Then we can update the joint distribution for the L.H.S. withϱl = ϱ 12 by exchanging the22 We prove the triangle inequality by contradictions similar to iii). Each agent has to resolve to select the action from its discrete action space to move around. Themixingnetwork56 has one hyper-layer as described in QMIX with64 units. The optimizer to optimize the neural57 networks is "Adam". Each URL algorithm is deployed to learn different joint policies (Z = 1058 for MPE andZ = 20 for GRF) and mixing networks every time.

We instead rely on weak supervision sources having some structure by virtue of being encoded programmatically.

The rapid expansion of generative AI is driving unprecedented demands for high-performance computing. Training large-scale AI models now requires vast interconnected GPU clusters across multiple data centers. Multi-scale AI training and inference demand uniform, ultra-low latency, and energy-efficient links to enable massive GPUs to function as a single cohesive unit. However, traditional electrical and optical interconnects, which rely on conventional digital signal processors (DSPs) for signal distortion compensation, are increasingly unable to meet these stringent requirements. To overcome these limitations, we present an integrated neuromorphic optical signal processor (OSP) that leverages deep reservoir computing and achieves DSP-free, all-optical, real-time processing. Experimentally, our OSP achieves a 100 Gbaud PAM4 per lane, 1.6 Tbit/s data center interconnect over a 5 km optical fiber in the C-band (equivalent to over 80 km optical fiber in the O-band), far exceeding the reach of state-of-the-art DSP solutions, which are fundamentally constrained by chromatic dispersion 1 arXiv:2504.15044v1 Simultaneously, it delivers a four-orders-of-magnitude reduction in processing latency and a three-orders-of-magnitude reduction in energy consumption. Unlike DSPs, which introduce increased latency at high data rates, our OSP maintains consistent, ultra-low latency regardless of data rate scaling, making it an ideal solution for future optical interconnects. Moreover, the OSP retains full optical field information for better impairment compensation and adapts to various modulation formats, data rates, and wavelengths. Fabricated using a mature silicon photonic process, the OSP can be monolithically integrated with silicon photonic transceivers, enhancing the compactness and reliability of all-optical interconnects. This research provides a highly scalable, energy-efficient, and high-speed solution, paving the way for next-generation AI infrastructure. Keywords: Photonic neural network, optical interconnect, AI infrastructure, data center 1 Introduction The surging demand for artificial intelligence and machine learning (AI/ML), especially in generative AI, has driven unprecedented requirements for high-performance computing infrastructure.

In safety-critical applications, guaranteeing the satisfaction of constraints over continuous environments is crucial, e.g., an autonomous agent should never crash into obstacles or go off-road. Neural models struggle in the presence of these constraints, especially when they involve intricate algebraic relationships. To address this, we introduce a differentiable probabilistic layer that guarantees the satisfaction of non-convex algebraic constraints over continuous variables. This probabilistic algebraic layer (PAL) can be seamlessly plugged into any neural architecture and trained via maximum likelihood without requiring approximations. PAL defines a distribution over conjunctions and disjunctions of linear inequalities, parameterized by polynomials. This formulation enables efficient and exact renormalization via symbolic integration, which can be amortized across different data points and easily parallelized on a GPU. We showcase PAL and our integration scheme on a number of benchmarks for algebraic constraint integration and on real-world trajectory data.

Cross-Domain Few-Shot Learning~(CDFSL) methods typically parameterize models with task-agnostic and task-specific parameters. To adapt task-specific parameters, recent approaches have utilized fixed optimization strategies, despite their potential sub-optimality across varying domains or target tasks. To address this issue, we propose a novel adaptation mechanism called Task-Specific Preconditioned gradient descent~(TSP). Our method first meta-learns Domain-Specific Preconditioners~(DSPs) that capture the characteristics of each meta-training domain, which are then linearly combined using task-coefficients to form the Task-Specific Preconditioner. The preconditioner is applied to gradient descent, making the optimization adaptive to the target task. We constrain our preconditioners to be positive definite, guiding the preconditioned gradient toward the direction of steepest descent. Empirical evaluations on the Meta-Dataset show that TSP achieves state-of-the-art performance across diverse experimental scenarios.

Topological signals are variables or features associated with both nodes and edges of a network. Recently, in the context of Topological Machine Learning, great attention has been devoted to signal processing of such topological signals. Most of the previous topological signal processing algorithms treat node and edge signals separately and work under the hypothesis that the true signal is smooth and/or well approximated by a harmonic eigenvector of the Hodge-Laplacian, which may be violated in practice. Here we propose Dirac-equation signal processing, a framework for efficiently reconstructing true signals on nodes and edges, also if they are not smooth or harmonic, by processing them jointly. The proposed physics-inspired algorithm is based on the spectral properties of the topological Dirac operator. It leverages the mathematical structure of the topological Dirac equation to boost the performance of the signal processing algorithm. We discuss how the relativistic dispersion relation obeyed by the topological Dirac equation can be used to assess the quality of the signal reconstruction. Finally, we demonstrate the improved performance of the algorithm with respect to previous algorithms. Specifically, we show that Dirac-equation signal processing can also be used efficiently if the true signal is a non-trivial linear combination of more than one eigenstate of the Dirac equation, as it generally occurs for real signals.

Obtaining enough labeled data to robustly train complex discriminative models is a major bottleneck in the machine learning pipeline. A popular solution is combining multiple sources of weak supervision using generative models. The structure of these models affects the quality of the training labels, but is difficult to learn without any ground truth labels. We instead rely on weak supervision sources having some structure by virtue of being encoded programmatically. We present Coral, a paradigm that infers generative model structure by statically analyzing the code for these heuristics, thus significantly reducing the amount of data required to learn structure. We prove that Coral's sample complexity scales quasilinearly with the number of heuristics and number of relations identified, improving over the standard sample complexity, which is exponential in n for learning n

Tensor Networks (TNs) are a computational paradigm used for representing quantum many-body systems. Recent works have shown how TNs can also be applied to perform Machine Learning (ML) tasks, yielding comparable results to standard supervised learning techniques. In this work, we study the use of Tree Tensor Networks (TTNs) in high-frequency real-time applications by exploiting the low-latency hardware of the Field-Programmable Gate Array (FPGA) technology. We present different implementations of TTN classifiers, capable of performing inference on classical ML datasets as well as on complex physics data. A preparatory analysis of bond dimensions and weight quantization is realized in the training phase, together with entanglement entropy and correlation measurements, that help setting the choice of the TTN architecture. The generated TTNs are then deployed on a hardware accelerator; using an FPGA integrated into a server, the inference of the TTN is completely offloaded. Eventually, a classifier for High Energy Physics (HEP) applications is implemented and executed fully pipelined with sub-microsecond latency.

In recent times, the swift evolution of adversarial attacks has captured widespread attention, particularly concerning their transferability and other performance attributes. These techniques are primarily executed at the sample level, frequently overlooking the intrinsic parameters of models. Such neglect suggests that the perturbations introduced in adversarial samples might have the potential for further reduction. Given the essence of adversarial attacks is to impair model integrity with minimal noise on original samples, exploring avenues to maximize the utility of such perturbations is imperative. Against this backdrop, we have delved into the complexities of adversarial attack algorithms, dissecting the adversarial process into two critical phases: the Directional Supervision Process (DSP) and the Directional Optimization Process (DOP). While DSP determines the direction of updates based on the current samples and model parameters, it has been observed that existing model parameters may not always be conducive to adversarial attacks. The impact of models on adversarial efficacy is often overlooked in current research, leading to the neglect of DSP. We propose that under certain conditions, fine-tuning model parameters can significantly enhance the quality of DSP. For the first time, we propose that under certain conditions, fine-tuning model parameters can significantly improve the quality of the DSP. We provide, for the first time, rigorous mathematical definitions and proofs for these conditions, and introduce multiple methods for fine-tuning model parameters within DSP. Our extensive experiments substantiate the effectiveness of the proposed P3A method. Our code is accessible at: https://anonymous.4open.science/r/P3A-A12C/