Computational social choice and algorithmic decision theory offer rich aggregation theory but no comprehensive process for egalitarian self-governance: aggregation, deliberation, amendment, and consensus are each considered in isolation, with key metric-space aggregators being NP-hard. Here, we propose constitutional governance in metric spaces, integrating these stages into a coherent polynomial-time protocol for constitutional governance. The constitution assigns, per amendable component including itself, a metric space, aggregation rule, and supermajority threshold. Amendments proceed by members voting with their ideal elements, followed by members submitting public proposals carrying supermajority public support under the revealed votes. Public proposals can be sourced from deliberation among members, vote aggregation, or AI mediation. The constitutional rule adopts a supported proposal with positive maximal score, if there is one, else retains the status quo. With Constitutional Consensus, a community can run the constitutional governance protocol on members' personal computing devices (e.g., smartphones), achieving digital sovereignty. We focus on the utility of the generalised median, prove that at majority threshold no misreport weakly dominates sincere voting, and study the compromise gap between best peak and unconstrained optimum. We instantiate the framework to seven canonical settings -- electing officers, setting rates, allocating budgets, ranking priorities, selecting boards, drafting bylaws, and amending the constitution. By unifying metric-space aggregation, reality-aware social choice, supermajority amendment, constitutional consensus, deliberative coalition formation, and AI mediation, this work delivers a comprehensive solution to the constitutional governance of digital communities and organisations.

Neural preconditioners for real-time physics simulation offer promising data-driven priors, but they often fail to capture long-range couplings efficiently because they inherit local message passing or sparse-operator access patterns. We introduce the Hierarchical Transformer Preconditioner, a neural preconditioner anchored to a weak-admissibility H-matrix partition. The partition provides a multiscale structural prior (dense diagonal leaves plus coarsening off-diagonal tiles) that enables full-graph approximate-inverse computation with O(N) scaling at fixed block sizes. The network models the inverse through low-rank far-field factors and uses highway connections (axial buffers plus a global summary token) to propagate context across transformer depth. At each PCG iteration, preconditioner application reduces to batched dense GEMMs with regular memory access. The key training contribution is a cosine-Hutchinson probe objective that learns the action of MA on convergence-critical spectral subspaces, optimizing angular alignment of MAz with z rather than forcing eigenvalue clusters to a prescribed location. This removes unnecessary spectral-placement constraints from SAI-style objectives and improves conditioning on irregular spectra. Because both inference and apply are dense, dependency-free tensor programs, the full solve loop is captured as a single CUDA Graph. On stiff multiphase Poisson systems (up to 100:1 density contrast, N = 1,024-16,384), the solver runs from ~143 to ~21 fps. At N = 8,192, it reaches 17.9 ms/frame, with 2.2x speedup over GPU Jacobi, ~28x over GPU IC/DILU (AMGX multicolor_dilu), and 2.7x over neural SPAI retrained per scale on the same benchmark.

Proving theorems in Lean 4 often requires identifying a scattered set of library lemmas whose joint use enables a concise proof -- a task we call global premise retrieval. Existing tools address adjacent problems: semantic search engines find individual declarations matching a query, while premise-selection systems predict useful lemmas one tactic step at a time. Neither recovers the full premise set an entire theorem requires. We present LeanSearch v2, a two-mode retrieval system for this task. Its standard mode applies a hierarchy-informalized Mathlib corpus with an embedding-reranker pipeline, achieving state-of-the-art single-query retrieval without domain-specific fine-tuning (nDCG@10 of 0.62 vs. 0.53 for the next-best system). Its reasoning mode builds on standard mode as its retrieval substrate, targeting global premise retrieval through iterative sketch-retrieve-reflect cycles. On a 69-query benchmark of research-level Mathlib theorems, reasoning mode recovers 46.1% of ground-truth premise groups within 10 retrieved candidates, outperforming strong reasoning retrieval systems (38.0%) and premise-selection baselines (9.3%) on the same benchmark. In a controlled downstream evaluation with a fixed prover loop, replacing alternative retrievers with LeanSearch v2 yields the highest proof success (20% vs. 16% for the next-best system and 4% without retrieval), confirming that retrieval quality propagates to proof generation. We have open-sourced all code, data, and benchmarks. Code and data: https://github.com/frenzymath/LeanSearch-v2 . The standard mode is publicly available with API access at https://leansearch.net/ .

Watermarking is widely proposed for provenance, attribution, and safety monitoring in generative models, yet is typically evaluated only under adversaries who attempt to evade detection or induce false positives at the level of individual samples. We argue that watermarking should be treated as a monitoring primitive, and that internal monitoring is unavoidable given per-entity attribution keys and messages, as well as detector access. We introduce an observer-based threat model in which observers can aggregate watermark signals across outputs to infer entity-level information, showing that even zero-bit watermarking enables attribution under multi-key settings. We further show that external monitoring can emerge over time from persistent, key-dependent statistical structure, although this depends on watermark design and may be mitigated by distribution-preserving or undetectable schemes. Our findings reveal a fundamental dual-use tension between attribution and monitoring, motivating evaluation of watermarking beyond per-sample robustness to account for aggregation and observer-based capabilities.

As over 200 million new malware samples are identified each year, antivirus systems must continuously adapt to the evolving threat landscape. However, retraining solely on new samples leads to catastrophic forgetting and exploitable blind spots, while retraining on the entire dataset incurs substantial computational cost. We propose FreeMOCA, a memory- and compute-efficient continual learning framework for malicious code analysis that preserves prior knowledge via adaptive layer-wise interpolation between consecutive task updates, leveraging the fact that warm-started task optima are connected by low-loss paths in parameter space. We evaluate FreeMOCA in both class-incremental (Class-IL) and domain-incremental (Domain-IL) settings on large-scale Windows (EMBER) and Android (AZ) malware benchmarks. FreeMOCA achieves substantial gains in Class-IL, outperforming 11 baselines on both EMBER and AZ benchmarks. It also significantly reduces forgetting, achieving the best retention across baselines, and improving accuracy by up to 42% and 37% on EMBER and AZ, respectively. These results demonstrate that warm-started interpolation in parameter space provides a scalable and effective alternative to replay for continual malware detection. Code is available at: https://github.com/IQSeC-Lab/FreeMOCA.

As LLM-powered agents are increasingly deployed in edge-cloud environments, personalized memory has become a key enabler of long-term adaptation and user-centric interaction. However, cloud-assisted memory management exposes sensitive user information, while existing privacy protection methods typically rely on aggressive masking that removes task-relevant semantics and consequently degrades memory utility and personalization quality. To address this challenge, We propose MemPrivacy, which identifies privacy-sensitive spans on edge devices, replaces them with semantically structured type-aware placeholders for cloud-side memory processing, and restores the original values locally when needed. By decoupling privacy protection from semantic destruction, MemPrivacy minimizes sensitive data exposure while retaining the information required for effective memory formation and retrieval. We also construct MemPrivacy-Bench for systematic evaluation, a dataset covering 200 users and over 155k privacy instances, and introduce a four-level privacy taxonomy for configurable protection policies. Experiments show that MemPrivacy achieves strong performance in privacy information extraction, substantially surpassing strong general-purpose models such as GPT-5.2 and Gemini-3.1-Pro, while also reducing inference latency. Across multiple widely used memory systems, MemPrivacy limits utility loss to within 1.6%, outperforming baseline masking strategies. Overall, MemPrivacy offers an effective balance between privacy protection and personalized memory utility for edge-cloud agents, enabling secure, practical, and user-transparent deployment.

We introduce Evolutionary Ensemble (EvE), a decentralized framework that organizes existing, highly capable coding agents into a live, co-evolving system for algorithmic discovery. Rather than reinventing the wheel within the "LLMs as optimizers" paradigm, EvE fixes the base agent substrate and focuses entirely on evolving the cumulative guidance and skills that dictate agent behaviors. By maintaining two co-evolving populations, namely functional code solvers and agent guidance states, the system evaluates agents through a synchronous race, updating their empirical Elo ratings based on the marginal gains they contribute to the current solver state. When applied to a research bottleneck in In-Context Operator Networks (ICON), EvE autonomously discovered a robust rescale-then-interpolate mechanism that enables reliable example-count generalization. Crucially, controlled ablations reveal the absolute necessity of stage-dependent agent adaptation to navigate the shifting search landscapes of complex codebases. Compared to variants driven by a fixed initial agent or even a frozen "best-evolved" agent, EvE uniquely avoids phase mismatch, demonstrating that organizing agents into a self-revising ensemble is the fundamental driver for breaking through static performance ceilings.

Physics-informed neural networks (PINNs) provide a mesh-free framework for solving PDE-constrained inverse problems, but their extension to Bayesian inversion still faces a fundamental difficulty: prior distributions are typically defined in the weight space of neural networks, whereas physically meaningful prior assumptions are more naturally expressed in function space. In this study, we introduce a unified framework, termed functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks (fpBPINN), to incorporate functional priors into Bayesian PINN-based inversion. We consider two complementary approaches. The first is a functional-prior-informed Bayesian PINN (FPI-BPINN), in which a neural network weight prior is learned to be consistent with a prescribed functional prior, and Bayesian inference is subsequently performed in weight space. The second is function-space particle-based variational inference for PINNs (fParVI-PINN), which performs Bayesian estimation using ParVI directly in function space. We also show that random Fourier features (RFF) play an important role in representing Gaussian functional priors with neural networks and in improving posterior approximation. We applied the proposed approaches to one-dimensional seismic traveltime tomography and two-dimensional Darcy-flow permeability inversion. These numerical experiments showed that both approaches accurately estimated posterior distributions, highlighting the significance of introducing physically interpretable functional priors into Bayesian PINN-based inverse problems. We also identified the contrasting advantages of FPI-BPINN and fParVI-PINN, namely flexibility and accuracy, respectively.

We develop interconnections between the complex normalizing flow for data drawn from Borel probability measures on the twofold realification of the complex manifold and a nonlinear flow nearly Kähler-Ricci. The complex normalizing flow relates the initial and target realified densities under the complex change of variables, necessitating the log determinant of the ensemble of Wirtinger Jacobians. The Ricci curvature of a Kähler manifold is the second order mixed Wirtinger partial derivative of the log of the local density of the volume form. Therefore, we reconcile these two facts by drawing forth the connection that the log determinant used in the complex normalizing flow matches a Ricci curvature term under differentiation and conditions. The log density under the normalizing flow is kindred to a spatial Fisher information metric under an augmented Jacobian and a Bayesian perspective to the parameter, thus under the continuum limit the log likelihood matches a Fisher metric, recovering a Kähler-Ricci flow variation up to a time derivative and expectation, or an average-valued Kähler-Einstein flow. Using this framework, we establish other relevant results, attempting to bridge the statistical and ordinary behaviors of the complex normalizing flow to the geometric features of our derived Kähler flow.

Speculative Decoding promises to accelerate the inference of Large Language Models, yet its efficacy often degrades in production-grade serving. Existing evaluations typically overlook the compute-bound nature of high-concurrency regimes, where verification compute becomes the dominant bottleneck. Consequently, prior methods face a dilemma: static trees incur massive verification waste, while dynamic trees suffer from cumulative misjudgments and kernel incompatibility. To bridge this gap, we introduce ECHO, a high concurrency-oriented framework integrated into SGLang that reformulates speculative execution as a budgeted scheduling problem. Crucially, ECHO employs sparse confidence gating to manage the batch as a unified super-tree, elastically pivoting budget between depth and width to co-optimize the trade-off between reducing global verification steps and maximizing per-step efficiency. Extensive evaluations across diverse model scales-particularly the industrial-grade Qwen3-235B-demonstrate that ECHO consistently outperforms SOTA methods in both low-load and high-load scenarios, achieving up to 5.35x walltime speedup and delivering over 20% relative speedup gain.

Speech separation in realistic acoustic environments remains challenging because overlapping speakers, background noise, and reverberation must be resolved simultaneously. Although recent time-frequency (TF) domain models have shown strong performance, most still rely on late-split architectures, where speaker disentanglement is deferred to the final stage, creating an information bottleneck and weakening discriminability under adverse conditions. To address this issue, we propose SR-CorrNet, an asymmetric encoder-decoder framework that introduces the separation-reconstruction (SepRe) strategy into a TF dual-path backbone. The encoder performs coarse separation from mixture observations, while the weight-shared decoder progressively reconstructs speaker-discriminative features with cross-speaker interaction, enabling stage-wise refinement. To complement this architecture, we formulate speech separation as a structured correlation-to-filter problem: spatio-spectro-temporal correlations computed from the observations are used as input features, and the corresponding deep filters are estimated to recover target signals. We further incorporate an attractor-based dynamic split module to adapt the number of output streams to the actual speaker configuration. Experimental results on WSJ0-{2,3,4,5}Mix, WHAMR!, and LibriCSS demonstrate consistent improvements across anechoic, noisy-reverberant, and real-recorded conditions in both single- and multi-channel settings, highlighting the effectiveness of TF-domain SepRe with correlation-based filter estimation for speech separation.

As LLMs are increasingly used as judges in code applications, they should be evaluated in realistic interactive settings that capture partial context and ambiguous intent. We present TRACE (Tool for Rubric Analysis in Code Evaluation), a framework that evaluates LLM judges' ability to predict human preferences and automatically extracts rubric items to reveal systematic biases in how humans and models weigh each item. Across three modalities -- chat-based programming, IDE autocompletion, and instructed code editing -- we use TRACE to measure how well LLM judges align with developer preferences. Among 13 different models, the best judges underperform human annotators by 12-23%. TRACE identifies 35 significant sources of misalignment between humans and judges across interaction modalities, the majority of which correspond to existing software engineering code quality criteria. For example, in chat-based coding, judges are biased towards longer code explanations while humans prefer shorter ones. We find significant misalignment on the majority of existing code quality dimensions, showing alignment gaps between LLM judges and human preference in realistic coding applications.

Generative Retrieval (GR) has emerged as a promising paradigm for modern search systems. Compared to multi-stage cascaded architecture, it offers advantages such as end-to-end joint optimization and high computational efficiency. OneSearch, as a representative industrial-scale deployed generative search framework, has brought significant commercial and operational benefits. However, its inadequate understanding of complex queries, inefficient exploitation of latent user intents, and overfitting to narrow historical preferences have limited its further performance improvement. To address these challenges, we propose OneSearch-V2, a latent reasoning enhanced self-distillation generative search framework. It contains three key innovations: (1) a thought-augmented complex query understanding module, which enables deep query understanding and overcomes the shallow semantic matching limitations of direct inference; (2) a reasoning-internalized self-distillation training pipeline, which uncovers users' potential yet precise e-commerce intentions beyond log-fitting through implicit in-context learning; (3) a behavior preference alignment optimization system, which mitigates reward hacking arising from the single conversion metric, and addresses personal preference via direct user feedback. Extensive offline evaluations demonstrate OneSearch-V2's strong query recognition and user profiling capabilities. Online A/B tests further validate its business effectiveness, yielding +3.98\% item CTR, +2.07\% buyer volume, and +2.11\% order volume. Manual evaluation further confirms gains in search experience quality, with +1.37\% in page good rate and +1.65\% in query-item relevance. More importantly, OneSearch-V2 effectively mitigates common search system issues such as information bubbles and long-tail sparsity, without incurring additional inference costs or serving latency.

Score-based generative models (SGMs) have achieved remarkable empirical success, motivating their application to a broad range of data distributions. However, extending them to heavy-tailed targets remains a largely open problem. Although dedicated models for heavy-tailed distributions have been proposed, their generative fidelity remains unclear and they lack solid theoretical foundations, leaving important questions open in this regime. In this paper, we address this gap through two theoretical contributions. First, we show that combining early stopping with a suitable initialization is sufficient to extend the diffusion framework to any target distribution; in particular, we establish the well-posedness of the backward process and prove convergence of the approximated diffusion in KL divergence. Second, we derive novel theoretical guarantees for generation with normalizing flows, obtaining convergence results that hold under mild conditions on the flow family and without any assumption on the tail behavior of the target distribution. Building on these results, we propose a unified generative framework for heavy-tailed distributions: a normalizing flow is first trained to capture the tail behavior and is then used as an initialization prior for an SGM, which refines the samples by recovering fine-grained structural details. This design leverages the complementary strengths of the two model classes within a theoretically principled pipeline, overcoming the limitations of existing approaches.

Phased-array Bluetooth systems have emerged as a low-cost alternative for performing aided inertial navigation in GNSS-denied use cases such as warehouse logistics, drone landings, and autonomous docking. Basing a navigation system off of commercial-off-the-shelf components may reduce the barrier of entry for phased-array radio navigation systems, albeit at the cost of significantly noisier measurements and relatively short feasible range. In this paper, we compare robust estimation strategies for a factor graph optimisation-based estimator using experimental data collected from multirotor drone flight. We evaluate performance in loss-of-GNSS scenarios when aided by Bluetooth angular measurements, as well as range or barometric pressure.

This study examines the distribution of Artificial Intelligence (AI) research across European NUTS-3 regions during the period 2015-2024. Using bibliometric data from Clarivate InCites and the Citation Topics classification system, we analyse two hierarchical thematic levels: Electrical Engineering, Electronics & Computer Science (Macro Citation Topic 4) and Artificial Intelligence & Machine Learning (Meso Citation Topic 4.61). Relative Specialization Index (RSI) and Relative Citation Impact (RCI) indicators are calculated for 781 European NUTS-3 regions. While major metropolitan hubs such as Paris, Warszawa, and Madrid dominate in absolute publication volume, the results reveal that the highest levels of relative AI specialization are concentrated in peripheral regions, particularly in Eastern Europe and Spain. Granada and Vilniaus apskritis stand out as regions combining high specialization with strong citation visibility. The analysis further suggests a weak relationship between regional specialization and citation impact, revealing multiple regional profiles, including highly specialized regions with limited citation visibility, highly visible regions with comparatively low specialization, and diversified scientific systems combining moderate specialization with strong citation impact. Fyn emerges as an extreme case of very high citation impact despite relatively low specialization.

We introduce a novel numerical framework for the exploration of Blaschke--Santaló diagrams, which are efficient tools characterizing the possible inequalities relating some given shape functionals. We introduce a parametrization of convex bodies in arbitrary dimensions using a specific invertible neural network architecture based on gauge functions, allowing an intrinsic conservation of the convexity of the sets during the shape optimization process. To achieve a uniform sampling inside the diagram, and thus a satisfying description of it, we introduce an interacting particle system that minimizes a Riesz energy functional via automatic differentiation in PyTorch. The effectiveness of the method is demonstrated on several diagrams involving both geometric and PDE-type functionals for convex bodies of $\mathbb{R}^2$ and $\mathbb{R}^3$, namely, the volume, the perimeter, the moment of inertia, the torsional rigidity, the Willmore energy, and the first two Neumann eigenvalues of the Laplacian.

Citations provide the basis for trusting scientific claims; when they are invalid or fabricated, this trust collapses. With the advent of Large Language Models (LLMs), this risk has intensified: LLMs are increasingly used for academic writing, but their tendency to fabricate citations (``ghost citations'') poses a systemic threat to citation validity. To quantify this threat, we develop \citeb, an open-source framework for large-scale citation verification, and conduct a comprehensive study of citation validity in the LLM era through three complementary experiments. First, we benchmark 13 LLMs on citation generation task in various research domains, finding that all models hallucinate citations at rate from 14.23\% to 94.93\%. Second, we analyze 2.2 million citations from 56,381 papers at AI/ML and Security venues (2020--2025), finding that 1.07\% of papers contain invalid citations, with an 80.9\% increase in 2025. Third, we survey 97 researchers, finding that 87.2\% use AI-powered tools in their workflows, 76.7\% of reviewers do not thoroughly check references, and 74.5\% view peer review as ineffective at catching citation errors. Based on these findings, we argue that ghost citations represent a systemic threat to academic integrity, and call for coordinated efforts from community to address this challenge.

The origin of the "theoretical limit of time-frequency resolution of Fourier analysis" is from its numerical implementation, especially from an assumption of "Periodic Boundary Condition (PBC)," which was introduced a century ago. We previously proposed to replace this condition with "Linear eXtrapolation Condition (LXC)," which does not require periodicity. This feature makes instantaneous spectra analysis of pulse series available, which replaces the short time Fourier transform (STFT). We applied the instantaneous spectra analysis to two lung sounds with abnormalities (crackles and wheezing) and to a normal lung sound, as a demonstration. Among them, crackles contains a random pulse series. The spectrum of each pulse is available, and the spectrogram of pulse series is available with assembling each spectrum. As a result, the time-frequency structure of given pulse series is visualized.

Understanding videos inherently requires reasoning over both visual and auditory information. To properly evaluate Omni-Large Language Models (Omni-LLMs), which are capable of processing multi-modal information including vision and audio, an effective benchmark must comprehensively cover three key aspects: (1) multi-modal dependency (i.e., questions that cannot be answered using vision or audio alone), (2) diverse audio information types (e.g., speech, sound events), and (3) varying scene spans. However, existing datasets fall short in one or more of these dimensions, limiting strict and comprehensive evaluation. To address this gap, we introduce JointAVBench, a novel benchmark with strict audio-video correlation, spanning five cognitive dimensions, four audio information types (speech, sound events, music, vocal traits), and three scene spans (single-, cross-, and full-scene). Given the high cost of manual annotation, we propose an automated pipeline that leverages state-of-the-art vision-LLMs, audio-LLMs, and general-purpose LLMs to synthesize questions and answers that strictly require joint audio-visual understanding. We evaluate leading vision-only, audio-only, and Omni-LLMs on our dataset. Results show that even the best-performing Omni-LLM achieves an average accuracy of only 65.3\%, outperforming uni-modal baselines but revealing substantial room for improvement, especially in cross-scene reasoning.

This paper introduces The Spheres dataset, multitrack orchestral recordings designed to advance machine learning research in music source separation and related MIR tasks within the classical music domain. The dataset is composed of over one hour recordings of musical pieces performed by the Colibrì Ensemble at The Spheres recording studio, capturing two canonical works - Tchaikovsky's Romeo and Juliet and Mozart's Symphony No. 40 - along with chromatic scales and solo excerpts for each instrument. The recording setup employed 23 microphones, including close spot, main, and ambient microphones, enabling the creation of realistic stereo mixes with controlled bleeding and providing isolated stems for supervised training of source separation models. In addition, room impulse responses were estimated for each instrument position, offering valuable acoustic characterization of the recording space. We present the dataset structure, acoustic analysis, and baseline evaluations using X-UMX based models for orchestral family separation and microphone debleeding. Results highlight both the potential and the challenges of source separation in complex orchestral scenarios, underscoring the dataset's value for benchmarking and for exploring new approaches to separation, localization, dereverberation, and immersive rendering of classical music.

Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations, yet their success in simulating incompressible flows at high Reynolds numbers remains limited. Existing approaches rely on auxiliary labeled data, supervised pretraining, or reference solutions, and no purely unsupervised method comparable to conventional finite-difference or finite-volume solvers has been demonstrated. We attribute this gap to the absence of a mechanism for enforcing the divergence-free constraint and boundary conditions to strict tolerances. To address this, we adopt the physics- and equality-constrained artificial neural network (PECANN) framework with a conditionally adaptive augmented Lagrangian method (CA-ALM), and introduce a pressure-Poisson-based objective. The residual of the pressure Poisson equation is minimized subject to the momentum and continuity equations and boundary conditions on the primitive variables as equality constraints, with CA-ALM enforcing all constraints tightly. For advection-dominated, high-Reynolds-number flows, we further propose an adaptive vanishing entropy viscosity that stabilizes early training without influencing the converged solution. A baseline that instead uses the momentum residual as the objective proves ineffective under the same machinery, underscoring the critical role of the pressure-Poisson objective. The method is assessed on lid-driven cavity flow up to $Re=7{,}500$, three-dimensional unsteady Beltrami flow, and steady and unsteady flow past a circular cylinder with general inflow-outflow boundary conditions, including an ablation study identifying admissible outlet conditions -- all without labeled data or supervised pretraining. Notably, it captures the spontaneous onset of periodic vortex shedding in unsteady cylinder flow without external perturbations, starting from a randomly initialized network.

Maximizing performance on available GPU hardware is an ongoing challenge for modern AI inference systems. Traditional approaches include writing custom GPU kernels and using specialized model compilers to tune high-level code for specific GPU targets. Recent work shows that LLM-based multi-agent systems can effectively perform such tuning, often outperforming existing compilers and eliminating the need for manual kernel development. However, the dynamics of multi-agent systems for this task remain unexplored. In this work, we present a logical framework for comparing multi-agent PyTorch optimization systems. Our evaluation shows that exploit-heavy strategies perform best when paired with error-fixing agents, and that performance correlates with the granularity of optimization steps. The best implementation achieves an average 2.88x speedup over PyTorch Eager (1.85x over torch.compile) on an H100 GPU across diverse tasks in KernelBench, a benchmark suite covering a range of machine learning architectures in PyTorch. Code is publicly available at: https://github.com/pike-project/pike

The rapid growth of Web APIs has made automated Web API recommendation essential for efficient mashup development. However, existing approaches suffer from two major limitations: 1) they rely on fixed top-N recommendation strategies that cannot adapt to mashup complexity, and 2) they provide little or no explanation for recommended APIs, limiting transparency and user trust. To address these challenges, we propose WAR-R1, an explainable Web API recommendation framework that integrates semantic reasoning with adaptive, variable-cardinality recommendation. Built on a lightweight large language model (LLM), WAR-R1 generates both a set of relevant APIs and a natural-language justification for each recommendation. To support adaptive recommendation size, we introduce special start and stop tokens that allow the model to learn when to begin and terminate API generation. WAR-R1 is trained in two stages: supervised fine-tuning on an annotated mashup-API corpus, followed by reinforcement learning using Group Relative Policy Optimization (GRPO) with low-rank adaptation to jointly optimize recommendation accuracy and reasoning quality. Experiments on the ProgrammableWeb dataset show that WAR-R1 outperforms state-of-the-art baselines by up to 10.89% in recommendation accuracy while consistently producing high-quality, semantically grounded explanations. Extensive ablation studies validate the effectiveness of reinforcement learning, special token design, and integrated reasoning.

Convex clustering is a well-regarded clustering method, resembling the similar centroid-based approach of Lloyd's $k$-means, without requiring a predefined cluster count. It starts with each data point as its centroid and iteratively merges them. Despite its advantages, this method can fail when dealing with data exhibiting linearly non-separable or non-convex structures. To mitigate the limitations, we propose a kernelized extension of the convex clustering method. This approach projects the data points into a Reproducing Kernel Hilbert Space (RKHS) using a feature map, enabling convex clustering in this transformed space. This kernelization not only allows for better handling of complex data distributions but also produces an embedding in a finite-dimensional vector space. We provide a comprehensive theoretical underpinning for our kernelized approach, proving algorithmic convergence and establishing finite sample bounds for our estimates. The effectiveness of our method is demonstrated through extensive experiments on both synthetic and real-world datasets, showing superior performance compared to state-of-the-art clustering techniques. This work marks a significant advancement in the field, offering an effective solution for clustering in non-linear and non-convex data scenarios.

We present a general strategy for turning generative models into candidate solution samplers for batch Bayesian optimization (BO). The use of generative models for BO enables large batch scaling as generative sampling, optimization of non-continuous design spaces, and high-dimensional and combinatorial design. Inspired by the success of direct preference optimization (DPO), we show that one can train a generative model with noisy, simple utility values directly computed from observations to then form proposal distributions whose densities are proportional to the expected utility, i.e., BO's acquisition function values. Furthermore, this approach is generalizable beyond preference-based feedback to general types of reward signals and loss functions. This perspective avoids the construction of surrogate (regression or classification) models, common in previous methods that have used generative models for black-box optimization. Theoretically, we show that the generative models within the BO process follow a sequence of distributions which asymptotically approximate an optimal target under certain conditions. We also evaluate the performance through experiments on challenging optimization problems involving large batches in high dimensions.

The path to higher network autonomy in 6G lies beyond the mere optimization of key performance indicators (KPIs), requiring systems that perceive and reason over the network environment as it is. This can be achieved through agentic AI, where large language model (LLM)-powered agents utilize multimodal telemetry, memory, and cross-domain negotiation to achieve multi-objective goals. However, deploying such agents introduces cognitive biases inherited from human design, which can severely distort reasoning and actuation. This paper provides a comprehensive tutorial on well-known cognitive biases, detailing their taxonomy, mathematical formulation, emergence in telecom systems, and tailored mitigation strategies. We validate these concepts through two distinct use-cases in 6G management. First, we tackle anchoring bias in inter-slice resource negotiation. To overcome the prohibitive execution delays of cloud-based LLMs, this use-case deploys a locally hosted 1B-parameter model on an RTX A4000 GPU, successfully achieving sub-second inference latencies compatible with near-real-time operations. By replacing fixed heuristic anchors with a Truncated Weibull randomized anchor strategy, the agents dismantle rigid biases, intelligently consume SLA slack, and dynamically double the system-wide energy savings (peaking at 25\%) without violating strict latency limits. Second, we mitigate temporal and confirmation biases in RAN-Edge cross-domain negotiation by designing an unbiased collective memory. By integrating semantic/temporal decay and an inflection bonus that actively highlights past negotiation failures, agents are prevented from over-relying on recent data or repeating past mistakes. Grounding decisions in this richer, debiased historical context yields highly robust agreements, achieving a $\times 5$ latency reduction and roughly 40\% higher energy savings compared to memoryless baselines.

Most existing manifold dimension estimators rely on the assumption that the underlying manifold is locally flat within the neighborhoods under consideration. More recently, curvature-adjusted principal component analysis (CA-PCA) has emerged as a powerful alternative by explicitly accounting for the manifold's curvature. Motivated by these ideas, we propose a manifold dimension estimation framework that captures the local graph structure of the manifold through regression on local PCA coordinates. Within this framework, we introduce two representative estimators: quadratic embedding (QE) and total least squares (TLS). Experiments on both synthetic and real-world datasets demonstrate that these methods perform competitively with, and often outperform, state-of-the-art approaches.

Causal discovery from i.i.d. observational data is known to be generally ill-posed. We demonstrate that if we have access to the distribution {induced} by a structural causal model, and additional data from (in the best case) \textit{only two} environments that sufficiently differ in the noise statistics, the unique causal graph is identifiable. Notably, this is the first result in the literature that guarantees the entire causal graph recovery with a constant number of environments and arbitrary nonlinear mechanisms. Our only constraint is the Gaussianity of the noise terms; however, we propose potential ways to relax this requirement. Of interest on its own, we expand on the well-known duality between independent component analysis (ICA) and causal discovery; recent advancements have shown that nonlinear ICA can be solved from multiple environments, at least as many as the number of sources: we show that the same can be achieved for causal discovery while having access to much less auxiliary information.

We revisit the post-processing phase of Chen's Karst-wave quantum lattice algorithm (Chen, 2024) in the Learning with Errors (LWE) parameter regime. Conditioned on a transcript $E$, the post-Step 7 coordinate state on $(\mathbb{Z}_M)^n$ is supported on an affine grid line $\{\, jΔ+ v^{\ast}(E) + M_2 k \bmod M : j \in \mathbb{Z},\ k \in \mathcal{K} \,\}$, with $Δ= 2D^2 b$, $M = 2M_2 = 2D^2 Q$, and $Q$ odd. The amplitudes include a quadratic Karst-wave chirp $\exp(-2πi j^2 / Q)$ and an unknown run-dependent offset $v^{\ast}(E)$. We show that Chen's Steps 8-9 can be replaced by a single exact post-processing routine: measure the deterministic residue $τ:= X_1 \bmod D^2$, obtain the run-local class $v_{1,Q} := v_1^{\ast}(E) \bmod Q$ as explicit side information in our access model, apply a $v_{1,Q}$-dependent diagonal quadratic phase on $X_1$ to cancel the chirp, and then apply $\mathrm{QFT}_{\mathbb{Z}_M}^{\otimes n}$ to the coordinate registers. The routine never needs the full offset $v^{\ast}(E)$. Under Additional Conditions AC1-AC5 on the front end, a measured Fourier outcome $u \in \mathbb{Z}_M^n$ satisfies the resonance $\langle b, u \rangle \equiv 0 \pmod Q$ with probability $1 - o(1)$. Moreover, conditioned on resonance, the reduced outcome $u \bmod Q$ is exactly uniform on the dual hyperplane $H = \{\, v \in \mathbb{Z}_Q^n : \langle b, v \rangle \equiv 0 \pmod Q \,\}$.