Prompt optimization has become a practical way to improve the performance of Large Language Models (LLMs) without retraining. However, most existing frameworks treat evaluation as a black box, relying solely on outcome scores without explaining why prompts succeed or fail. Moreover, they involve repetitive trial-and-error refinements that remain implicit, offering limited interpretability or actionable guidance for systematic improvement. In this paper, we propose MA-SAPO: a new Multi-Agent Reasoning for Score Aware Prompt Optimization framework that links evaluation outcomes directly to targeted refinements. Specifically, in the Training Phase, multiple agents interpret evaluation scores, diagnose weaknesses, and generate concrete revision directives, which are stored as reusable reasoning assets. In the Test Phase, an analyzer agent retrieves relevant exemplars and assets for a new prompt, and a refiner agent applies evidence-based edits to improve the prompt and its response. By grounding optimization in structured reasoning, MA-SAPO ensures edits are interpretable, auditable, and controllable. Experiments on the HelpSteer1/2 benchmarks show that our framework consistently outperforms single-pass prompting, retrieval-augmented generation, and prior multi-agent methods across multiple evaluation metrics.

Datasets often possess an intrinsic multiscale structure with meaningful descriptions at different levels of coarseness. Such datasets are naturally described as multi-resolution clusterings, i.e., not necessarily hierarchical sequences of partitions across scales. To analyse and compare such sequences, we use tools from topological data analysis and define the Multiscale Clustering Bifiltration (MCbiF), a 2-parameter filtration of abstract simplicial complexes that encodes cluster intersection patterns across scales. The MCbiF is a complete invariant of (non-hierarchical) sequences of partitions and can be interpreted as a higher-order extension of Sankey diagrams, which reduce to dendrograms for hierarchical sequences. We show that the multiparameter persistent homology (MPH) of the MCbiF yields a finitely presented and block decomposable module, and its stable Hilbert functions characterise the topological autocorrelation of the sequence of partitions. In particular, at dimension zero, the MPH captures violations of the refinement order of partitions, whereas at dimension one, the MPH captures higher-order inconsistencies between clusters across scales. We then demonstrate through experiments the use of MCbiF Hilbert functions as interpretable topological feature maps for downstream machine learning tasks, and show that MCbiF feature maps outperform both baseline features and representation learning methods on regression and classification tasks for non-hierarchical sequences of partitions. We also showcase an application of MCbiF to real-world data of non-hierarchical wild mice social grouping patterns across time.

Traditional bug-tracking systems rely heavily on manual reporting, reproduction, classification, and resolution, involving multiple stakeholders such as end users, customer support, developers, and testers. This division of responsibilities requires substantial coordination and human effort, widens the communication gap between non-technical users and developers, and significantly slows the process from bug discovery to deployment. Moreover, current solutions are highly asynchronous, often leaving users waiting long periods before receiving any feedback. In this paper, we examine the evolution of bug-tracking practices, from early paper-based methods to today's web-based platforms, and present a forward-looking vision of an AI-powered bug tracking framework. The framework augments existing systems with large language model (LLM) and agent-driven automation, and we report early adaptations of its key components, providing initial empirical grounding for its feasibility. The proposed framework aims to reduce time to resolution and coordination overhead by enabling end users to report bugs in natural language while AI agents refine reports, attempt reproduction, classify bugs, validate reports, suggest no-code fixes, generate patches, and support continuous integration and deployment. We discuss the challenges and opportunities of integrating LLMs into bug tracking and show how intelligent automation can transform software maintenance into a more efficient, collaborative, and user-centric process.

Quasar-convex functions form a broad nonconvex class with applications to linear dynamical systems, generalized linear models, and Riemannian optimization, among others. Current nearly optimal algorithms work only in affine spaces due to the loss of one degree of freedom when working with general convex constraints. Obtaining an accelerated algorithm that makes nearly optimal $\widetilde{O}(1/(γ\sqrt{\varepsilon}))$ first-order queries to a $γ$-quasar convex smooth function \emph{with constraints} was independently asked as an open problem in Martínez-Rubio (2022); Lezane, Langer, and Koolen (2024). In this work, we solve this question by designing an inexact accelerated proximal point algorithm that we implement using a first-order method achieving the aforementioned rate and, as a consequence, we improve the complexity of the accelerated geodesically Riemannian optimization solution in Martínez-Rubio (2022). We also analyze projected gradient descent and Frank-Wolfe algorithms in this constrained quasar-convex setting. To the best of our knowledge, our work provides the first analyses of first-order methods for quasar-convex smooth functions with general convex constraints.

Recent advances in large language model (LLM) embeddings have enabled powerful representations for biological data, but most applications to date focus on gene-level information. We present one of the first systematic frameworks to generate genetic variant-level embeddings across the entire human genome. Using curated annotations from FAVOR, ClinVar, and the GWAS Catalog, we construct functional text descriptions for 8.9 billion possible variants and generated embeddings at three scales: 1.5 million HapMap3/MEGA variants, 90 million imputed UK Biobank (UKB) variants, and 9 billion all possible variants. Embeddings were produced using general purpose models including both OpenAI's text-embedding-3-large and the open-source Qwen3-Embedding-0.6B models. Baseline quality control experiments demonstrate high predictive accuracy for variant-level properties, validating the embeddings as structured representations of genomic variation. We further apply them to real-world embedding-augmented genetic risk predictions that demonstrate the performance of using LLM embeddings in polygenic risk score (PRS) style predictions over the UK Biobank cohort data. These resources, publicly available on Hugging Face, provide a foundation for advancing large-scale genomic discovery and precision medicine.

Classifying hadronic jets using their constituents' kinematic information is a critical task in modern high-energy collider physics. Often, classifiers are designed by targeting the best performance using metrics such as accuracy, AUC, or rejection rates. However, the use of a single metric can lead to the use of architectures that are more model-dependent than competitive alternatives, leading to potential uncertainty and bias in analysis. We explore such trade-offs and demonstrate the consequences of using networks with high performance metrics but low resilience.

The integration of cooperative and non-cooperative localization is fundamentally important, as these two modes frequently coexist in wireless sensor networks, especially when sensor positions are uncertain and targets are unable to communicate with the network. This paper presents a joint modeling approach that formulates cooperative and non-cooperative localization as a single optimization problem. By processing both tasks jointly, the proposed method eliminates the latency inherent in sequential approaches that perform cooperative localization first, followed by non-cooperative localization. However, this joint formulation introduces complex variable coupling, posing challenges in both modeling and optimization. To address this coupling, we introduce auxiliary variables that enable structural decoupling and facilitate distributed computation. Building on this formulation, we develop the Scaled Proximal Alternating Direction Method of Multipliers for Joint Cooperative and Non-Cooperative Localization (SP-ADMM-JCNL). Leveraging the structured design of the problem, we provide theoretical guarantees that the algorithm generates a sequence converging globally to a KKT point of the reformulated problem, and further to a critical point of the original non-convex objective function, with the convergence rate of O(1/T). Experiments demonstrate that SP-ADMM-JCNL achieves accurate and reliable localization performance.

In general, multi-channel source separation has utilized inter-microphone phase differences (IPDs) concatenated with magnitude information in time-frequency domain, or real and imaginary components stacked along the channel axis. However, the spatial information of a sound source is fundamentally contained in the differences between microphones, specifically in the correlation between them, while the power of each microphone also provides valuable information about the source spectrum, which is why the magnitude is also included. Therefore, we propose a network that directly leverages a correlation input with phase transform (PHAT)-beta to estimate the separation filter. In addition, the proposed TF-CorrNet processes the features alternately across time and frequency axes as a dual-path strategy in terms of spatial information. Furthermore, we add a spectral module to model source-related direct time-frequency patterns for improved speech separation. Experimental results demonstrate that the proposed TF-CorrNet effectively separates the speech sounds, showing high performance with a low computational cost in the LibriCSS dataset.

Swarm based optimization algorithms have demonstrated remarkable success in solving complex optimization problems. However, their widespread adoption remains sceptical due to limited transparency in how different algorithmic components influence the overall performance of the algorithm. This work presents a multi-faceted interpretability related investigations of Particle Swarm Optimization (PSO). Through this work, we provide a framework that makes the PSO interpretable and explainable using novel machine learning approach. We first developed a comprehensive landscape characterization framework using Exploratory Landscape Analysis to quantify problem difficulty and identify critical features in the problem that affects the optimization performance of PSO. Secondly, we develop an explainable benchmarking framework for PSO. The work successfully decodes how swarm topologies affect information flow, diversity, and convergence. Through systematic experimentation across 24 benchmark functions in multiple dimensions, we establish practical guidelines for topology selection and parameter configuration. A systematic design of decision tree is developed to identify the decision making inside PSO. These findings uncover the black-box nature of PSO, providing more transparency and interpretability to swarm intelligence systems. The source code is available at https://github.com/GitNitin02/ioh_pso.

Bayesian Additive Regression Trees (BART) is a powerful statistical model that leverages the strengths of Bayesian inference and regression trees. It has received significant attention for capturing complex non-linear relationships and interactions among predictors. However, the accuracy of BART often comes at the cost of interpretability. To address this limitation, we propose ANOVA Bayesian Additive Regression Trees (ANOVA-BART), a novel extension of BART based on the functional ANOVA decomposition, which is used to decompose the variability of a function into different interactions, each representing the contribution of a different set of covariates or factors. Our proposed ANOVA-BART enhances interpretability, preserves and extends the theoretical guarantees of BART, and achieves comparable prediction performance. Specifically, we establish that the posterior concentration rate of ANOVA-BART is nearly minimax optimal, and further provides the same convergence rates for each interaction that are not available for BART. Moreover, comprehensive experiments confirm that ANOVA-BART is comparable to BART in both accuracy and uncertainty quantification, while also demonstrating its effectiveness in component selection. These results suggest that ANOVA-BART offers a compelling alternative to BART by balancing predictive accuracy, interpretability, and theoretical consistency.

Recent years have witnessed remarkable achievements in perceptual image restoration (IR), creating an urgent demand for accurate image quality assessment (IQA), which is essential for both performance comparison and algorithm optimization. Unfortunately, the existing IQA metrics exhibit inherent weakness for IR task, particularly when distinguishing fine-grained quality differences among restored images. To address this dilemma, we contribute the first-of-its-kind fine-grained image quality assessment dataset for image restoration, termed FGRestore, comprising 18,408 restored images across six common IR tasks. Beyond conventional scalar quality scores, FGRestore was also annotated with 30,886 fine-grained pairwise preferences. Based on FGRestore, a comprehensive benchmark was conducted on the existing IQA metrics, which reveal significant inconsistencies between score-based IQA evaluations and the fine-grained restoration quality. Motivated by these findings, we further propose FGResQ, a new IQA model specifically designed for image restoration, which features both coarse-grained score regression and fine-grained quality ranking. Extensive experiments and comparisons demonstrate that FGResQ significantly outperforms state-of-the-art IQA metrics. Codes and model weights have been released in https://sxfly99.github.io/FGResQ-Home.

Constructing confidence intervals for the value of an (unknown) optimal treatment policy is a fundamental problem in causal inference. Insight into the optimal policy value can guide the development of reward-maximizing, individualized treatment regimes. However, because the functional that defines the optimal value is non-differentiable, standard semi-parametric approaches for performing inference fail to be directly applicable. Many existing works circumvent non-differentiability by making the unrealistic assumption of zero probability of treatment non-response, i.e. that every unit responds (either positively or negatively) to an assigned treatment. Further, works that don't circumvent this restriction rely on refitting nuisance models a number of times proportional to the sample size. In this paper, we construct and analyze a simple, softmax smoothing-based estimator for the value of an optimal treatment policy. Our estimator applies in both static and dynamic treatment regimes, only requires fitting a constant number of nuisance models, and is statistically efficient when there is zero probability of non-response to treatment. Also, while our estimator does not require making semi-parametric restrictions, it can exploit them when they exist. We further show how our softmax smoothing approach can be used to estimate general parameters that are specified as a maximum of scores involving nuisance components, and look at conditional Balke and Pearl bounds and $L^1$ calibration error as salient examples.

Tree ensembles are non-parametric methods widely recognized for their accuracy and ability to capture complex interactions. While these models excel at prediction, they are difficult to interpret and may fail to uncover useful relationships in the data. We propose an estimator to extract compact sets of decision rules from tree ensembles. The extracted models are accurate and can be manually examined to reveal relationships between the predictors and the response. A key novelty of our estimator is the flexibility to jointly control the number of rules extracted and the interaction depth of each rule, which improves accuracy. We develop a tailored exact algorithm to efficiently solve optimization problems underlying our estimator and an approximate algorithm for computing regularization paths, sequences of solutions that correspond to varying model sizes. We also establish novel non-asymptotic prediction error bounds for our proposed approach, comparing it to an oracle that chooses the best data-dependent linear combination of the rules in the ensemble subject to the same complexity constraint as our estimator. The bounds illustrate that the large-sample predictive performance of our estimator is on par with that of the oracle. Through experiments, we demonstrate that our estimator outperforms existing algorithms for rule extraction.

We introduce a hierarchical framework that combines ab initio many-body calculations with a Bayesian neural network, developing emulators capable of accurately predicting nuclear properties across isotopic chains simultaneously and being applicable to different regions of the nuclear chart. We benchmark our developments using the oxygen isotopic chain, achieving accurate results for ground-state energies and nuclear charge radii, while providing robust uncertainty quantification. Our framework enables global sensitivity analysis of nuclear binding energies and charge radii with respect to the low-energy constants that describe the nuclear force.

Positron emission tomography (PET) is a critical tool for diagnosing tumors and neurological disorders but poses radiation risks to patients, particularly to sensitive populations. While reducing injected radiation dose mitigates this risk, it often compromises image quality. To reconstruct full-dose-quality images from low-dose scans, we propose a Cycle-constrained Adversarial Denoising Convolutional Network (Cycle-DCN). This model integrates a noise predictor, two discriminators, and a consistency network, and is optimized using a combination of supervised loss, adversarial loss, cycle consistency loss, identity loss, and neighboring Structural Similarity Index (SSIM) loss. Experiments were conducted on a large dataset consisting of raw PET brain data from 1,224 patients, acquired using a Siemens Biograph Vision PET/CT scanner. Each patient underwent a 120-seconds brain scan. To simulate low-dose PET conditions, images were reconstructed from shortened scan durations of 30, 12, and 5 seconds, corresponding to 1/4, 1/10, and 1/24 of the full-dose acquisition, respectively, using a custom-developed GPU-based image reconstruction software. The results show that Cycle-DCN significantly improves average Peak Signal-to-Noise Ratio (PSNR), SSIM, and Normalized Root Mean Square Error (NRMSE) across three dose levels, with improvements of up to 56%, 35%, and 71%, respectively. Additionally, it achieves contrast-to-noise ratio (CNR) and Edge Preservation Index (EPI) values that closely align with full-dose images, effectively preserving image details, tumor shape, and contrast, while resolving issues with blurred edges. The results of reader studies indicated that the images restored by Cycle-DCN consistently received the highest ratings from nuclear medicine physicians, highlighting their strong clinical relevance.

The non-convex nature of trained neural networks has created significant obstacles in their incorporation into optimization models. In this context, Anderson et al. (2020) provided a framework to obtain the convex hull of the graph of a piecewise linear convex activation function composed with an affine function; this effectively convexifies activations such as the ReLU together with the affine transformation that precedes it. In this article, we contribute to this line of work by developing a recursive formula that yields a tight convexification for the composition of an activation with an affine function for a wide scope of activation functions, namely, convex or ``S-shaped". Our approach can be used to efficiently compute separating hyperplanes or determine that none exists in various settings, including non-polyhedral cases.

Inspired by the gradient flow viewpoint of the Landau equation and the corresponding dynamic formulation of the Landau metric in [arXiv:2007.08591], we develop a novel implicit particle method for the Landau equation in the framework of the JKO scheme. We first reformulate the Landau metric in a computationally friendly form, and then translate it into the Lagrangian viewpoint using the flow map. A key observation is that, while the flow map evolves according to a rather complicated integral equation, the unknown component is simply a score function of the corresponding density plus an additional term in the null space of the collision kernel. This insight guides us in designing and training the neural network for the flow map. Additionally, the objective function is in a double summation form, making it highly suitable for stochastic methods. Consequently, we design a tailored version of stochastic gradient descent that maintains particle interactions and significantly reduces the computational complexity. Compared to other deterministic particle methods, the proposed method enjoys exact entropy dissipation and unconditional stability, therefore making it suitable for large-scale plasma simulations over extended time periods.

The paper presents a framework for online learning of the Koopman operator using streaming data. Many complex systems for which data-driven modeling and control are sought provide streaming sensor data, the abundance of which can present computational challenges but cannot be ignored. Streaming data can intermittently sample dynamically different regimes or rare events which could be critical to model and control. Using ideas from subspace identification, we present a method where the Grassmannian distance between the subspace of an extended observability matrix and the streaming segment of data is used to assess the `novelty' of the data. If this distance is above a threshold, it is added to an archive and the Koopman operator is updated if not it is discarded. Therefore, our method identifies data from segments of trajectories of a dynamical system that are from different dynamical regimes, prioritizes minimizing the amount of data needed in updating the Koopman model and furthermore reduces the number of basis functions by learning them adaptively. Therefore, by dynamically adjusting the amount of data used and learning basis functions, our method optimizes the model's accuracy and the system order.

Large language models (LLMs) present an enormous evolution in the strategic potential of conversational recommender systems (CRS). Yet to date, research has predominantly focused upon technical frameworks to implement LLM-driven CRS, rather than end-user evaluations or strategic implications for firms, particularly from the perspective of a small to medium enterprises (SME) that makeup the bedrock of the global economy. In the current paper, we detail the design of an LLM-driven CRS in an SME setting, and its subsequent performance in the field using both objective system metrics and subjective user evaluations. While doing so, we additionally outline a short-form revised ResQue model for evaluating LLM-driven CRS, enabling replicability in a rapidly evolving field. Our results reveal good system performance from a user experience perspective (85.5% recommendation accuracy) but underscore latency, cost, and quality issues challenging business viability. Notably, with a median cost of $0.04 per interaction and a latency of 5.7s, cost-effectiveness and response time emerge as crucial areas for achieving a more user-friendly and economically viable LLM-driven CRS for SME settings. One major driver of these costs is the use of an advanced LLM as a ranker within the retrieval-augmented generation (RAG) technique. Our results additionally indicate that relying solely on approaches such as Prompt-based learning with ChatGPT as the underlying LLM makes it challenging to achieve satisfying quality in a production environment. Strategic considerations for SMEs deploying an LLM-driven CRS are outlined, particularly considering trade-offs in the current technical landscape.

This paper presents a novel approach at the intersection of machine learning and number theory, focusing on the classification of prime and non-prime numbers. At the core of our research is the development of a highly sparse encoding method, integrated with conventional neural network architectures. This combination has shown promising results, achieving a recall of over 99\% in identifying prime numbers and 79\% for non-prime numbers from an inherently imbalanced sequential series of integers, while exhibiting rapid model convergence before the completion of a single training epoch. We performed training using $10^6$ integers starting from a specified integer and tested on a different range of $2 \times 10^6$ integers extending from $10^6$ to $3 \times 10^6$, offset by the same starting integer. While constrained by the memory capacity of our resources, which limited our analysis to a span of $3\times10^6$, we believe that our study contribute to the application of machine learning in prime number analysis. This work aims to demonstrate the potential of such applications and hopes to inspire further exploration and possibilities in diverse fields.

In speaker verification, ECAPA-TDNN has shown remarkable improvement by utilizing one-dimensional(1D) Res2Net block and squeeze-and-excitation(SE) module, along with multi-layer feature aggregation (MFA). Meanwhile, in vision tasks, ConvNet structures have been modernized by referring to Transformer, resulting in improved performance. In this paper, we present an improved block design for TDNN in speaker verification. Inspired by recent ConvNet structures, we replace the SE-Res2Net block in ECAPA-TDNN with a novel 1D two-step multi-scale ConvNeXt block, which we call TS-ConvNeXt. The TS-ConvNeXt block is constructed using two separated sub-modules: a temporal multi-scale convolution (MSC) and a frame-wise feed-forward network (FFN). This two-step design allows for flexible capturing of inter-frame and intra-frame contexts. Additionally, we introduce global response normalization (GRN) for the FFN modules to enable more selective feature propagation, similar to the SE module in ECAPA-TDNN. Experimental results demonstrate that NeXt-TDNN, with a modernized backbone block, significantly improved performance in speaker verification tasks while reducing parameter size and inference time. We have released our code for future studies.

Stochastic gradient descent (SGD) or stochastic approximation has been widely used in model training and stochastic optimization. While there is a huge literature on analyzing its convergence, inference on the obtained solutions from SGD has only been recently studied, yet it is important due to the growing need for uncertainty quantification. We investigate two computationally cheap resampling-based methods to construct confidence intervals for SGD solutions. One uses multiple, but few, SGDs in parallel via resampling with replacement from the data, and another operates this in an online fashion. Our methods can be regarded as enhancements of established bootstrap schemes to substantially reduce the computation effort in terms of resampling requirements, while bypassing the intricate mixing conditions in existing batching methods. We achieve these via a recent so-called cheap bootstrap idea and refinement of a Berry-Esseen-type bound for SGD.

Biomimetic underwater robots use lateral periodic oscillatory motion to propel forward, which is seen in most fishes known as body caudal fin (BCF) propulsion. The lateral oscillatory motion makes slender-bodied fish-like robots roll unstable. Unlike the case of human-engineered aquatic robots, many species of fish can stabilize their roll motion to perturbations arising from the periodic motions of propulsors. To first understand the origin of the roll instability, the objective of this paper is to analyze the parameters affecting the roll-angle stability of an autonomous fish-like underwater swimmer. Eschewing complex models of fluid-structure interaction, we instead consider the roll motion of a nonholonomic system inspired by the Chaplygin sleigh, whose center of mass is above the ground. In past work, the dynamics of a fish-like periodic swimmer have been shown to be similar to that of a Chaplygin sleigh. The Chaplygin sleigh is propelled by periodic torque in the yaw direction. The roll dynamics of the Chaplygin sleigh are linearized and around a nominal limit cycle solution of the planar hydrodynamic Chaplygin sleigh in the reduced velocity space. It is shown that the roll dynamics are then described as a nonhomogeneous Mathieu equation where the periodic yaw motion provides the parametric excitation. We study the added mass effects on the sleigh's linear dynamics and use the Floquet theory to investigate the roll stability due to parametric excitation. We show that fast motions of the model for swimming are frequently associated with roll instability. The paper thus sheds light on the fundamental mechanics that present trade-offs between speed, efficiency, and stability of motion of fish-like robots.

Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously validate its applicability to general convex numerical optimization problems. We introduce a novel variant of the Quadratic Gradient that departs from the conventional fixed Hessian Newton framework. We present a new way to build a new version of the quadratic gradient. This new quadratic gradient doesn't satisfy the convergence conditions of the fixed Hessian Newton's method. However, experimental results show that it sometimes has a better performance than the original one in convergence rate. While this variant relaxes certain classical convergence constraints, it maintains a positive-definite Hessian proxy and demonstrates comparable, or in some cases superior, empirical performance in convergence rates. Furthermore, we demonstrate that both the original and the proposed QG variants can be effectively applied to non-convex optimization landscapes. A key motivation of our work is the limitation of traditional scalar learning rates. We argue that a diagonal matrix can more effectively accelerate gradient elements at heterogeneous rates. Our findings establish the Quadratic Gradient as a versatile and potent framework for modern optimization. Furthermore, we integrate Hutchinson's Estimator to estimate the Hessian diagonal efficiently via Hessian-vector products. Notably, we demonstrate that the proposed Quadratic Gradient variant is highly effective for Deep Learning architectures, providing a robust second-order alternative to standard adaptive optimizers.

The non quantum relativistic version of the proof of Feynman for the Maxwell equations is discussed in a framework with a minimum number of hypotheses required. From the present point of view it is clear that the classical equations of motion corresponding to the gauge field interactions can be deduced from the minimal coupling rule, and we claim here resides the essence of the proof of Feynman.

In this paper we discuss how to associate a suitable non-transitive version of a Cartan connection to sub-Riemannian manifolds of corank 1 (including contact and quasi-contact sub-Riemannian manifolds) with non-necessarily constant sub-Riemannian symbols. In particular, we recast the variation of the sub-Riemannian symbols into a suitable "type" map, which is constant if and only if the symbols are constant. We then consider the (non-transitive) groupoid of sub-Riemannian symmetries and investigate its smoothness, properness, regularity, and other properties in relation with the type map. Last, we describe how to build a "non-transitive" analogue of a Cartan connection on top of such (Lie) groupoid, obtained as the sum of a tautological form with a multiplicative Ehresmann connection. We conclude by illustrating our results on concrete examples in dimension 5.

The Grothendieck constant $K_{G}$ is a fundamental quantity in functional analysis, with important connections to quantum information, combinatorial optimization, and the geometry of Banach spaces. Despite decades of study, the value of $K_{G}$ is unknown. The best known lower bound on $K_{G}$ was obtained independently by Davie and Reeds in the 1980s. In this paper we show that their bound is not optimal. We prove that $K_{G} \ge K_{DR} + 10^{-12}$, where $K_{DR}$ denotes the Davie-Reeds lower bound. Our argument is based on a perturbative analysis of the Davie-Reeds operator. We show that every near-extremizer for the Davie-Reeds problem has $Ω(1)$ weight on its degree-3 Hermite coefficients, and therefore introducing a small cubic perturbation increases the integrality gap of the operator.

Random subspace method has wide security applications such as providing certified defenses against adversarial and backdoor attacks, and building robustly aligned LLM against jailbreaking attacks. However, the explanation of random subspace method lacks sufficient exploration. Existing state-of-the-art feature attribution methods, such as Shapley value and LIME, are computationally impractical and lacks security guarantee when applied to random subspace method. In this work, we propose EnsembleSHAP, an intrinsically faithful and secure feature attribution for random subspace method that reuses its computational byproducts. Specifically, our feature attribution method is 1) computationally efficient, 2) maintains essential properties of effective feature attribution (such as local accuracy), and 3) offers guaranteed protection against privacy-preserving attacks on feature attribution methods. To the best of our knowledge, this is the first work to establish provable robustness against explanation-preserving attacks. We also perform comprehensive evaluations for our explanation's effectiveness when faced with different empirical attacks, including backdoor attacks, adversarial attacks, and jailbreak attacks. The code is at https://github.com/Wang-Yanting/EnsembleSHAP. WARNING: This document may include content that could be considered harmful.

Modular software deployed on mini compute units in controlled distributed environments often needs two messaging paths: low-overhead in-process coordination and selective cross-node distribution. In practice, event identity, serialization, and transport bridging are frequently implemented as ad hoc glue, which complicates inter-process communication (IPC), structured routing, and shutdown behavior. This paper presents CNS, a lightweight local-first hybrid event fabric centered on asynchronous fire-and-forget messaging. CNS combines a typed event key, per-family serialization and validation, a local publish/subscribe context for in-process coordination, and a NATS-backed distributed context for inter-node distribution. A bridge runtime moves events between the two contexts while preserving a common routing vocabulary. The primary operating model is fire-and-forget publication and subscription; bidirectional request-reply remains available as a secondary extension on the same subject space. A Python prototype and single-machine measurements are reported. Local-only delivery averaged about 30 $μ$s. Distributed-only delivery averaged 1.26-1.37 ms, and the hybrid bridge averaged 1.64-1.89 ms. Validation introduced modest overhead relative to serialization choice. The resulting artifact is suited to structured IPC and practical message movement within modular services and across bounded sets of controlled nodes.

This paper evaluates whether commercial large language models (LLMs) can function as reliable political advisory tools by comparing their outputs against official legislative reasoning. Using a dataset of 15 Romanian Senate law proposals paired with their official explanatory memoranda (expuneri de motive), we test six LLMs spanning three provider families and multiple capability tiers: GPT-5-mini, GPT-5-chat (OpenAI), Claude Haiku 4.5 (Anthropic), and Llama 4 Maverick, Llama 3.3 70B, and Llama 3.1 8B (Meta). Each model generates predicted rationales evaluated through a dual framework combining LLM-as-Judge semantic scoring and programmatic text similarity metrics. We frame the LLM-politician relationship through principal-agent theory and bounded rationality, conceptualizing the legislator as a principal delegating advisory tasks to a boundedly rational agent under structural information asymmetry. Results reveal a sharp two-tier structure: frontier models (Claude Haiku 4.5, GPT-5-chat, GPT-5-mini) achieve statistically indistinguishable semantic closeness scores above 4.6 out of 5.0, while open-weight models cluster a full tier below (Cohen's d larger than 1.4). However, all models exhibit task-dependent confabulation, performing well on standardized legislative templates (e.g., EU directive transpositions) but generating plausible yet unfounded reasoning for politically idiosyncratic proposals. We introduce the concept of cascading bounded rationality to describe how failures compound across bounded principals, agents, and evaluators, and argue that the operative risk for legislators is not stable ideological bias but contextual ignorance shaped by training data coverage.