Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz constant in neural networks has emerged as an essential area of research to enhance adversarial robustness and network certifiability. This paper presents a rigorous approach to the general design of $\mathcal{L}$-Lipschitz deep residual networks using a Linear Matrix Inequality (LMI) framework. Initially, the ResNet architecture was reformulated as a cyclic tridiagonal LMI, and closed-form constraints on network parameters were derived to ensure $\mathcal{L}$-Lipschitz continuity; however, using a new $LDL^\top$ decomposition approach for certifying LMI feasibility, we extend the construction of $\mathcal{L}$-Lipchitz networks to any other nonlinear architecture. Our contributions include a provable parameterization methodology for constructing Lipschitz-constrained residual networks and other hierarchical architectures. Cholesky decomposition is also used for efficient parameterization. These findings enable robust network designs applicable to adversarial robustness, certified training, and control systems. The $LDL^\top$ formulation is shown to be a tight relaxation of the SDP-based network, maintaining full expressiveness and achieving 3\%-13\% accuracy gains over SLL Layers on 121 UCI data sets.

Bug localization in multi-repository microservice architectures is challenging due to the semantic gap between natural language bug reports and code, LLM context limitations, and the need to first identify the correct repository. We propose reframing this as a natural language reasoning task by transforming codebases into hierarchical NL summaries and performing NL-to-NL search instead of cross-modal retrieval. Our approach builds context-aware summaries at file, directory, and repository levels, then uses a two-phase search: first routing bug reports to relevant repositories, then performing top-down localization within those repositories. Evaluated on DNext, an industrial system with 46 repositories and 1.1M lines of code, our method achieves Pass@10 of 0.82 and MRR of 0.50, significantly outperforming retrieval baselines and agentic RAG systems like GitHub Copilot and Cursor. This work demonstrates that engineered natural language representations can be more effective than raw source code for scalable bug localization, providing an interpretable repository -> directory -> file search path, which is vital for building trust in enterprise AI tools by providing essential transparency.

Modern extensible compiler frameworks-such as MLIR-enable rapid creation of domain-specific language dialects. This flexibility, however, makes correctness harder to ensure as the same extensibility that accelerates development also complicates maintaining the testing infrastructure. Extensible languages require automated test generation that is both dialect-agnostic (works across dialects without manual adaptation) and dialect-effective (targets dialect-specific features to find bugs). Existing approaches typically sacrifice one of these goals by either requiring manually constructed seed corpora for each dialect, or by failing to be effective. We present a dialect-agnostic and dialect-effective grammar-based and coverage-guided fuzzing approach for extensible compilers that combines two key insights from existing work: (i) the grammars of dialects, which already encode the structural and type constraints, can often be extracted automatically from the dialect specification; and (ii) these grammars can be used in combination with pre-trained large language models to automatically generate representative and diverse seed inputs from the full dialect space without requiring any manual input or training data. These seeds can then be used to bootstrap coverage-guided fuzzers. We built this approach into a tool, Germinator. When evaluated on six MLIR projects spanning 91 dialects, Germinator generated seeds improve line coverage by 10-120% over grammar-based baselines. We compare against grammar-based baselines because they are the only class of existing automatic seed generators that can be applied uniformly across MLIR's heterogeneous dialect ecosystem. Germinator discovers 88 previously unknown bugs (40 confirmed), including 23 in dialects with no prior automated test generators, demonstrating effective and controllable testing of low-resource dialects at scale.

Traditional physics-informed neural networks (PINNs) do not always satisfy physics based constraints, especially when the constraints include differential operators. Rather, they minimize the constraint violations in a soft way. Strict satisfaction of differential-algebraic equations (DAEs) to embed domain knowledge and first-principles in data-driven models is generally challenging. This is because data-driven models consider the original functions to be black-box whose derivatives can only be obtained after evaluating the functions. We introduce DAE-HardNet, a physics-constrained (rather than simply physics-informed) neural network that learns both the functions and their derivatives simultaneously, while enforcing algebraic as well as differential constraints. This is done by projecting model predictions onto the constraint manifold using a differentiable projection layer. We apply DAE-HardNet to several systems and test problems governed by DAEs, including the dynamic Lotka-Volterra predator-prey system and transient heat conduction. We also show the ability of DAE-HardNet to estimate unknown parameters through a parameter estimation problem. Compared to multilayer perceptrons (MLPs) and PINNs, DAE-HardNet achieves orders of magnitude reduction in the physics loss while maintaining the prediction accuracy. It has the added benefits of learning the derivatives which improves the constrained learning of the backbone neural network prior to the projection layer. For specific problems, this suggests that the projection layer can be bypassed for faster inference. The current implementation and codes are available at https://github.com/SOULS-TAMU/DAE-HardNet.

Modern high-frequency trading (HFT) environments are characterized by sudden price spikes that present both risk and opportunity, but conventional financial models often fail to capture the required fine temporal structure. Spiking Neural Networks (SNNs) offer a biologically inspired framework well-suited to these challenges due to their natural ability to process discrete events and preserve millisecond-scale timing. This work investigates the application of SNNs to high-frequency price-spike forecasting, enhancing performance via robust hyperparameter tuning with Bayesian Optimization (BO). This work converts high-frequency stock data into spike trains and evaluates three architectures: an established unsupervised STDP-trained SNN, a novel SNN with explicit inhibitory competition, and a supervised backpropagation network. BO was driven by a novel objective, Penalized Spike Accuracy (PSA), designed to ensure a network's predicted price spike rate aligns with the empirical rate of price events. Simulated trading demonstrated that models optimized with PSA consistently outperformed their Spike Accuracy (SA)-tuned counterparts and baselines. Specifically, the extended SNN model with PSA achieved the highest cumulative return (76.8%) in simple backtesting, significantly surpassing the supervised alternative (42.54% return). These results validate the potential of spiking networks, when robustly tuned with task-specific objectives, for effective price spike forecasting in HFT.

We introduce a simple post-training method that makes transformer attention sparse without sacrificing performance. Applying a flexible sparsity regularisation under a constrained-loss objective, we show on models up to 1B parameters that it is possible to retain the original pretraining loss while reducing attention connectivity to $\approx 0.3 \%$ of its edges. Unlike sparse-attention methods designed for computational efficiency, our approach leverages sparsity as a structural prior: it preserves capability while exposing a more organized and interpretable connectivity pattern. We find that this local sparsity cascades into global circuit simplification: task-specific circuits involve far fewer components (attention heads and MLPs) with up to 100x fewer edges connecting them. These results demonstrate that transformer attention can be made orders of magnitude sparser, suggesting that much of its computation is redundant and that sparsity may serve as a guiding principle for more structured and interpretable models.

The Price of Anarchy (PoA) is a standard metric for quantifying inefficiency in socio-technical systems, widely used to guide policies like traffic tolling. Conventional PoA analysis relies on exact numerical costs. However, in many settings, costs represent agents' preferences and may be defined only up to possibly arbitrary scaling and shifting, representing informational and modeling ambiguities. We observe that while such transformations preserve equilibrium and optimal outcomes, they change the PoA value. To resolve this issue, we rely on results from Social Choice Theory and define the Invariant PoA. By connecting admissible transformations to degrees of comparability of agents' costs, we derive the specific social welfare functions which ensure that efficiency evaluations do not depend on arbitrary rescalings or translations of individual costs. Case studies on a toy example and the Zurich network demonstrate that identical tolling strategies can lead to substantially different efficiency estimates depending on the assumed comparability. Our framework thus demonstrates that explicit axiomatic foundations are necessary in order to define efficiency metrics and to appropriately guide policy in large-scale infrastructure design robustly and effectively.

Recent advances in psychotherapy have focused on treatment personalization, such as by selecting treatment modules based on personalized networks. However, estimating personalized networks typically requires intensive longitudinal data, which is not always feasible. A solution to facilitate scalability of network-driven treatment personalization is leveraging LLMs. In this study, we present an end-to-end pipeline for automatically generating client networks from 77 therapy transcripts to support case conceptualization and treatment planning. We annotated 3364 psychological processes and their corresponding dimensions in therapy transcripts. Using these data, we applied in-context learning to jointly identify psychological processes and their dimensions. The method achieved high performance even with a few training examples. To organize the processes into networks, we introduced a two-step method that grouped them into clinically meaningful clusters. We then generated explanation-augmented relationships between clusters. Experts found that networks produced by our multi-step approach outperformed those built with direct prompting for clinical utility and interpretability, with up to 90% preferring our approach. In addition, the networks were rated favorably by experts, with scores for clinical relevance, novelty, and usefulness ranging from 72-75%. Our findings provide a proof of concept for using LLMs to create clinically relevant networks from therapy transcripts. Advantages of our approach include bottom-up case conceptualization from client utterances in therapy sessions and identification of latent themes. Networks generated from our pipeline may be used in clinical settings and supervision and training. Future research should examine whether these networks improve treatment outcomes relative to other methods of treatment personalization, including statistically estimated networks.

Low-grade gliomas frequently present IDH1 mutations that define clinically distinct subgroups with specific prognostic and therapeutic implications. This work introduces a Multimodal Oncology Agent (MOA) integrating a histology tool based on the TITAN foundation model for IDH1 mutation prediction in low-grade glioma, combined with reasoning over structured clinical and genomic inputs through PubMed, Google Search, and OncoKB. MOA reports were quantitatively evaluated on 488 patients from the TCGA-LGG cohort against clinical and histology baselines. MOA without the histology tool outperformed the clinical baseline, achieving an F1-score of 0.826 compared to 0.798. When fused with histology features, MOA reached the highest performance with an F1-score of 0.912, exceeding both the histology baseline at 0.894 and the fused histology-clinical baseline at 0.897. These results demonstrate that the proposed agent captures complementary mutation-relevant information enriched through external biomedical sources, enabling accurate IDH1 mutation prediction.

Conventional Data Processing Workflow Conventional MD analysis, which has been used in previous data evaluation [2, 32, 33] and can serve labeling and validation purposes for ML model construction and preparation, employs a multi-tiered data distillation process to derive robust trends, see Figure 1. In the left column of this figure, we show representative examples of computational tomographs through the 3D MD model, with the atoms colored by (a) grain orientation in electron backscatter diffraction (EBSD) standard, (b) lattice type, grain boundaries, and defects, (c) advection (drift) velocity to visualize shearing, and (d) local stresses. As a first step in the data distillation process, these 3D data that are stored for each atom are averaged across the lateral system dimensions, revealing depth-resolved, time-dependent quantities of interest, as visualized in the heat map at the top of the middle column (e). Further elimination of the sample depth and time dimensions leads to time-resolved global quantities (f) and contact pressure dependent trends (g), which can be fitted with characteristic pressures that mark the transition between deformation patterns (h). As an outlook to the utility of such highly distilled data, we propose their incorporation into Ashby-style charts, as schematically shown in Figure 1 (i), which link material properties with tribological properties. This conventional approach 2 accommodates the complexities of polycrystalline materials under tribological loading conditions and is guided by the underlying physics, resulting in this time-consuming procedure. Thus, substituting this approach with a well-trained ML model is highly relevant. The conventional approach can serve as the ground truth for training this ML model or to refine and validate said model based on newly generated MD data.