This paper presents El0ps, a Python toolbox providing several utilities to handle L0-regularized problems related to applications in machine learning, statistics, and signal processing, among other fields. In contrast to existing toolboxes, El0ps allows users to define custom instances of these problems through a flexible framework, provides a dedicated solver achieving state-of-the-art performance, and offers several built-in machine learning pipelines. Our aim with El0ps is to provide a comprehensive tool which opens new perspectives for the integration of L0-regularized problems in practical applications.

Bilevel optimization poses a significant computational challenge due to its nested structure, where each upper-level candidate solution requires solving a corresponding lower-level problem. While evolutionary algorithms (EAs) are effective at navigating such complex landscapes, their high resource demands remain a key bottleneck -- particularly the redundant evaluation of numerous unpromising lower-level tasks. Despite recent advances in multitasking and transfer learning, resource waste persists. To address this issue, we propose a novel resource allocation framework for bilevel EAs that selectively identifies and focuses on promising lower-level tasks. Central to our approach is a contrastive ranking network that learns relational patterns between paired upper- and lower-level solutions online. This knowledge guides a reference-based ranking strategy that prioritizes tasks for optimization and adaptively controls resampling based on estimated population quality. Comprehensive experiments across five state-of-the-art bilevel algorithms show that our framework significantly reduces computational cost while preserving -- or even enhancing -- solution accuracy. This work offers a generalizable strategy to improve the efficiency of bilevel EAs, paving the way for more scalable bilevel optimization.

Significant investments have been made towards the com-modification of diffusion models for generation of diverse media. Their mass-market adoption is however still hobbled by the intense hardware resource requirements of diffusion model inference. Model quantization strategies tailored specifically towards diffusion models have been useful in easing this burden, yet have generally explored the Uniform Scalar Quantization (USQ) family of quantization methods. In contrast, V ector Quantization (VQ) methods, which operate on groups of multiple related weights as the basic unit of compression, have seen substantial success in Large Language Model (LLM) quantization. In this work, we apply codebook-based additive vector quantization to the problem of diffusion model compression. Our resulting approach achieves a new Pareto frontier for the extremely low-bit weight quantization on the standard class-conditional benchmark of LDM-4 on ImageNet at 20 inference time steps. Notably, we report sFID 1.92 points lower than the full-precision model at W4A8 and the best-reported results for FID, sFID and ISC at W2A8. W e are also able to demonstrate FLOPs savings on arbitrary hardware via an efficient inference kernel, as opposed to savings resulting from small integer operations which may lack broad hardware support.

-- Mixed Integer Linear Programs (MILPs) are essential tools for solving planning and scheduling problems across critical industries such as construction, manufacturing, and logistics. However, their widespread adoption is limited by long computational times, especially in large-scale, real-time scenarios. T o address this, we present a learning-based framework that leverages Behavior Cloning (BC) and Reinforcement Learning (RL) to train Graph Neural Networks (GNNs), producing high-quality initial solutions for warm-starting MILP solvers in Multi-Agent T ask Allocation and Scheduling Problems. Experimental results demonstrate that our method reduces optimization time and variance compared to traditional techniques while maintaining solution quality and feasibility. I. INTRODUCTION Mixed Integer Linear Programs (MILPs) serve as a fundamental framework for combinatorial optimization problems, facilitating solutions across a wide range of planning and scheduling tasks in logistics [1], construction [2] and manufacturing [3].

Zeroth-order methods are extensively used in machine learning applications where gradients are infeasible or expensive to compute, such as black-box attacks, reinforcement learning, and language model fine-tuning. Existing optimization theory focuses on convergence to an arbitrary stationary point, but less is known on the implicit regularization that provides a fine-grained characterization on which particular solutions are finally reached. We show that zeroth-order optimization with the standard two-point estimator favors solutions with small trace of Hessian, which is widely used in previous work to distinguish between sharp and flat minima. We further provide convergence rates of zeroth-order optimization to approximate flat minima for convex and sufficiently smooth functions, where flat minima are defined as the minimizers that achieve the smallest trace of Hessian among all optimal solutions. Experiments on binary classification tasks with convex losses and language model fine-tuning support our theoretical findings.

Binary Neural Networks (BiNNs), which employ single-bit precision weights, have emerged as a promising solution to reduce memory usage and power consumption while maintaining competitive performance in large-scale systems. However, training BiNNs remains a significant challenge due to the limitations of conventional training algorithms. Quantum HyperNetworks offer a novel paradigm for enhancing the optimization of BiNN by leveraging quantum computing. Specifically, a Variational Quantum Algorithm is employed to generate binary weights through quantum circuit measurements, while key quantum phenomena such as superposition and entanglement facilitate the exploration of a broader solution space. In this work, we establish a connection between this approach and Bayesian inference by deriving the Evidence Lower Bound (ELBO), when direct access to the output distribution is available (i.e., in simulations), and introducing a surrogate ELBO based on the Maximum Mean Discrepancy (MMD) metric for scenarios involving implicit distributions, as commonly encountered in practice. Our experimental results demonstrate that the proposed methods outperform standard Maximum Likelihood Estimation (MLE), improving trainability and generalization.

A recent breakthrough in biologically-plausible normative frameworks for dimensionality reduction is based upon the similarity matching cost function and the low-rank matrix approximation problem. Despite clear biological interpretation, successful application in several domains, and experimental validation, a formal complete convergence analysis remains elusive. Building on this framework, we consider and analyze a continuous-time neural network, the \emph{similarity matching network}, for principal subspace projection. Derived from a min-max-min objective, this biologically-plausible network consists of three coupled dynamics evolving at different time scales: neural dynamics, lateral synaptic dynamics, and feedforward synaptic dynamics at the fast, intermediate, and slow time scales, respectively. The feedforward and lateral synaptic dynamics consist of Hebbian and anti-Hebbian learning rules, respectively. By leveraging a multilevel optimization framework, we prove convergence of the dynamics in the offline setting. Specifically, at the first level (fast time scale), we show strong convexity of the cost function and global exponential convergence of the corresponding gradient-flow dynamics. At the second level (intermediate time scale), we prove strong concavity of the cost function and exponential convergence of the corresponding gradient-flow dynamics within the space of positive definite matrices. At the third and final level (slow time scale), we study a non-convex and non-smooth cost function, provide explicit expressions for its global minima, and prove almost sure convergence of the corresponding gradient-flow dynamics to the global minima. These results rely on two empirically motivated conjectures that are supported by thorough numerical experiments. Finally, we validate the effectiveness of our approach via a numerical example.

We introduce ROLL, an efficient, scalable, and user-friendly library designed for Reinforcement Learning Optimization for Large-scale Learning. ROLL caters to three primary user groups: tech pioneers aiming for cost-effective, fault-tolerant large-scale training, developers requiring flexible control over training workflows, and researchers seeking agile experimentation. ROLL is built upon several key modules to serve these user groups effectively. First, a single-controller architecture combined with an abstraction of the parallel worker simplifies the development of the training pipeline. Second, the parallel strategy and data transfer modules enable efficient and scalable training. Third, the rollout scheduler offers fine-grained management of each sample's lifecycle during the rollout stage. Fourth, the environment worker and reward worker support rapid and flexible experimentation with agentic RL algorithms and reward designs. Finally, AutoDeviceMapping allows users to assign resources to different models flexibly across various stages.

With the integration of renewable sources in electricity distribution networks, the need to develop intelligent mechanisms for balancing the energy market has arisen. In the absence of such mechanisms, the energy market may face imbalances that can lead to power outages, financial losses or instability at the grid level. In this context, the grouping of microgrids into optimal coalitions that can absorb energy from the market during periods of surplus or supply energy to the market during periods of is a key aspect in the efficient management of distribution networks. In this article, we propose a method that identify an optimal microgrids coalition capable of addressing the dynamics of the energy market. The proposed method models the problem of identifying the optimal coalition as an optimization problem that it solves by combining a strategy inspired by cooperative game theory with a memetic algorithm. An individual is represented as a coalition of microgrids and the evolution of population of individuals over generations is assured by recombination and mutation. The fitness function is defined as the difference between the total value generated by the coalition and a penalty applied to the coalition when the energy traded by coalition exceeds the energy available/demanded on/by the energy market. The value generated by the coalition is calculated based on the profit obtained by the collation if it sells energy on the market during periods of deficit or the savings obtained by the coalition if it buys energy on the market during periods of surplus and the costs associated with the trading process. This value is divided equitably among the coalition members, according to the Shapley value, which considers the contribution of each one to the formation of collective value.

Standard uncertainty estimation techniques, such as dropout, often struggle to clearly distinguish reliable predictions from unreliable ones. We attribute this limitation to noisy classifier weights, which, while not impairing overall class-level predictions, render finer-level statistics less informative. To address this, we propose a novel test-time optimization method that accounts for the impact of such noise to produce more reliable confidence estimates. This score defines a monotonic subset-selection function, where population accuracy consistently increases as samples with lower scores are removed, and it demonstrates superior performance in standard risk-based metrics such as AUSE and AURC. Additionally, our method effectively identifies discrepancies between training and test distributions, reliably differentiates in-distribution from out-of-distribution samples, and elucidates key differences between CNN and ViT classifiers across various vision datasets.