In this paper, we analyze the convergence properties of the Lion optimizer. First, we establish that the Lion optimizer attains a convergence rate of $\mathcal{O}(d^{1/2}T^{-1/4})$ under standard assumptions, where $d$ denotes the problem dimension and $T$ is the iteration number. To further improve this rate, we introduce the Lion optimizer with variance reduction, resulting in an enhanced convergence rate of $\mathcal{O}(d^{1/2}T^{-1/3})$. We then analyze in distributed settings, where the standard and variance reduced version of the distributed Lion can obtain the convergence rates of $\mathcal{O}(d^{1/2}(nT)^{-1/4})$ and $\mathcal{O}(d^{1/2}(nT)^{-1/3})$, with $n$ denoting the number of nodes. Furthermore, we investigate a communication-efficient variant of the distributed Lion that ensures sign compression in both communication directions. By employing the unbiased sign operations, the proposed Lion variant and its variance reduction counterpart, achieve convergence rates of $\mathcal{O}\left( \max \left\{\frac{d^{1/4}}{T^{1/4}}, \frac{d^{1/10}}{n^{1/5}T^{1/5}} \right\} \right)$ and $\mathcal{O}\left( \frac{d^{1/4}}{T^{1/4}} \right)$, respectively.

End-to-end deep learning has achieved impressive results but remains limited by its reliance on large labeled datasets, poor generalization to unseen scenarios, and growing computational demands. In contrast, classical optimization methods are data-efficient and lightweight but often suffer from slow convergence. While learned optimizers offer a promising fusion of both worlds, most focus on first-order methods, leaving learned second-order approaches largely unexplored. We propose a novel learned second-order optimizer that introduces a trainable preconditioning unit to enhance the classical Symmetric-Rank-One (SR1) algorithm. This unit generates data-driven vectors used to construct positive semi-definite rank-one matrices, aligned with the secant constraint via a learned projection. Our method is evaluated through analytic experiments and on the real-world task of Monocular Human Mesh Recovery (HMR), where it outperforms existing learned optimization-based approaches. Featuring a lightweight model and requiring no annotated data or fine-tuning, our approach offers strong generalization and is well-suited for integration into broader optimization-based frameworks.

In distributed optimization and federated learning, asynchronous alternating direction method of multipliers (ADMM) serves as an attractive option for large-scale optimization, data privacy, straggler nodes and variety of objective functions. However, communication costs can become a major bottleneck when the nodes have limited communication budgets or when the data to be communicated is prohibitively large. In this work, we propose introducing coarse quantization to the data to be exchanged in aynchronous ADMM so as to reduce communication overhead for large-scale federated learning and distributed optimization applications. We experimentally verify the convergence of the proposed method for several distributed learning tasks, including neural networks.

--Industry adoption of Artificial Intelligence (AI)- native wireless receivers, or even modular, Machine Learning (ML)-aided wireless signal processing blocks, has been slow. The main concern is the lack of explainability of these trained ML models and the significant risks posed to network functionalities in case of failures, especially since (i) testing on every exhaustive case is infeasible and (ii) the data used for model training may not be available. This paper proposes A TLAS, an AI-guided approach that generates a battery of tests for pre-trained AI-native receiver models and benchmarks the performance against a classical receiver architecture. Using gradient-based optimization, it avoids spanning the exhaustive set of all environment and channel conditions; instead, it generates the next test in an online manner to further probe specific configurations that offer the highest risk of failure. We implement and validate our approach by adopting the well-known DeepRx AI-native receiver model as well as a classical receiver using differentiable tensors in NVIDIA's Sionna environment. A TLAS uncovers specific combinations of mobility, channel delay spread, and noise, where fully and partially trained variants of AI-native DeepRx perform suboptimally compared to the classical receivers. Our proposed method reduces the number of tests required per failure found by 19% compared to grid search for a 3-parameters input optimization problem, demonstrating greater efficiency.

In large language model (LLM) adaptation, balancing multiple optimization objectives such as improving factuality (heat) and increasing confidence (via low entropy) poses a fundamental challenge, especially when prompt parameters (e.g., hidden-layer insertions h and embedding modifications w) interact in non-trivial ways. Existing multi-objective optimization strategies often rely on scalar gradient aggregation, ignoring the deeper geometric structure between objectives and parameters. We propose J6, a structured Jacobian-based method that decomposes the gradient interaction matrix into six interpretable components. This decomposition enables both hard decision-making (e.g., choosing the dominant update direction via argmax) and soft strategies (e.g., attention-style weighting via softmax over J6), forming a dynamic update framework that adapts to local conflict and synergy. Moreover, the interpretable structure of J6 provides insight into parameter attribution, task interference, and geometry-aligned adaptation. Our work introduces a principled and extensible mechanism for conflict-aware prompt optimization, and opens a new avenue for incorporating structured Jacobian reasoning into multi-objective neural tuning.

Federated Learning (FL) has emerged as a vital paradigm in modern machine learning that enables collaborative training across decentralized data sources without exchanging raw data. This approach not only addresses privacy concerns but also allows access to overall substantially larger and potentially more diverse datasets, without the need for centralized storage or hardware resources. However, heterogeneity in client data may cause certain clients to have disproportionate impacts on the global model, leading to disparities in the clients' performances. Fairness, therefore, becomes a crucial concern in FL and can be addressed in various ways. However, the effectiveness of existing fairness-aware methods, particularly in heterogeneous data settings, remains unclear, and the relationships between different approaches are not well understood. In this work, we focus on performance equitable fairness, which aims to minimize differences in performance across clients. We restrict our study to fairness-aware methods that explicitly regularize client losses, evaluating both existing and newly proposed approaches. We identify and theoretically explain connections between the investigated fairness methods, and empirically show that FairGrad (approximate) and FairGrad* (exact) (two variants of a gradient variance regularization method introduced here for performance equitable fairness) improve both fairness and overall model performance in heterogeneous data settings.

Optimizing data mixtures for supervised fine-tuning (SFT) of large language models (LLMs) is critical for developing general-purpose models, yet this area remains underexplored. In this paper, we frame data mixing as an optimization problem and introduce a novel method designed to minimize validation loss. Our approach parametrizes the loss by modeling effective data transferred and leveraging scaling laws for fine-tuning. By experimenting with various small-scale data mixtures, we fit these parameters and derive the optimal weights. We provide both mathematical proofs and empirical results demonstrating that our algorithm achieves excellent overall and individual performance across all domains. Through controlled experiments, we show that models trained with our optimized weights perform on par with those using optimal weights determined via grid search, with per-domain loss only 0.66% higher than the best domain loss from grid search on average. Additionally, we show that reweighting popular SFT datasets using our method improves both validation loss and downstream performance. Finally, we discuss how our method can generalize to guide data selection for domain-specific models and provide insights into SFT.

Neural network-based Marked Temporal Point Process (MTPP) models have been widely adopted to model event sequences in high-stakes applications, raising concerns about the trustworthiness of outputs from these models. This study focuses on Explanation for MTPP, aiming to identify the minimal and rational explanation, that is, the minimum subset of events in history, based on which the prediction accuracy of MTPP matches that based on full history to a great extent and better than that based on the complement of the subset. This study finds that directly defining Explanation for MTPP as counterfactual explanation or factual explanation can result in irrational explanations. To address this issue, we define Explanation for MTPP as a combination of counterfactual explanation and factual explanation. This study proposes Counterfactual and Factual Explainer for MTPP (CFF) to solve Explanation for MTPP with a series of deliberately designed techniques. Experiments demonstrate the correctness and superiority of CFF over baselines regarding explanation quality and processing efficiency.

Algorithm design and analysis is a cornerstone of computer science, but it confronts a major challenge. Proving an algorithm's performance guarantee across all inputs has traditionally required extensive and often error-prone human effort. While AI has shown great success in finding solutions to specific problem instances, automating the discovery of general algorithms with such provable guarantees has remained a significant barrier. This challenge stems from the difficulty of integrating the creative process of algorithm design with the rigorous process of formal analysis. To address this gap, we propose LegoNE, a framework that tightly fuses these two processes for the fundamental and notoriously difficult problem of computing approximate Nash equilibria. LegoNE automatically translates any algorithm written by a simple Python-like language into a constrained optimization problem. Solving this problem derives and proves the algorithm's approximation bound. Using LegoNE, a state-of-the-art large language model rediscovered the state-of-the-art algorithm for two-player games within hours, a feat that had taken human researchers 15 years to achieve. For three-player games, the model discovered a novel algorithm surpassing all existing human-designed ones. This work demonstrates a new human-machine collaborative paradigm for theoretical science: humans reason at a higher-abstract level, using symbols to compress the search space, and AI explores within it, achieving what neither could alone.

Integer programming lies at the heart of crucial combinatorial optimization tasks but remains challenging due to its NP-hard nature. An effective approach for practically solving integer programs is the manual design of acceleration cuts, i.e. inequalities that improve solver performance. However, this creative process demands deep expertise and is yet to be automated. Our proposed framework, EvoCut, automates the generation of acceleration cuts by combining large language models (LLMs) with an evolutionary search. EvoCut (i) initializes a diverse population of candidate cuts via an LLM-based initializer agent; (ii) for each cut empirically evaluates both preservation of the optimal solution and its ability to cut off fractional solutions across a verification set; and (iii) iteratively refines the population through evolutionary crossover and mutation agents. We quantify each cut's utility by its relative reduction in the solver's optimality gap. Our comparisons against standard integer programming practice show that EvoCut reduces optimality gap by 17-57% within a fixed time. It obtains the same solutions up to 4 times as fast, and obtains higher-quality solutions within the same time limit. Requiring no human expert input, EvoCut reliably generates, improves, and empirically verifies cuts that generalize to unseen instances. The code is available at https://github.com/milad1378yz/EvoCut.