We consider bidding in repeated Bayesian first-price auctions. Bidding algorithms that achieve optimal regret have been extensively studied, but their strategic robustness to the seller's manipulation remains relatively underexplored. Bidding algorithms based on no-swap-regret algorithms achieve both desirable properties, but are suboptimal in terms of statistical and computational efficiency. In contrast, online gradient ascent is the only algorithm that achieves $O(\sqrt{TK})$ regret and strategic robustness [KSS24], where $T$ denotes the number of auctions and $K$ the number of bids. In this paper, we explore whether simple online linear optimization (OLO) algorithms suffice for bidding algorithms with both desirable properties. Our main result shows that sublinear linearized regret is sufficient for strategic robustness. Specifically, we construct simple black-box reductions that convert any OLO algorithm into a strategically robust no-regret bidding algorithm, in both known and unknown value distribution settings. For the known value distribution case, our reduction yields a bidding algorithm that achieves $O(\sqrt{T \log K})$ regret and strategic robustness (with exponential improvement on the $K$-dependence compared to [KSS24]). For the unknown value distribution case, our reduction gives a bidding algorithm with high-probability $O(\sqrt{T (\log K+\log(T/δ)})$ regret and strategic robustness, while removing the bounded density assumption made in [KSS24].

Search-Augmented Generative Engines (SAGE) have emerged as a new paradigm for information access, bridging web-scale retrieval with generative capabilities to deliver synthesized answers. This shift has fundamentally reshaped how web content gains exposure online, giving rise to Search-Augmented Generative Engine Optimization (SAGEO), the practice of optimizing web documents to improve their visibility in AI-generated responses. Despite growing interest, no evaluation environment currently supports comprehensive investigation of SAGEO. Specifically, existing benchmarks lack end-to-end visibility evaluation of optimization strategies, operating on pre-determined candidate documents that abstract away retrieval and reranking preceding generation. Moreover, existing benchmarks discard structural information (e.g., schema markup) present in real web documents, overlooking the rich signals that search systems actively leverage in practice. Motivated by these gaps, we introduce SAGEO Arena, a realistic and reproducible environment for stage-level SAGEO analysis. Our objective is to jointly target search-oriented optimization (SEO) and generation-centric optimization (GEO). To achieve this, we integrate a full generative search pipeline over a large-scale corpus of web documents with rich structural information. Our findings reveal that existing approaches remain largely impractical under realistic conditions and often degrade performance in retrieval and reranking. We also find that structural information helps mitigate these limitations, and that effective SAGEO requires tailoring optimization to each pipeline stage. Overall, our benchmark paves the way for realistic SAGEO evaluation and optimization beyond simplified settings.

Convex Markov Games (cMGs) were recently introduced as a broad class of multi-agent learning problems that generalize Markov games to settings where strategic agents optimize general utilities beyond additive rewards. While cMGs expand the modeling frontier, their theoretical foundations, particularly the structure of Nash equilibria (NE) and guarantees for learning algorithms, are not yet well understood. In this work, we address these gaps for an extension of cMGs, which we term General Utility Markov Games (GUMGs), capturing new applications requiring coupling between agents' occupancy measures. We prove that in GUMGs, Nash equilibria coincide with the fixed points of projected pseudo-gradient dynamics (i.e., first-order stationary points), enabled by a novel agent-wise gradient domination property. This insight also yields a simple proof of NE existence using Brouwer's fixed-point theorem. We further show the existence of Markov perfect equilibria. Building on this characterization, we establish a policy gradient theorem for GUMGs and design a model-free policy gradient algorithm. For potential GUMGs, we establish iteration complexity guarantees for computing approximate-NE under exact gradients and provide sample complexity bounds in both the generative model and on-policy settings. Our results extend beyond prior work restricted to zero-sum cMGs, providing the first theoretical analysis of common-interest cMGs.

AI coding agents are increasingly contributing to software development, yet their impact on mobile development has received little empirical attention. In this paper, we present the first category-level empirical study of agent-generated code in open-source mobile app projects. We analyzed PR acceptance behaviors across mobile platforms, agents, and task categories using 2,901 AI-authored pull requests (PRs) in 193 verified Android and iOS open-source GitHub repositories in the AIDev dataset. We find that Android projects have received 2x more AI-authored PRs and have achieved higher PR acceptance rate (71%) than iOS (63%), with significant agent-level variation on Android. Across task categories, PRs with routine tasks (feature, fix, and ui) achieve the highest acceptance, while structural changes like refactor and build achieve lower success and longer resolution times. Furthermore, our evolution analysis shows improvement in PR resolution time on Android through mid-2025 before it declined again. Our findings offer the first evidence-based characterization of AI agents effects on OSS mobile projects and establish empirical baselines for evaluating agent-generated contributions to design platform aware agentic systems.

Model checking in TLA+ provides strong correctness guarantees, yet practitioners continue to face significant challenges in interpreting counterexamples, understanding large state-transition graphs, and repairing faulty models. These difficulties stem from the limited explainability of raw model-checker output and the substantial manual effort required to trace violations back to source specifications. Although the TLA+ Toolbox includes a state diagram viewer, it offers only a static, fully expanded graph without folding, color highlighting, or semantic explanations, which limits its scalability and interpretability. We present ModelWisdom, an interactive environment that uses visualization and large language models to make TLA+ model checking more interpretable and actionable. ModelWisdom offers: (i) Model Visualization, with colorized violation highlighting, click-through links from transitions to TLA+ code, and mapping between violating states and broken properties; (ii) Graph Optimization, including tree-based structuring and node/edge folding to manage large models; (iii) Model Digest, which summarizes and explains subgraphs via large language models (LLMs) and performs preprocessing and partial explanations; and (iv) Model Repair, which extracts error information and supports iterative debugging. Together, these capabilities turn raw model-checker output into an interactive, explainable workflow, improving understanding and reducing debugging effort for nontrivial TLA+ specifications. The website to ModelWisdom is available: https://model-wisdom.pages.dev. A demonstrative video can be found at https://www.youtube.com/watch?v=plyZo30VShA.

Vulnerability detection is crucial to protect software security. Nowadays, deep learning (DL) is the most promising technique to automate this detection task, leveraging its superior ability to extract patterns and representations within extensive code volumes. Despite its promise, DL-based vulnerability detection remains in its early stages, with model performance exhibiting variability across datasets. Drawing insights from other well-explored application areas like computer vision, we conjecture that the imbalance issue (the number of vulnerable code is extremely small) is at the core of the phenomenon. To validate this, we conduct a comprehensive empirical study involving nine open-source datasets and two state-of-the-art DL models. The results confirm our conjecture. We also obtain insightful findings on how existing imbalance solutions perform in vulnerability detection. It turns out that these solutions perform differently as well across datasets and evaluation metrics. Specifically: 1) Focal loss is more suitable to improve the precision, 2) mean false error and class-balanced loss encourages the recall, and 3) random over-sampling facilitates the F1-measure. However, none of them excels across all metrics. To delve deeper, we explore external influences on these solutions and offer insights for developing new solutions.

Artificial intelligence (AI) has the potential to transform healthcare, education, governance and socioeconomic equity, but its benefits remain concentrated in a small number of languages (Bender, 2019; Blasi et al., 2022; Joshi et al., 2020; Ranathunga and de Silva, 2022; Young, 2015). Language AI - the technologies that underpin widely-used conversational systems such as ChatGPT - could provide major benefits if available in people's native languages, yet most of the world's 7,000+ linguistic communities currently lack access and face persistent digital marginalization. Here we present a global longitudinal analysis of social, economic and infrastructural conditions across languages to assess systemic inequalities in language AI. We first analyze the existence of AI resources for 6003 languages. We find that despite efforts of the community to broaden the reach of language technologies (Bapna et al., 2022; Costa-Jussà et al., 2022), the dominance of a handful of languages is exacerbating disparities on an unprecedented scale, with divides widening exponentially rather than narrowing. Further, we contrast the longitudinal diffusion of AI with that of earlier IT technologies, revealing a distinctive hype-driven pattern of spread. To translate our findings into practical insights and guide prioritization efforts, we introduce the Language AI Readiness Index (EQUATE), which maps the state of technological, socio-economic, and infrastructural prerequisites for AI deployment across languages. The index highlights communities where capacity exists but remains underutilized, and provides a framework for accelerating more equitable diffusion of language AI. Our work contributes to setting the baseline for a transition towards more sustainable and equitable language technologies.

A widespread practice in software development is to tailor coding agents to repositories using context files, such as AGENTS.md, by either manually or automatically generating them. Although this practice is strongly encouraged by agent developers, there is currently no rigorous investigation into whether such context files are actually effective for real-world tasks. In this work, we study this question and evaluate coding agents' task completion performance in two complementary settings: established SWE-bench tasks from popular repositories, with LLM-generated context files following agent-developer recommendations, and a novel collection of issues from repositories containing developer-committed context files. Across multiple coding agents and LLMs, we find that context files tend to reduce task success rates compared to providing no repository context, while also increasing inference cost by over 20%. Behaviorally, both LLM-generated and developer-provided context files encourage broader exploration (e.g., more thorough testing and file traversal), and coding agents tend to respect their instructions. Ultimately, we conclude that unnecessary requirements from context files make tasks harder, and human-written context files should describe only minimal requirements.

While no-reference point cloud quality assessment (NR-PCQA) approaches have achieved significant progress over the past decade, their performance often degrades substantially when a distribution gap exists between the training (source domain) and testing (target domain) data. However, to date, limited attention has been paid to transferring NR-PCQA models across domains. To address this challenge, we propose the first unsupervised progressive domain adaptation (UPDA) framework for NR-PCQA, which introduces a two-stage coarse-to-fine alignment paradigm to address domain shifts. At the coarse-grained stage, a discrepancy-aware coarse-grained alignment method is designed to capture relative quality relationships between cross-domain samples through a novel quality-discrepancy-aware hybrid loss, circumventing the challenges of direct absolute feature alignment. At the fine-grained stage, a perception fusion fine-grained alignment approach with symmetric feature fusion is developed to identify domain-invariant features, while a conditional discriminator selectively enhances the transfer of quality-relevant features. Extensive experiments demonstrate that the proposed UPDA effectively enhances the performance of NR-PCQA methods in cross-domain scenarios, validating its practical applicability. The code is available at https://github.com/yokeno1/UPDA-main.

The brain interprets visual information through learned regularities, a computation formalized as probabilistic inference under a prior. The visual cortex establishes priors for this inference, some delivered through established top-down connections that inform low-level cortices about statistics represented at higher levels in the cortical hierarchy. While evidence shows that adaptation leads to priors reflecting the structure of natural images, it remains unclear whether similar priors can be flexibly acquired when learning a specific task. To investigate this, we built a generative model of V1 optimized for a simple discrimination task and analyzed it together with large-scale recordings from mice performing an analogous task. In line with recent approaches, we assumed that neuronal activity in V1 corresponds to latent posteriors in the generative model, enabling investigation of task-related priors in neuronal responses. To obtain a flexible test bed, we extended the VAE formalism so that a task can be acquired efficiently by reusing previously learned representations. Task-specific priors learned by this Task-Amortized VAE were used to investigate biases in mice and model when presenting stimuli that violated trained task statistics. Mismatch between learned task statistics and incoming sensory evidence produced signatures of uncertainty in stimulus category in the TAVAE posterior, reflecting properties of bimodal response profiles in V1 recordings. The task-optimized generative model accounted for key characteristics of V1 population activity, including within-day updates to population responses. Our results confirm that flexible task-specific contextual priors can be learned on demand by the visual system and deployed as early as the entry level of visual cortex.

Muon updates weight matrices along (approximate) polar factors of the gradients and has shown strong empirical performance in large-scale training. Existing attempts at explaining its performance largely focus on single-step comparisons (on quadratic proxies) and worst-case guarantees that treat the inexactness of the polar-factor as a nuisance ``to be argued away''. We show that already on simple strongly convex functions such as $L(W)=\frac12\|W\|_{\text{F}}^2$, these perspectives are insufficient, suggesting that understanding Muon requires going beyond local proxies and pessimistic worst-case bounds. Instead, our analysis exposes two observations that already affect behavior on simple quadratics and are not well captured by prevailing abstractions: (i) approximation error in the polar step can qualitatively alter discrete-time dynamics and improve reachability and finite-time performance -- an effect practitioners exploit to tune Muon, but that existing theory largely treats as a pure accuracy compromise; and (ii) structural properties of the objective affect finite-budget constants beyond the prevailing conditioning-based explanations. Thus, any general theory covering these cases must either incorporate these ingredients explicitly or explain why they are irrelevant in the regimes of interest.

Multimodal Information Retrieval has made significant progress in recent years, leveraging the increasingly strong multimodal abilities of deep pre-trained models to represent information across modalities. Music Information Retrieval (MIR), in particular, has considerably increased in quality, with neural representations of music even making its way into everyday life products. However, there is a lack of high-quality benchmarks for evaluating music retrieval performance. To address this issue, we introduce \textbf{IncompeBench}, a carefully annotated benchmark comprising $1,574$ permissively licensed, high-quality music snippets, $500$ diverse queries, and over $125,000$ individual relevance judgements. These annotations were created through the use of a multi-stage pipeline, resulting in high agreement between human annotators and the generated data. The resulting datasets are publicly available at https://huggingface.co/datasets/mixedbread-ai/incompebench-strict and https://huggingface.co/datasets/mixedbread-ai/incompebench-lenient with the prompts available at https://github.com/mixedbread-ai/incompebench-programs.

LLMs are increasingly supporting decision-making across high-stakes domains, requiring critical reflection on the socio-technical factors that shape how humans and LLMs are assigned roles and interact during human-in-the-loop decision-making. This paper introduces the concept of human-LLM archetypes -- defined as re-curring socio-technical interaction patterns that structure the roles of humans and LLMs in collaborative decision-making. We describe 17 human-LLM archetypes derived from a scoping literature review and thematic analysis of 113 LLM-supported decision-making papers. Then, we evaluate these diverse archetypes across real-world clinical diagnostic cases to examine the potential effects of adopting distinct human-LLM archetypes on LLM outputs and decision outcomes. Finally, we present relevant tradeoffs and design choices across human-LLM archetypes, including decision control, social hierarchies, cognitive forcing strategies, and information requirements. Through our analysis, we show that selection of human-LLM interaction archetype can influence LLM outputs and decisions, bringing important risks and considerations for the designers of human-AI decision-making systems

Software languages evolve over time for reasons such as feature additions. When grammars evolve, textual instances that originally conformed to them may become outdated. While model-driven engineering provides many techniques for co-evolving models with metamodel changes, these approaches are not designed for textual DSLs and may lose human-relevant information such as layout and comments. This study systematically evaluates the potential of large language models (LLMs) for co-evolving grammars and instances of textual DSLs. Using Claude Sonnet 4.5 and GPT-5.2 across ten case languages with ten runs each, we assess both correctness and preservation of human-oriented information. Results show strong performance on small-scale cases ($\geq$94% precision and recall for instances requiring fewer than 20 modified lines), but performance degraded with scale: Claude maintains 85% recall at 40 lines, while GPT fails on the largest instances. Response time increases substantially with instance size, and grammar evolution complexity and deletion granularity affect performance more than change type. These findings clarify when LLM-based co-evolution is effective and where current limitations remain.

Modeling vessel activity at sea is critical for a wide range of applications, including route planning, transportation logistics, maritime safety, and environmental monitoring. Over the past two decades, the Automatic Identification System (AIS) has enabled real-time monitoring of hundreds of thousands of vessels, generating huge amounts of data daily. One major challenge in using AIS data is the presence of large gaps in vessel trajectories, often caused by coverage limitations or intentional transmission interruptions. These gaps can significantly degrade data quality, resulting in inaccurate or incomplete analysis. State-of-the-art imputation approaches have mainly been devised to tackle gaps in vehicle trajectories, even when the underlying road network is not considered. But the motion patterns of sailing vessels differ substantially, e.g., smooth turns, maneuvering near ports, or navigating in adverse weather conditions. In this application paper, we propose HABIT, a lightweight, configurable H3 Aggregation-Based Imputation framework for vessel Trajectories. This data-driven framework provides a valuable means to impute missing trajectory segments by extracting, analyzing, and indexing motion patterns from historical AIS data. Our empirical study over AIS data across various timeframes, densities, and vessel types reveals that HABIT produces maritime trajectory imputations performing comparably to baseline methods in terms of accuracy, while performing better in terms of latency while accounting for vessel characteristics and their motion patterns.

Scale-invariance in games has recently emerged as a widely valued desirable property. Yet, almost all fast convergence guarantees in learning in games require prior knowledge of the utility scale. To address this, we develop learning dynamics that achieve fast convergence while being both scale-free, requiring no prior information about utilities, and scale-invariant, remaining unchanged under positive rescaling of utilities. For two-player zero-sum games, we obtain scale-free and scale-invariant dynamics with external regret bounded by $\tilde{O}(A_{\mathrm{diff}})$, where $A_{\mathrm{diff}}$ is the payoff range, which implies an $\tilde{O}(A_{\mathrm{diff}} / T)$ convergence rate to Nash equilibrium after $T$ rounds. For multiplayer general-sum games with $n$ players and $m$ actions, we obtain scale-free and scale-invariant dynamics with swap regret bounded by $O(U_{\mathrm{max}} \log T)$, where $U_{\mathrm{max}}$ is the range of the utilities, ignoring the dependence on the number of players and actions. This yields an $O(U_{\mathrm{max}} \log T / T)$ convergence rate to correlated equilibrium. Our learning dynamics are based on optimistic follow-the-regularized-leader with an adaptive learning rate that incorporates the squared path length of the opponents' gradient vectors, together with a new stopping-time analysis that exploits negative terms in regret bounds without scale-dependent tuning. For general-sum games, scale-free learning is enabled also by a technique called doubling clipping, which clips observed gradients based on past observations.

Collaborative Intrusion Detection Systems (CIDS) are increasingly adopted to counter cyberattacks, as their collaborative nature enables them to adapt to diverse scenarios across heterogeneous environments. As distributed critical infrastructure operates in rapidly evolving environments, such as drones in both civil and military domains, there is a growing need for CIDS architectures that can flexibly accommodate these dynamic changes. In this study, we propose a novel CIDS framework designed for easy deployment across diverse distributed environments. The framework dynamically optimizes detector allocation per node based on available resources and data types, enabling rapid adaptation to new operational scenarios with minimal computational overhead. We first conducted a comprehensive literature review to identify key characteristics of existing CIDS architectures. Based on these insights and real-world use cases, we developed our CIDS framework, which we evaluated using several distributed datasets that feature different attack chains and network topologies. Notably, we introduce a public dataset based on a realistic cyberattack targeting a ground drone aimed at sabotaging critical infrastructure. Experimental results demonstrate that the proposed CIDS framework can achieve adaptive, efficient intrusion detection in distributed settings, automatically reconfiguring detectors to maintain an optimal configuration, without requiring heavy computation, since all experiments were conducted on edge devices.

Neural retrievers are effective but brittle: underspecified or ambiguous queries can misdirect ranking even when relevant documents exist. Existing approaches address this brittleness only partially: LLMs rewrite queries without retriever feedback, and explainability methods identify misleading tokens but are used for post-hoc analysis. We close this loop and propose an attribution-guided query rewriting method that uses token-level explanations to guide query rewriting. For each query, we compute gradient-based token attributions from the retriever and then use these scores as soft guidance in a structured prompt to an LLM that clarifies weak or misleading query components while preserving intent. Evaluated on BEIR collections, the resulting rewrites consistently improve retrieval effectiveness over strong baselines, with larger gains for implicit or ambiguous information needs.

While machine learning (ML)-based receiver algorithms have received a great deal of attention in the recent literature, they often suffer from poor scaling with increasing spatial multiplexing order and lack of explainability and generalization. This paper presents EqDeepRx, a practical deep-learning-aided multiple-input multiple-output (MIMO) receiver, which is built by augmenting linear receiver processing with carefully engineered ML blocks. At the core of the receiver model is a shared-weight DetectorNN that operates independently on each spatial stream or layer, enabling near-linear complexity scaling with respect to multiplexing order. To ensure better explainability and generalization, EqDeepRx retains conventional channel estimation and augments it with a lightweight DenoiseNN that learns frequency-domain smoothing. To reduce the dimensionality of the DetectorNN inputs, the receiver utilizes two linear equalizers in parallel: a linear minimum mean-square error (LMMSE) equalizer with interference-plus-noise covariance estimation and a regularized zero-forcing (RZF) equalizer. The parallel equalized streams are jointly consumed by the DetectorNN, after which a compact DemapperNN produces bit log-likelihood ratios for channel decoding. 5G/6G-compliant end-to-end simulations across multiple channel scenarios, pilot patterns, and inter-cell interference conditions show improved error rate and spectral efficiency over a conventional baseline, while maintaining low-complexity inference and support for different MIMO configurations without retraining.

Maximum-a-posteriori (MAP) approaches are an effective framework for inverse problems with known forward operators, particularly when combined with expressive priors and careful parameter selection. In blind settings, however, their use becomes significantly less stable due to the inherent non-convexity of the problem and the potential non-identifiability of the solutions. (Linear) minimum mean square error (MMSE) estimators provide a compelling alternative that can circumvent these limitations. In this work, we study synthetic two-dimensional blind deconvolution problems under fully controlled conditions, with complete prior knowledge of both the signal and kernel distributions. We compare tailored MAP algorithms with simple LMMSE estimators whose functional form is closely related to that of an optimal Tikhonov estimator. Our results show that, even in these highly controlled settings, MAP methods remain unstable and require extensive parameter tuning, whereas the LMMSE estimator yields a robust and reliable baseline. Moreover, we demonstrate empirically that the LMMSE solution can serve as an effective initialization for MAP approaches, improving their performance and reducing sensitivity to regularization parameters, thereby opening the door to future theoretical and practical developments.

Watermarking has emerged as a crucial technique for detecting and attributing content generated by large language models. While recent advancements have utilized watermark ensembles to enhance robustness, prevailing methods typically prioritize maximizing the strength of the watermark at every individual layer. In this work, we identify a critical limitation in this "stronger-is-better" approach: strong watermarks significantly reduce the entropy of the token distribution, which paradoxically weakens the effectiveness of watermarking in subsequent layers. We theoretically and empirically show that detectability is bounded by entropy and that watermark ensembles induce a monotonic decrease in both entropy and the expected green-list ratio across layers. To address this inherent trade-off, we propose a general framework that utilizes weaker single-layer watermarks to preserve the entropy required for effective multi-layer ensembling. Empirical evaluations demonstrate that this counter-intuitive strategy mitigates signal decay and consistently outperforms strong baselines in both detectability and robustness.

Decentralized optimization is critical for solving large-scale machine learning problems over distributed networks, where multiple nodes collaborate through local communication. In practice, the variances of stochastic gradient estimators often differ across nodes, yet their impact on algorithm design and complexity remains unclear. To address this issue, we propose D-NSS, a decentralized algorithm with node-specific sampling, and establish its sample complexity depending on the arithmetic mean of local standard deviations, achieving tighter bounds than existing methods that rely on the worst-case or quadratic mean. We further derive a matching sample complexity lower bound under heterogeneous variance, thereby proving the optimality of this dependence. Moreover, we extend the framework with a variance reduction technique and develop D-NSS-VR, which under the mean-squared smoothness assumption attains an improved sample complexity bound while preserving the arithmetic-mean dependence. Finally, numerical experiments validate the theoretical results and demonstrate the effectiveness of the proposed algorithms.

The rapid emergence of autonomous large language model agents has given rise to persistent, large-scale agent ecosystems whose collective behavior cannot be adequately understood through anecdotal observation or small-scale simulation. This paper introduces data-driven silicon sociology as a systematic empirical framework for studying social structure formation among interacting artificial agents. We present a pioneering large-scale data mining investigation of an in-the-wild agent society by analyzing Moltbook, a social platform designed primarily for agent-to-agent interaction. At the time of study, Moltbook hosted over 150,000 registered autonomous agents operating across thousands of agent-created sub-communities. Using programmatic and non-intrusive data acquisition, we collected and analyzed the textual descriptions of 12,758 submolts, which represent proactive sub-community partitioning activities within the ecosystem. Treating agent-authored descriptions as first-class observational artifacts, we apply rigorous preprocessing, contextual embedding, and unsupervised clustering techniques to uncover latent patterns of thematic organization and social space structuring. The results show that autonomous agents systematically organize collective space through reproducible patterns spanning human-mimetic interests, silicon-centric self-reflection, and early-stage economic and coordination behaviors. Rather than relying on predefined sociological taxonomies, these structures emerge directly from machine-generated data traces. This work establishes a methodological foundation for data-driven silicon sociology and demonstrates that data mining techniques can provide a powerful lens for understanding the organization and evolution of large autonomous agent societies.

We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated using finite approximations of continuous probability distributions. Such an approximation might be the result of representing a continuous real-valued distribution using a discrete representation or from constructing an empirical distribution from samples (or might be the output of another distributional computational graph). We establish non-asymptotic error bounds in terms of the Wasserstein-1 distance, without imposing structural assumptions on the computational graph.

Spiking Neural Networks (SNNs) are dynamical systems that operate on spatiotemporal data, yet their learnable parameters are often limited to synaptic weights, contributing little to temporal pattern recognition. Learnable parameters that delay spike times can improve classification performance in temporal tasks, but existing methods rely on large networks and offline learning, making them unsuitable for real-time operation in resource-constrained environments. In this paper, we introduce synaptic and axonal delays to leaky integrate and fire (LIF)-based feedforward and recurrent SNNs, and propose three-factor learning rules to simultaneously learn delay parameters online. We employ a smooth Gaussian surrogate to approximate spike derivatives exclusively for the eligibility trace calculation, and together with a top-down error signal determine parameter updates. Our experiments show that incorporating delays improves accuracy by up to 20% over a weights-only baseline, and for networks with similar parameter counts, jointly learning weights and delays yields up to 14% higher accuracy. On the SHD speech recognition dataset, our method achieves similar accuracy to offline backpropagation-based approaches. Compared to state-of-the-art methods, it reduces model size by 6.6x and inference latency by 67%, with only a 2.4% drop in classification accuracy. Our findings benefit the design of power and area-constrained neuromorphic processors by enabling on-device learning and lowering memory requirements.

Physics-Informed Neural Networks (PINNs) solve physical systems by incorporating governing partial differential equations directly into neural network training. In electromagnetism, where well-established methodologies such as FDTD and FEM already exist, new methodologies are expected to provide clear advantages to be accepted. Despite their mesh-free nature and applicability to inverse problems, PINNs can exhibit deficiencies in accuracy and energy metrics compared to FDTD. This study demonstrates that hybrid training strategies can bring PINNs closer to FDTD-level accuracy and energy consistency. A hybrid methodology addressing common challenges in wave propagation is presented. Causality collapse in time-dependent PINN training is addressed via time marching and causality-aware weighting. To mitigate discontinuities introduced by time marching, a two stage interface continuity loss is applied. To suppress cumulative energy drift in electromagnetic waves, a local Poynting-based regularizer is developed. In the developed PINN model, high field accuracy is achieved with an average 0.09% NRMSE and 1.01% $L^2$ error over time. Energy conservation is achieved with only a 0.02% relative energy mismatch in the 2D PEC cavity scenario. Training is performed without labeled field data, using only physics-based residual losses; FDTD is used solely for post-training evaluation. The results demonstrate that PINNs can achieve competitive results with FDTD in canonical electromagnetic examples and are a viable alternative.

Monitoring contact pressure in hospital beds is essential for preventing pressure ulcers and enabling real-time patient assessment. Current methods can predict pressure maps but often lack physical plausibility, limiting clinical reliability. This work proposes a framework that enhances plausibility via Informed Latent Space (ILS) and Weight Optimization Loss (WOL) with conditional generative modeling to produce high-fidelity, physically consistent pressure estimates. This study also applies diffusion based conditional Brownian Bridge Diffusion Model (BBDM) and proposes training strategy for its latent counterpart Latent Brownian Bridge Diffusion Model (LBBDM) tailored for pressure synthesis in lying postures. Experiment results shows proposed method improves physical plausibility and performance over baselines: BBDM with ILS delivers highly detailed maps at higher computational cost and large inference time, whereas LBBDM provides faster inference with competitive performance. Overall, the approach supports non-invasive, vision-based, real-time patient monitoring in clinical environments.

Modern vector databases enable efficient retrieval over high-dimensional neural embeddings, powering applications from web search to retrieval-augmented generation. However, classical theory predicts such tasks should suffer from the curse of dimensionality, where distances between points become nearly indistinguishable, thereby crippling efficient nearest-neighbor search. We revisit this paradox through the lens of stability, the property that small perturbations to a query do not radically alter its nearest neighbors. Building on foundational results, we extend stability theory to three key retrieval settings widely used in practice: (i) multi-vector search, where we prove that the popular Chamfer distance metric preserves single-vector stability, while average pooling aggregation may destroy it; (ii) filtered vector search, where we show that sufficiently large penalties for mismatched filters can induce stability even when the underlying search is unstable; and (iii) sparse vector search, where we formalize and prove novel sufficient stability conditions. Across synthetic and real datasets, our experimental results match our theoretical predictions, offering concrete guidance for model and system design to avoid the curse of dimensionality.

Symbolic regression seeks to uncover physical laws from experimental data by searching for closed-form expressions, which is an important task in AI-driven scientific discovery. Yet the exponential growth of the search space of expression renders the task computationally challenging. A promising yet underexplored direction for reducing the search space and accelerating training lies in *symbolic equivalence*: many expressions, although syntactically different, define the same function -- for example, $\log(x_1^2x_2^3)$, $\log(x_1^2)+\log(x_2^3)$, and $2\log(x_1)+3\log(x_2)$. Existing algorithms treat such variants as distinct outputs, leading to redundant exploration and slow learning. We introduce EGG-SR, a unified framework that integrates symbolic equivalence into a class of modern symbolic regression methods, including Monte Carlo Tree Search (MCTS), Deep Reinforcement Learning (DRL), and Large Language Models (LLMs). EGG-SR compactly represents equivalent expressions through the proposed EGG module (via equality graphs), accelerating learning by: (1) pruning redundant subtree exploration in EGG-MCTS, (2) aggregating rewards across equivalent generated sequences in EGG-DRL, and (3) enriching feedback prompts in EGG-LLM. Theoretically, we show the benefit of embedding EGG into learning: it tightens the regret bound of MCTS and reduces the variance of the DRL gradient estimator. Empirically, EGG-SR consistently enhances a class of symbolic regression models across several benchmarks, discovering more accurate expressions within the same time limit. Project page is at: https://nan-jiang-group.github.io/egg-sr.

Electronic health records (EHRs) are central to modern healthcare delivery and research; yet, many researchers lack the database expertise necessary to write complex SQL queries or generate effective visualizations, limiting efficient data use and scientific discovery. To address this barrier, we introduce CELEC, a large language model (LLM)-powered framework for automated EHR data extraction and analytics. CELEC translates natural language queries into SQL using a prompting strategy that integrates schema information, few-shot demonstrations, and chain-of-thought reasoning, which together improve accuracy and robustness. CELEC also adheres to strict privacy protocols: the LLM accesses only database metadata (e.g., table and column names), while all query execution occurs securely within the institutional environment, ensuring that no patient-level data is ever transmitted to or shared with the LLM. On a subset of the EHRSQL benchmark, CELEC achieves execution accuracy comparable to prior systems while maintaining low latency, cost efficiency, and strict privacy by exposing only database metadata to the LLM. Ablation studies confirm that each component of the SQL generation pipeline, particularly the few-shot demonstrations, plays a critical role in performance. By lowering technical barriers and enabling medical researchers to query EHR databases directly, CELEC streamlines research workflows and accelerates biomedical discovery.