on the IEEE benchmark justifies that, our method bests mainstream learning ways on UC feasibility, and surpasses traditional solver on efficiency.

The Mixture-of-Expert (MoE) technique plays a crucial role in expanding the size of DNN model parameters. However, it faces the challenge of extended all-to-all communication latency during the training process. Existing methods attempt to mitigate this issue by overlapping all-to-all with expert computation. Yet, these methods frequently fall short of achieving sufficient overlap, consequently restricting the potential for performance enhancements. In our study, we extend the scope of this challenge by considering overlap at the broader training graph level. During the forward pass, we enable non-MoE computations to overlap with all-to-all through careful partitioning and pipelining. In the backward pass, we achieve overlap with all-to-all by scheduling gradient weight computations. We implement these techniques in Lancet, a system using compiler-based optimization to automatically enhance MoE model training. Our extensive evaluation reveals that Lancet significantly reduces the time devoted to non-overlapping communication, by as much as 77%. Moreover, it achieves a notable end-to-end speedup of up to 1.3 times when compared to the state-of-the-art solutions.

The pervasive integration of Artificial Intelligence (AI) has introduced complex challenges in the responsibility and accountability in the event of incidents involving AI-enabled systems. The interconnectivity of these systems, ethical concerns of AI-induced incidents, coupled with uncertainties in AI technology and the absence of corresponding regulations, have made traditional responsibility attribution challenging. To this end, this work proposes a Computational Reflective Equilibrium (CRE) approach to establish a coherent and ethically acceptable responsibility attribution framework for all stakeholders. The computational approach provides a structured analysis that overcomes the limitations of conceptual approaches in dealing with dynamic and multifaceted scenarios, showcasing the framework's explainability, coherence, and adaptivity properties in the responsibility attribution process. We examine the pivotal role of the initial activation level associated with claims in equilibrium computation. Using an AI-assisted medical decision-support system as a case study, we illustrate how different initializations lead to diverse responsibility distributions. The framework offers valuable insights into accountability in AI-induced incidents, facilitating the development of a sustainable and resilient system through continuous monitoring, revision, and reflection.