arXiv:2607.05677v1 Announce Type: new Abstract: AI coding assistants such as GitHub Copilot and Cursor have evolved from code-suggestion tools into conversational collaborators, enabling vibe-coding workflows in which developers guide AI-generated code through natural-language dialogue. Although researchers have increasingly recognized the importance of AI coding agents and begun examining their impact on open-source development, a comprehensive understanding of how developers' chat-based interactions with AI relate to subsequent open-source development and collaboration remains limited. This hinders efforts to effectively design, evaluate, and govern AI-assisted open-source software development. To address this gap, we collected 13,360 AI conversation sessions comprising 79,172 user messages from 1,356 OSS repositories, linked them to repository development histories, and complemented this analysis with a targeted developer survey. We find heavier AI use in smaller, less mature, and less collaborative repositories. After AI adoption, projects tended to show more active contributors and lower contributor concentration (p < .001), although communication remained highly concentrated. Code Writing was the dominant chat purpose, and nearly all AI chat sessions were followed by subsequent commits. We find no broad deterioration in code-quality signals or pull request merging rates. However, developers perceive others' AI-generated code as harder to maintain than their own (p = .029) and view AI as lowering barriers to OSS contribution. While most developers (68%) are willing to share their chat, concerns remain around appearing incompetent, increasing reviewer burden, and exposing ideas to competitors. These findings provide a large-scale empirical characterization of AI-assisted OSS contribution and offer practical insights for designing and governing responsible vibe-coding practices in open-source development.
Science Journals
arXiv:2607.06320v1 Announce Type: new Abstract: We present the dithered Gaussian mechanism, a novel alternative to the discrete Gaussian mechanism for differential privacy that discretizes the private output rather than the noise distribution itself. By interpreting this discretization as post-processing of the Gaussian mechanism, our construction directly inherits the privacy guarantees of the standard Gaussian mechanism while avoiding vulnerabilities caused by finite-precision floating-point outputs. We show that the mechanism is provably randomness-efficient: by sampling the discretized output values directly, the number of high-quality random bits required for privacy can be reduced significantly and made independent of the noise level. This is achieved by separating the randomness into two sources: a high-quality source used for the privacy-critical sampling step, and a high-performance public source, possibly known to the adversary, that supplies the additional randomness needed for randomized discretization. This separation enables the use of cryptographically secure randomness without substantial performance loss. As an application, we study model training with DP-SGD and show that cryptographically secure noise generation with reduced exposure to floating-point vulnerabilities can be achieved with modest practical overhead.
arXiv:2607.05638v1 Announce Type: new Abstract: Teams deploying large language models in business contexts need evaluation systems, yet most treat evaluation as static model selection: run benchmarks, rank models, deploy the winner. This framing misses evaluation's primary value for production systems--diagnosing why a system underperforms and guiding what to fix. We present EvalLoop, a methodology for evaluation-driven iterative improvement. EvalLoop organizes evaluation around three mechanisms: (1) dimensional metric grouping that decomposes quality into business-relevant dimensions enabling orthogonal failure diagnosis; (2) failure mode classification that categorizes why outputs fail within weak dimensions, bridging diagnosis to action; and (3) a structured iteration workflow where each evaluation run varies one system variable and compares dimensional profiles before and after. We validate EvalLoop through a case study on sales intelligence briefing generation (10 models, 3 providers, 18 metrics, 5 dimensions, 3 iterations). Dimensional diagnosis identified that 69% of hallucination failures were prompt-induced interpretation errors--invisible in aggregate scoring. A targeted prompt fix improved the best model from 82.6% to 94.6% overall, with improvement concentrated in diagnosed dimensions (Content Accuracy +16.8pp, Synthesis Power +26.4pp). An undirected configuration change in a prior iteration produced zero impact, illustrating the cost of iterating without diagnosis. We additionally demonstrate that dimensional profiling enables deployment-specific model selection, and that a one-time blind human gate on a finalist panel (4 models, 16 cases) confirms dimensional rankings while resolving multi-criteria deployment trade-offs--a 94% reduction in review burden compared to evaluating the full design. EvalLoop is packaged as reusable artifacts (playbook, agent specification, template repository) for adoption by other teams.
arXiv:2607.06326v1 Announce Type: new Abstract: Large language models deployed in open-world applications require safety guardrails that are both robust to complex risks and efficient enough for low-latency runtime moderation. Existing guardrails face a practical trade-off between lightweight classification-based models, which are efficient but often struggle with concealed intent, ambiguous semantics, and borderline safety decisions, and reasoning-based guards, which improve judgment quality but introduce additional token generation and inference latency. We present DT-Guard, a content safety guardrail model based on a Reasoning-Active Training, Reasoning-Free Inference paradigm. The key idea is to use reasoning supervision during training while emitting only structured safety labels at inference time. DT-Guard formulates safety judgment as a progressive decision process, Intent - Category - Safety, and constructs an intent-driven dataset with intent labels, risk categories, safety labels, and structured reasoning trajectories. To further improve hard-case robustness, we propose Rollout-Guided Progressive Hard-Case Optimization (RG-PHO), which uses multi-rollout consistency to identify stably mastered, persistently failed, and preference-unstable samples, and applies targeted supervised and preference optimization accordingly. At inference time, DT-Guard directly generates structured labels without explicit reasoning traces, preserving deployment efficiency. Experiments on prompt-side and response-side safety benchmarks show that DT-Guard achieves average F1 scores of 0.886 and 0.870, respectively. With only a 4B backbone, it reaches a dual-side average F1 of 0.878, outperforming strong 8B guardrail baselines. These results demonstrate that reasoning supervision can be effectively internalized into low-latency safety discrimination.
arXiv:2607.06356v1 Announce Type: cross Abstract: Accurate quantification of lung disease severity from chest imaging is critical for clinical decision-making and resource allocation. We propose a tri-modal deep learning framework, TMF-RSE (Tri-Modal Fusion with Regional Semantics and Evidential Uncertainty), that combines appearance features from two-dimensional chest inputs, structural features from lung segmentation masks, and semantic features from vision-language models (VLMs) for severity quantification. Our approach employs complementary fusion mechanisms that integrate semantic guidance, structural priors, and hierarchical interactions across modalities. The model employs evidential regression to provide both severity predictions and uncertainty estimates. Experiments on the Per-COVID-19 CT and RALO datasets show that TMF-RSE outperforms recent transformer-based baselines, achieving MAE of 4.02 and Pearson correlation of 0.9629 on Per-COVID-19 validation, and 0.339 MAE / 0.973 PC on RALO geographic extent.
arXiv:2607.05711v1 Announce Type: new Abstract: Diffusion models have become a dominant paradigm for high-quality generative modeling, while post-training is essential for adapting them to diverse downstream applications. However, post-training of large diffusion models is still challenging due to the prohibitive memory footprints and slow training speed, which existing parameter-efficient fine-tuning methods only partially address. To overcome these limitations, we propose FourTune, an efficient post-training framework for diffusion models based on an end-to-end W4A4G4 paradigm. FourTune introduces a triple-branch hybrid pipeline that augments the standard LoRA architecture with a frozen numerical stabilizer to isolate quantization-sensitive outliers, enabling stable training under native 4-bit computation. In addition, FourTune employs hardware-efficient block-wise quantization and customized fused kernels to support efficient quantized backpropagation and reduce memory bandwidth overhead. Across customization, reinforcement learning, and distillation tasks, FourTune matches the quality of full-precision fine-tuning. On FLUX.1-dev (12B), FourTune reduces memory overhead by 2.25$\times$ and increases end-to-end training throughput by 2.27$\times$ compared to BF16 LoRA.
An adaptive, space-time discretized linear iterative scheme for doubly-degenerate parabolic problems
arXiv:2607.05714v1 Announce Type: new Abstract: Degenerate diffusion problems, where the governing parabolic equation can change type to either an ordinary differential equation or an elliptic equation, model many real life applications. Due to the presence of free-boundaries, accurate numerical simulation of such problems require extremely small mesh and time step sizes locally. To remediate this issue, in this work, we consider a space-time formulation of the problem based on an efficient splitting of the nonlinearities. First, an iterative linearization scheme is proposed to resolve the nonlinearities that effectively reduces to solving a sequence of heat equations. Unconditional convergence of the scheme is proven even for double degenerate cases with linear convergence achieved if the problem is non-degenerate. Next, the dual norm of the nonlinear residual is decomposed into a linearization error component and a discretization error component corresponding to the heat equation. This leads to reliable and fully computable a posteriori estimates for the problem that are robust with respect to the nonlinearities/degeneracies. These estimates are used then in a fully adaptive (discretization + linearization) space-time solver. Numerical experiments for multiple test cases (one and two dimensions in space) demonstrate that this solver efficiently allocates the computational resources in the space-time domain, resulting in a rapid decay of error in terms of total degrees of freedom spent.
arXiv:2607.05751v1 Announce Type: new Abstract: We revisit several fundamental graph problems in the deterministic two-party communication model. Our main contributions include: (1) a new $\widetilde{O}(n^{3/2})$-bit protocol for computing a maximum matching in general graphs. While the same upper bound can be obtained by simulating the classic algorithms of Micali-Vazirani and Gabow, our protocol is conceptually simple and avoids the intricacies of finding a maximal set of shortest augmenting paths; (2) a new $\widetilde{O}(n)$-bit protocol for negative-cycle detection and negative-weight single-source shortest paths. Our protocol simplifies that of Blikstad et al. by replacing a long chain of reductions with a more direct approach based on vertex potentials; (3) a combinatorial $\widetilde{O}(n)$-bit protocol for computing a maximum matching in bipartite graphs, obtained by reinterpreting the near-linear communication protocol of Blikstad et al. through a discretized analysis. Together, these results provide simpler protocols for several basic graph problems. We hope they will inspire further advances on the communication complexity of a wide range of graph problems.
arXiv:2607.06329v1 Announce Type: new Abstract: In Numerical Algebraic Geometry (NAG) isolated solutions of polynomial systems are usually computed by tracking a solution curve defined by a homotopy equation. The tracking problem becomes especially challenging close to a singular root (the ``endgame'' regime). Existing approaches include power series endgames, Cauchy endgames, and various methods that regularize the system via dual-space-based {\em deflation}. We make the following contributions. (1) For corank-1 systems we introduce a new ``Arclength Endgame'' which combines the idea of the classical {\em pseudo-arclength continuation method} with the estimation of the Puiseux series of the curve. We formally prove that it has a superlinear rate of convergence in some neighborhood of the root. The method uses only evaluations of the system and its Jacobian, whereas previous techniques with proven superlinear convergence (such as deflation) require computing additional derivatives of the system. (2) For systems with a larger corank we propose a heuristic ``Lifted Arclength Endgame'', which shows promising experimental results. (3) A key step in our approach (as well as in the standard power series endgame) is estimating the Puiseux series of the curve, which is characterized by fractional exponents $k_i/c$ for $i\ge 1$ together with associated coefficients. Previous work addressed only estimating the ratio $k_1/c$. We present a new method for that which empirically appears to be more stable than previous methods, and also show how to estimate $k_i/c$ for $i\ge 2$.
arXiv:2607.05761v1 Announce Type: new Abstract: Modern data-driven marketing relies on large amounts of consumer data, yet collecting such data can be costly, time-consuming, and difficult to scale. This research examines whether large language models (LLMs) can be used to generate synthetic consumer data for projective techniques, a set of methods designed to elicit consumer associations, emotions, wants, and needs. We test LLM-generated responses across multiple projective tasks, LLMs, prompting strategies, and temperature settings, and compare them with human responses from a primary research study on perceptions of city tourism destinations. Human and LLM responses were analyzed using linguistic measures, diversity and concentration metrics, topic models, and top-term analyses. The results show substantial overlap between human and LLM responses in broad topics and associations, but also important differences in style, linguistic structure, and the way diversity is generated. Recommendations are given on how to best utilize LLMs for generating synthetic consumer data, how model and prompt choices shape response quality, and on recognizing the limitations of LLM synthetic consumer data generation.
arXiv:2607.05782v1 Announce Type: new Abstract: Converters-based systems like wind farms manifest themselves as control-intensive systems, where control-driven stability issues frequently occur, e.g., oscillations. Such issues are popularly studied via circuit impedance-based methods. However, given its implicit controller modeling trait, the impedance-based methods have limitations in system analysis and designs involving large-scale controllers. To address this issue, this paper presents a novel frequency domain modeling framework, as a perspective shift from the circuit to the control system. Since the obtained model features a multi-input-multi-output (MIMO) feedback control structure and explicit controller placement, it is termed the Generalized Feedback Control (GFC) model. GFC modeling is conducted for both single and multi-converter cases, and the resulting models are validated by frequency scan and stability test. Moreover, advantages of the GFC method in achieving interaction analysis and stability-oriented designs of multi-controllers are demonstrated by three application examples, further suggesting its great potential for being applied to the analysis and design issues of converter systems involving large-scale controllers.
arXiv:2607.05787v1 Announce Type: new Abstract: Synthesizing physically plausible human-scene interactions (HSI) remains a critical challenge in computer vision and the development of human avatars. Although recent generative models enable diverse motion synthesis, they suffer from an inductive bias referred to as semantic-geometric entanglement. Because spatial constraints often strongly correlate with specific actions in training data, monolithic models will learn the shortcut bias, aggressively overriding the semantic intent when faced with strict geometric cues. Furthermore, this entanglement exacerbates physical hallucinations, such as body-scene penetrations. To address these limitations, we propose DeSeG, a hierarchical framework that explicitly decouples semantic intent from geometric constraints. First, we introduce a Residual Semantic Planner that encodes textual instructions and canonicalized goal voxels into a compact latent space, enabling fine-grained semantic control independent of spatial trajectories. Second, we propose a physics regularized diffusion executor that incorporates differentiable repulsive potential fields directly into the diffusion objective, enforcing collision-aware motion generation. Extensive experiments on the Lingo dataset demonstrate that DeSeG achieves state-of-the-art performance, reducing mean scene penetration by 47% and improving semantic alignment by 29% over the SOTA baselines.
arXiv:2605.22775v2 Announce Type: replace Abstract: Real-time cognitive load assessment from eye-tracking signals could enable adaptive human-centered AI in safety-critical applications such as driver vigilance monitoring or automated flight deck assistance, yet two challenges persist: handling frequent data missingness from blinks and tracking failures, and efficiently modeling long-range temporal dependencies. We propose MambaGaze (Bi-Mamba), a framework that addresses these challenges through (1)~XMD encoding, which augments raw features with observation masks and time-deltas to explicitly model data uncertainty, and (2)~bidirectional Mamba-2, which captures temporal dependencies with linear computational complexity. Experiments on CLARE and CL-Drive datasets under leave-one-subject-out evaluation show that MambaGaze achieves 77.1\% accuracy and 59.2\% macro-F1 on CLARE, and 69.4\% accuracy and 51.5\% macro-F1 on CL-Drive, attaining the highest average LOSO macro-F1 (55.3\%) across all ten compared models. Input-stream ablation indicates that log-scaled time-deltas are the strongest single channel in our setting, and combining all three XMD streams provides consistent gains of 5--20\,pp macro-F1. Edge deployment benchmarks on three NVIDIA Jetson Orin platforms show real-time inference at 27--36\,FPS with power consumption below 6.6\,W, supporting feasibility for embedded cognitive load monitoring.
arXiv:2605.23128v2 Announce Type: replace Abstract: Currently, Vision-Language-Action (VLA) models have become the most adopted paradigm for robotic manipulation for its great potential for task generalization. While most generative flow-matching action decoders for VLA control are often deployed with fixed sampling horizons, limiting state-dependent compute and temporal reuse across control cycles. We present $\pi_0$-EqM, which replaces the flow-matching expert in $\pi_0$ with an Equilibrium Matching (EqM) decoder while leaving the upstream VLA stack unchanged. Under a matched 300-step budget, $\pi_0$-EqM improves RoboTwin average success from 40.4% to 50.2% across 19 tasks and remains competitive on LIBERO, with its clearest gain on LIBERO-10 (87.0%). Two threshold scans reveal a task-dependent non-monotonic relation between residual and success, which we term the stationarity--executability gap. The results suggest that inference depth in iterative VLA control is part of policy design and introduce an energy-based VLA perspective that may inform future work on composable action generation across tasks and embodiments.
arXiv:2605.23826v2 Announce Type: replace Abstract: Keyframe selection is a direct way to provide verifiable visual evidence for long-video question answering (QA). Queries differ in what they require, and finding the right frames depends on knowing what to look for. Existing keyframe selectors either score every frame against a single query, or decompose the query into a fixed schema evaluated by a single visual tool. We propose ToolMerge, a keyframe retrieval method based on decomposition and merging: an Large Language Model (LLM) based planner decomposes the query into tool calls and specifies how their per-tool rankings are merged using boolean operators. To evaluate retrieval directly, we construct Molmo-2 Moments (M2M), a benchmark in which every question is anchored to a specific time interval by construction. Across QA, question retrieval, and caption retrieval, ToolMerge is competitive with prior keyframe selectors, most notably on caption retrieval, outperforming other methods by 5%. Code and data can be found at https://github.com/michalsr/ToolMerge .
arXiv:2605.24709v2 Announce Type: replace Abstract: Streaming reinforcement learning has emerged as an online learning paradigm that conforms to the restrictions of natural learning agents that process data incrementally, i.e. with a batch size of 1 and no replay buffer. While streaming RL has recently been shown to scale with deep function approximation with full observability, partially observable settings have remained out of reach. Truncated backpropagation through time collapses to a one-step gradient horizon under the streaming setting, and exact real-time recurrent learning is prohibitively expensive. We close this gap using recurrent trace units, a diagonal recurrent architecture that enables exact RTRL with linear time and memory complexity in the parameter count, and show that they integrate cleanly into existing streaming algorithms across both discrete and continuous control. On a MemoryChain diagnostic with chain lengths from 2 to 128, our method sustains performance where streaming TBPTT(1) baselines using feedforward, GRU, and RTU networks collapse. On five POPGym tasks and on partially observable MuJoCo continuous control, the streaming approach is competitive with batched PPO on POPGym and recovers a substantial fraction of batched performance on masked MuJoCo, despite using no replay buffer or batched updates.
arXiv:2607.06385v1 Announce Type: new Abstract: We propose an inverse biomechanical design framework for sectorial customized corneal crosslinking in keratoconus. The cornea is modeled as an anisotropic reduced shell with spatially varying crosslinking-induced stiffening, enabling the optimization of localized treatment patterns rather than uniform irradiation profiles. Numerical simulations show that sectorial stiffening can redistribute curvature, reduce localized steepening, and improve corneal regularity in decentered keratoconus models while preserving biomechanical plausibility. These results support the use of patient-specific computational planning for customized crosslinking protocols and provide a basis for future integration with corneal tomography and programmable ultraviolet delivery systems.
arXiv:2607.05397v1 Announce Type: new Abstract: Agent systems increasingly execute rather than advise. When an AI agent queries regulated data, invokes effectful tools, and mutates persistent state, correctness is not captured by whether a terminal output looks plausible. The operative questions are whether each step was authorized under a contract, whether the recorded history is tamper-evident, and whether the trajectory can be reconstructed deterministically. We formalize this as runtime proof of execution. An execution is a triple $x = (C, T, R)$: a contract $C$, an Execution Causal Event Stream (ECES) $T$, and a replay context $R$. A well-formedness predicate and five validator-checkable invariants form the PoE validity predicate. Five semantic guarantees describe authorization, path compliance, null effect on deny, history integrity, and replayability. We prove soundness under explicit cryptographic and deployment assumptions: any PPT adversary that produces a PoE-valid execution violating a semantic guarantee yields a signature forgery, a hash collision, or a quantified deployment-failure event. The Prime Execution Model (PEM) separates planning, enforcement, effect, and recordkeeping into distinct authority planes; a lemma reduces trace completeness to Effector-exclusive credentialing. An Execution Attestation Certificate is issued only when PoE = 1. In a single-node TypeScript prototype, PoE adds approximately 2.7 ms on a minimal flow and 4.4% overhead on concurrent batch workloads; a standard eight-event trace compresses to approximately 1.1 KB; injected Gateway-bypass and trace-mutation attacks are rejected. PoE does not replace consensus, TEEs, or zkVMs; it binds authorization, effect, history, and replay into a single runtime-checkable object so that governed execution becomes attestable under contract.
arXiv:2607.06402v1 Announce Type: new Abstract: Images tell us what a scene looks like, but rarely what it would feel like to be there. While recent datasets pair visual scenes with electronic-nose measurements, aligning smell signals with images remains challenging because many olfactory cues arise from contextual environmental factors that are not directly visible in pixels. We introduce SCENT, a multimodal framework that uses language guidance as a semantic bridge between vision and olfaction. Our approach leverages Vision-Language Models (VLMs) to generate scene descriptors capturing objects, environmental context, and plausible ambient smell cues suggested by the visual scene. These descriptors provide semantic guidance for learning olfactory representations. We train a smell encoder that maps electronic-nose signals into a shared embedding space aligned with both visual and textual representations, and introduce a languageguided latent decomposition that separates object-specific odors from contextual environmental contributions. Experiments on the New York Smells dataset demonstrate that SCENT significantly improves crossmodal retrieval compared to vision-only baselines, achieving state-of-theart performance on smell-to-image and smell-to-text retrieval tasks. In addition, our framework produces interpretable olfactory representations that enable the disentanglement of complex smell mixtures. Our results reveal the importance of contextual semantic information for grounding olfactory perception in multimodal learning and pave the way for future research in this area.
arXiv:2605.25451v3 Announce Type: replace Abstract: Training multimodal large language models (MLLMs) is challenged by both model and data heterogeneity. Existing systems redesign the training pipeline to address these challenges, but remain bound by a Pareto frontier between compute and memory efficiency, improving one only at the expense of the other. We present BigMac, a new training pipeline for multimodal LLMs. The core idea of BigMac is to elegantly nest the encoder and generator computation into the original LLM pipeline, forming a dependency-safe nested pipeline structure. With this design, BigMac reduces the activation memory complexity of the encoder and generator to O(1) while keeping the activation memory complexity of the LLM unchanged. At the same time, it achieves the same computational efficiency as the idealized setting with unlimited memory. As a result, BigMac breaks the Pareto frontier between computational efficiency and memory usage, enabling simultaneous optimization of both computation and memory in MLLM training. We evaluate BigMac on multiple MLLMs and training workloads. Experimental results show that BigMac achieves a 1.08$\times$-1.9$\times$ training speedup over baseline systems while maintaining stable memory usage as batch size increases.
arXiv:2605.29655v3 Announce Type: replace Abstract: Autoregressive multimodal large language models (MLLMs) enable 3D generation but struggle to scale to high-resolution shapes due to inadequate 3D tokenizations. Compact set-based representations discard deterministic spatial ordering, leading to ambiguous sequence prediction, while uniform or octree-based voxel grids preserve ordering at the cost of severe redundancy and excessively long sequences. This structural trade-off limits stable and efficient autoregressive 3D generation. We present SuperVoxelGPT, a representation-first framework that resolves this tension through adaptive and deterministically ordered supervoxel tokenization. Given a prompt, we first predict a coarse geometric saliency distribution and construct a shape-adaptive supervoxel partition using saliency-guided centroidal Voronoi tessellation, allocating fine-grained cells to complex regions and larger cells to smooth regions. Conditioned on this prompt and ordered supervoxel layout, we introduce a SuperVoxelVAE and fine-tune a pretrained MLLM to autoregressively generate supervoxel tokens. Experiments using Trellis-500K data show that SuperVoxelGPT reduces token sequence length to 12.8% of uniform voxel tokenization while achieving state-of-the-art generation quality and an average 10x speedup over prior methods.
arXiv:2605.30794v2 Announce Type: replace Abstract: Multimodal Large Language Models (MLLMs) have demonstrated significant achievements in general visual question answering (VQA) tasks. However, they remain brittle on mechanical engineering drawings, where high annotation density and weak domain knowledge, compounded by unreliable spatial relation reasoning under strict projection rules and geometric constraints, make decisive cues easy to miss and frequently lead to wrong answers. To bridge this gap, we introduce the first comprehensive mechanical drawing understanding dataset, MechVQA, created through a semi-automated construction and quality-control pipeline. MechVQA contains 3.3k high-density pictures with 21K question-answer pairs, spanning 10 different fine-grained tasks across three capability levels: Recognition, Reasoning, and Judging, providing a testbed to evaluate and improve MLLM understanding on real-world mechanical drawings. On top of MechVQA, we then develop the MechVL model through a multi-stage training paradigm, building a strong domain-specialized baseline. Extensive experimental results demonstrate that MechVL outperforms the strongest closed-source baseline by 7.57 percentage points on the MechVQA total score, significantly enhancing mechanical drawing understanding ability and providing a reusable foundation for deploying MLLMs in mechanical design and inspection scenarios.
arXiv:2605.30796v5 Announce Type: replace Abstract: This paper presents a rigorous convergence analysis for the lightning plus polynomial approximation scheme, which employs rational approximations constructed with preassigned tapered, exponentially clustered poles. This pole placement strategy was originally introduced by Trefethen and his collaborators for the resolution of corner singularities. Ample numerical results indicate that this scheme achieves root-exponential convergence, and in particular attains the same optimal convergence rate as the best rational approximation to $x^\alpha$ on $[0,1]$ established by Stahl.% which is conjectured in [SIAM J. Numer. Anal., 61:2580-2600, 2023]. In this work, we establish optimal root-exponential convergence for the class of prototype functions of the form $g(z)z^\alpha$ or $g(z)z^\alpha\log z$, where $g$ is analytic on a neighborhood of the sector domain. These results confirm the validity of Conjectures 3.1 and 5.3 stated in [SIAM J. Numer. Anal., 61:2580-2600, 2023], and demonstrate that the choice $\sigma_{\mathrm{opt}} =\frac{\sqrt{2(2 - \beta)}\pi}{\sqrt{\alpha}}$ achieves the theoretically optimal convergence rate $\mathcal{O}\left(e^{-\sqrt{2(2 - \beta)N\alpha}\pi}\right)$. Notably, for the specific case of $\beta = 0$, the scheme recovers Stahl's optimal convergence rate for $x^\alpha$. Furthermore, working within the decomposition framework for corner domains proposed by Gopal and Trefethen, this paper provides a rigorous proof of optimal root-exponential convergence for lightning plus polynomial approximation problems on corner domains, and explicitly derives the optimal pole clustering parameter.
arXiv:2607.06420v1 Announce Type: new Abstract: Visual counting is a fundamental pillar of multimodal intelligence, requiring a seamless integration of fine-grained grounding and spatial reasoning. While Multimodal Large Language Models (MLLMs) have achieved remarkable success in qualitative scene understanding, their quantitative precision remains a significant bottleneck, often characterized by persistent numerical hallucinations. Existing counting benchmarks primarily focus on basic perception in simplified contexts, failing to capture the complex failure modes that emerge under logical constraints or adversarial conditions. To address these limitations, we introduce HoloCount, a holistic and diagnostically rich benchmark structured around a three-level hierarchical taxonomy. HoloCount evaluates MLLMs across: (1) Semantic Counting, focusing on atomic and property-based enumeration; (2) Analytical Counting, assessing logical composition through spatial and set-based reasoning; and (3) Robustness Testing, probing model integrity against adverse scenarios and grounded counter-priors, such as high-density scenes and linguistic biases. Through an exhaustive evaluation of over 20 state-of-the-art MLLMs, we reveal a critical performance gap: even top-tier models degrade significantly as tasks transition from perception to complex analytical reasoning and adverse scenarios. Our findings provide a systematic landscape of current MLLM counting capabilities and offer a roadmap for developing more grounded and reliable multimodal systems. The dataset is available at https://mm-mvr.github.io/HoloCount/.
arXiv:2511.05350v3 Announce Type: replace Abstract: We argue that training autoencoders to reconstruct inputs from noised versions of their encodings, when combined with perceptually motivated losses, yields encodings that are structured according to a perceptual hierarchy. We demonstrate the emergence of this hierarchy by showing that, after training an audio autoencoder in this manner, perceptually salient information is captured in coarser representation structures than with conventional training. Furthermore, we show that such perceptual hierarchies improve latent diffusion decoding in the context of estimating pitch surprisal in music and predicting EEG-brain responses to music listening. In both cases, our results surpass those of previous methods. Pretrained weights are available on github.com/CPJKU/pa-audioic.