arXiv:2604.24226v2 Announce Type: replace-cross
Abstract: In this paper we study continuum-marginal optimal transport. Given a time-continuous family of probability marginals, the problem is to recover the minimum-energy velocity field whose flow reproduces every marginal. This problem is the continuum limit of the classical two-marginal Benamou--Brenier formulation, and also the deterministic limit of the Nelson problem of stochastic optimal transport. We propose a practical mesh-free solver for this problem. The weak continuity equation is embedded in a reproducing kernel Hilbert space, yielding a sample-only objective that requires no spatial discretization. The velocity is parametrized by any linear-in-parameters dictionary or neural network, and is optimized by mini-batch stochastic methods. Synthetic experiments confirm that the method achieves accurate drift recovery and marginal consistency. The same computational framework also applies to the stochastic Nelson problem.
Science Journals
arXiv:2603.26025v2 Announce Type: replace-cross
Abstract: Self-organized dynamic patterns in dense active matter are striking manifestations of non-equilibrium physics. A prominent example is the macroscopic elliptical motion observed in quasi-2D bacterial suspensions, which has lacked a physical explanation. Here, we examine a minimal linear response framework coupling bacterial swimming dynamics with fluid flow, treating long-range hydrodynamic interactions as a macroscopic communication channel. We demonstrate that microscopic swim motion, via Jeffery coupling, manifests as a ``phase-leading'' response to local shear flows. System-wide sustained oscillations, on the other hand, require both a critical bacterial density and strict geometric confinement. By analytically predicting the onset cell density and maximum film thickness, our model achieves excellent quantitative agreement with experiments, establishing a unified physical framework for self-organized periodic motion of elongated body in active fluids.
arXiv:2605.09114v2 Announce Type: replace
Abstract: Every distributed system is a message-passing system, and every message-passing system is a growing causal DAG observed by a set of observers. We treat each observer's consistency as two operators on its visible sub-DAG (a causal-closure filter $C$, fixing which dependencies it must have seen, and a fork resolution $O$, ordering the concurrent forks the filter admits) and give the resulting space the structure the flat catalog of named models lacks. The operators are coupled, asymmetrically: an order that refines causality supplies closure its filter never demanded. That coupling yields a decidable readability order (which configuration's data another can read honestly) with a factoring dichotomy: the order splits across the $C$ and $O$ axes exactly when ordering does not refine causality, and refuses to when it does, the cross-axis gap being the closure ordering supplies. On that order sit a consistency ratchet (a level lost under migration is never regained) and a Detection = Prevention bound: a system can tell its order inverted causality only if it retained exactly what would have prevented the inversion.
The classical results land at clean coordinates in the same system, not as new claims: resolving a fork demands retaining the causal history that distinguishes its branches (database folklore, here an impossibility for every message-passing system) and linearizability resolves as a composite of two systems, a store and a global real-time serializer supplying an order no single observer's light cone can. The named models are configurations of $(C, O)$, exact over the standard-safety fragment and generative past it, predicting configurations the catalog has not named. LCC is a formalization of the observer-relative consistency model of Burgess and Gerlits.
arXiv:2403.13717v4 Announce Type: replace
Abstract: We theoretically study the radiance properties of a pair of qubits inside a single-mode cavity driven by a two-photon drive. Our results show that, when the two qubits are strongly coupled to the cavity field, the collective radiation emitted from the qubits exhibits hyperradiance which can be detected as a signature of two qubit entanglement in the weak-driving regime. We quantify the entanglement in terms of concurrence. Additionally, we study the radiance behaviour in the presence of an intracavity Kerr-nonlinear medium that leads to two-photon blockade. Our results suggest that this system with nonlinearity may act as a quadrature-squeezed and hyperradiant two-photon source.
arXiv:2603.14377v2 Announce Type: replace
Abstract: Prevailing High Dynamic Range (HDR) video reconstruction methods are fundamentally trapped in a fragile alignment-and-fusion paradigm. While explicit spatial alignment can successfully recover fine details in controlled environments, it becomes a severe bottleneck in unconstrained dynamic scenes. By forcing rigid alignment across unpredictable motions and varying exposures, these methods inevitably translate registration errors into severe ghosting artifacts and temporal flickering. In this paper, we rethink this conventional prerequisite. Recognizing that explicit alignment is inherently vulnerable to real-world complexities, we propose LoCAtion, a Long-time Collaborative Attention framework that reformulates HDR video generation from a fragile spatial warping task into a robust, alignment-free collaborative feature routing problem. Guided by this new formulation, our architecture explicitly decouples the highly entangled reconstruction task. Rather than struggling to rigidly warp neighboring frames, we anchor the scene on a continuous medium-exposure backbone and utilize collaborative attention to dynamically harvest and inject reliable irradiance cues from unaligned exposures. Furthermore, we introduce a learned global sequence solver. By leveraging bidirectional context and long-range temporal modeling, it propagates corrective signals and structural features across the entire sequence, inherently enforcing whole-video coherence and eliminating jitter. Extensive experiments demonstrate that LoCAtion achieves state-of-the-art visual quality and temporal stability, offering a highly competitive balance between accuracy and computational efficiency.
arXiv:2606.02842v1 Announce Type: new
Abstract: Multimodal spatial reasoning often relies on long chains of intermediate textual and visual thoughts, where accumulating visual tokens and dense cross-modal attention incur substantial computation and memory overhead. To address this challenge, we propose Spectral-Progressive Thought Flow (SpecFlow), a novel lightweight multimodal spatial reasoning framework that represents intermediate visual thoughts in a fixed-size discrete cosine space. By exploiting strong energy compaction, SpecFlow preserves global layout and relational structure while introducing high-frequency details only when increased spatial precision is required. To align visual state evolution with linguistic intent, classifier-free guidance enables autoregressive textual thoughts to steer flow-based updates of the visual workspace/state without expanding the context. As a result, SpecFlow maintains a bounded visual workspace whose updates depend only on the current visual state and accumulated textual trace, enabling long-horizon inference with stable latency and memory usage independent of reasoning depth. Empirical results show that SpecFlow achieves competitive or superior reasoning performance while reducing computation and KV cache costs by up to 2.1 times.
arXiv:2510.22491v3 Announce Type: replace
Abstract: Generating high-fidelity 3D geometries under explicit parameter constraints is central to engineering design, yet current methods often require large datasets and fail to provide reliable control beyond the training distribution. We introduce LAMP, a data-efficient framework for controllable and interpretable 3D generation that aligns signed distance function (SDF) decoders by overfitting each exemplar from a shared initialization, then generates new designs by solving a parameter-constrained affine mixing problem in the aligned weight space. To improve reliability, we propose a linearity-mismatch safety metric that detects when mixed decoders leave the valid local regime. We evaluate LAMP on DrivAerNet++, BlendedNet, and additional industry-level vehicle families, including sports cars, SUVs, and convertibles. LAMP enables controlled interpolation with as few as 50 samples, safe extrapolation up to 100% beyond training ranges, and performance-guided optimization under fixed parameters, outperforming conditional autoencoder and Deep Network Interpolation (DNI) baselines in extrapolation, data efficiency, and parameter fidelity. Our results demonstrate that LAMP advances controllable, data-efficient, and safe 3D generation for design exploration, dataset generation, and performance-driven optimization.
arXiv:2507.23035v4 Announce Type: replace
Abstract: Large language models (LLMs) have demonstrated impressive capabilities across a wide range of applications, but demand substantial memory and compute resources during inference. Existing quantization methods expose a trade-off between efficiency and accuracy: weight-only quantization (WOQ) incurs costly dequantization overheads, while integer weight-and-activation quantization (INT-WAQ) reduces precision and degrades model quality. Non-uniform weight-and-activation quantization (NU-WAQ) can better capture the non-uniform distributions of LLM weights and activations, yet remains incompatible with conventional low-precision compute units.
This paper presents OASIS, a lookup table (LUT)-based architecture that enables efficient general matrix multiplication (GEMM) between non-uniformly quantized weights and activations without requiring dequantization. OASIS employs pre-computed Cartesian Product LUTs, achieving a 64x reduction in LUT size and enabling a 1024x higher computational parallelism over existing LUT-based GEMM methods. To preserve accuracy under aggressive activation quantization, OASIS introduces an outlier-aware quantization scheme with concurrent LUT-based GEMM and error compensation for outliers. Furthermore, we design Orizuru, an efficient top-k detection engine for real-time activation outlier identification.
According to extensive evaluations, OASIS incurs an average accuracy drop of only 1.98% compared to the FP16 baseline, which is 5.18% lower than Atom. On the hardware side, OASIS achieves an average 3.00x speedup and a 1.44x energy efficiency improvement compared to the FIGLUT accelerator.
arXiv:2606.02631v1 Announce Type: cross
Abstract: This paper studies whether audio, images, and video can share a common wavelet token schema rather than relying on separate modality-specific latent grids. It introduces a preliminary continuous-token model built around a one-level Haar DWT/IDWT frontend, a shared coefficient-token layout, optional structural metadata, lightweight modality value adapters, and a shared token-wise encoder-decoder trunk. On Speech Commands, EuroSAT RGB, and DAVIS 2017 data, a dense shared model reaches 39.92 dB audio, 29.37 dB image, and 23.93 dB video PSNR. A matched-rate sweep under continuous latent scalar budgets indicates that the visual gains are not explained solely by latent capacity, while also showing that additive metadata embeddings are not a universal source of improvement. Finally, fixed-rate energy selection provides a strong non-parametric baseline: energy_global improves average PSNR over uniform selection by 16.73 dB for audio, 16.90 dB for images, and 15.86 dB for video under compressed keep ratios. Masked sparse training reaches 34.45 dB video PSNR with 50% of dense tokens. The results support a unified wavelet token schema and sparse token interface, while stopping short of establishing a universal discrete vocabulary.
arXiv:2606.02841v1 Announce Type: new
Abstract: Deep neural networks learn representations where individual features often lack interpretable meaning; a single neuron may activate for scattered, unrelated inputs. We introduce coherence, a geometric property inspired by neural coding in the brain, where neurons like grid cells and head direction cells respond to contiguous regions of state space. A non-negative matrix is coherent if each row (sample) attends to geometrically clustered columns (features) and vice versa, and in addition every sample is well described by some feature and every feature is needed by some sample. We prove that coherent matrices induce a bounded interleaving between the Vietoris-Rips filtrations of samples and features, guaranteeing that both spaces share compatible topological structure. This geometric constraint facilitates interpretability. For example, if data lies on a circle, coherent features must tile that circle into contiguous arcs. We introduce Coh, a differentiable objective function based on Fr\'echet variance that enforces coherence during training. Unlike sparsity, which bounds how many samples a feature activates on, coherence bounds which samples, requiring geometric connectivity rather than only rarity. This yields not just interpretable features but an interpretable feature space. We validate Coh in an auto-encoder using synthetic and rotated MNIST datasets and in a token embedding of BERT using language data.
arXiv:2508.03098v2 Announce Type: replace
Abstract: Retrieval-Augmented Generation (RAG) enhances the factual accuracy of large language models (LLMs) by conditioning outputs on external knowledge sources. However, when retrieval involves private or sensitive data, RAG systems are susceptible to extraction attacks that can leak confidential information through generated responses. We propose Privacy-Aware Decoding (PAD), a lightweight, inference-time defense that adaptively injects calibrated Gaussian noise into token logits during generation. PAD integrates confidence-based screening to selectively protect high-risk tokens, efficient sensitivity estimation to minimize unnecessary noise, and context-aware noise calibration to balance privacy with generation quality. A \renyi Differential Privacy (RDP) accountant rigorously tracks cumulative privacy loss, enabling explicit per-response $(\varepsilon, \delta)$-DP guarantees for sensitive outputs. Unlike prior approaches requiring retraining or corpus-level filtering, PAD is model-agnostic and operates entirely at decoding time with minimal computational overhead. Experiments on three real-world datasets demonstrate that PAD substantially reduces private information leakage while preserving response utility, outperforming existing retrieval- and post-processing-based defenses. Our work takes an important step toward mitigating privacy risks in RAG via decoding strategies, paving the way for universal and scalable privacy solutions in sensitive domains. Our code is available: https://github.com/wang2226/PAD.
arXiv:2604.25417v3 Announce Type: replace
Abstract: We present a novel and unifying framework for constructing spectral approximations to fractional integral operators. These spectral approximations are based on transplanted Chebyshev polynomials, which are obtained by composing Chebyshev polynomials with a variable transform. When an algebraic transform is used, the framework produces spectral approximations based on Jacobi fractional polynomials. When an exponential transform is used, it yields a versatile spectral approximation that is applicable to a much broader class of fractional calculus problems. The construction of such spectral approximations is both numerically stable and optimal in terms of complexity. These spectral approximations lead to stable and fast spectral methods for fractional calculus. The spectral approximation based on the double-exponential transform is demonstrated through extensive numerical examples that are intractable for existing spectral methods.
arXiv:2605.28556v2 Announce Type: replace
Abstract: As agent capabilities advance, existing benchmarks, such as $\tau^2$-Bench, are becoming increasingly saturated. Yet constructing new benchmark tasks remains complex, costly, and labor-intensive. Moreover, the standard approach, in which scenarios are first written in natural language and then mapped to tool sequences, captures only a narrow subset of the tool-use patterns agents exercise. In this paper, we address these problems by reversing the task construction process. We propose TASTE: Task Synthesis from Tool Sequence Evolution, an automatic method that generates challenging tasks with broader tool-use coverage. TASTE utilizes an Adaptive Contrastive $n$-gram model trained on LLM-judged validity signals. This enables sampling valid tool sequences that cover a vast range of tool combinations. TASTE then selects representative sequences from the pool via clustering, instantiates them into complete benchmark tasks, and refines them through iterative difficulty evolution. Using TASTE, we construct $\tau^c$-Bench, a challenging extension of the three domains of $\tau^2$-Bench. We evaluate $11$ agent/user LLM pairs and find that models nearly saturating $\tau^2$-Bench suffer severe performance drops on our tasks (e.g., Gemini-3-Flash falls from $0.82\!-\!0.94$ to $0.28\!-\!0.61$). Beyond increasing difficulty, our generated tasks more than double the number of unique tool combinations agents must execute. Our results suggest high scores on existing benchmarks often reflect saturation rather than robust task-solving ability. By automating the generation of difficult, high-coverage benchmarks, TASTE enables continuous, scalable evaluation of future agents.
arXiv:2508.15130v3 Announce Type: replace
Abstract: Despite significant progress in no-reference image quality assessment (NR-IQA), dataset biases and reliance on subjective labels continue to hinder their generalization performance. We propose HiRQA (Hierarchical Ranking and Quality Alignment), a self-supervised, opinion-unaware framework that offers a hierarchical, quality-aware embedding through a combination of ranking and contrastive learning. Unlike prior approaches that depend on pristine references or auxiliary modalities at inference time, HiRQA predicts quality scores using only the input image. We introduce a novel higher-order ranking loss that supervises quality predictions through relational ordering across distortion pairs, along with an embedding distance loss that enforces consistency between feature distances and perceptual differences. A training-time contrastive alignment loss, guided by structured textual prompts, further enhances the learned representation. Trained only on synthetic image distortions, HiRQA generalizes to authentic degradations, as demonstrated through comprehensive evaluations on various unseen distortions such as lens flare, haze, motion blur, and low-light conditions. For real-time deployment, we introduce HiRQA-S, a lightweight variant with an inference time of only 3.5 ms per image. Extensive experiments across synthetic and authentic benchmarks validate HiRQA's competitive performance, strong generalization ability, and scalability. The HiRQA model and inference pipeline are available at: https://github.com/uf-robopi/HiRQA.
arXiv:2605.15572v2 Announce Type: replace
Abstract: The dynamic range of activations is a first-order constraint for low-bit quantization, activation scaling, and stable LLM inference. Prior work characterized outlier features and massive activations on pre-2024 LLaMA-style models, and the downstream activation-quantization stack inherits that picture without revisiting it for the post-LLaMA open-model boom. We ask the deployment-oriented question: how large can activations get in modern open LLMs, and how does this magnitude vary across families, generations, and training stages? Under a unified pipeline (5,000-sample multi-domain corpus, family-specific tokenization, identical hooks across embeddings, hidden states, attention, MLP/MoE, SwiGLU gates, and final norm), we measure global and layerwise maxima on 27 checkpoints from 8 open families spanning dense, MoE, vision-language, intermediate-training, and instruction-tuned variants. We find that (i) global maxima span over nearly four orders of magnitude at comparable parameter counts, with Qwen3.5 and MoE checkpoints in the 10^2 to 10^3 range and Gemma3-27B-it reaching ~7 x 10^5; (ii) cross-family and cross-generation comparisons break simple monotonic scaling; and (iii) MoE checkpoints exhibit 14.0-23.4x lower peaks than matched-scale dense counterparts, while the residual stream carries the global maximum in 22/24 checkpoints. A lightweight INT-8 sanity check shows that measured maxima co-vary with low-bit reconstruction error via activation-scale selection. We conclude that maximum activation magnitude is a model property tied to family, architecture, and training stage - not a simple byproduct of size - and should be measured and reported alongside any open-weight release before low-bit deployment. The code is publicly available at https://github.com/clx1415926/Max_act_llm.
arXiv:2606.03839v1 Announce Type: new
Abstract: Text-Attributed Graph (TAG) is an important type of graph structured data, where each node has a text description. TAG models usually train a Graph Neural Network (GNN) and language model jointly, which leads to high space and time consumption, especially on large datasets. To mitigate this, we propose TAGSAM, a condensation method that compresses TAGs while preserving training accuracy. TAGSAM comes with two key designs, i.e., subgraph text Selection and Attribute similarity Matching, which compress the text description and graph topology of TAG, respectively. For the texts, subgraph text selection selects and merges representative text chunks from multiple related text descriptions by maximizing mutual information. For the graph topology, popular condensation methods based on Matching Training Trajectories (MTT) suffer from high variance, which hinders accuracy. Our attribute similarity matching mitigates this issue by aligning stable similarity matrices. We evaluate TAGSAM against six state-of-the-art baselines, where it showcases superior performance. For the same compressed size, TAGSAM improves upon the best-performing baseline by an average of 4.9% in accuracy. Furthermore, it maintains competitive training accuracy even when the TAG is condensed to just 1% size. Our code is available at https://github.com/SundayVHan/TAGSAM
arXiv:2606.02624v1 Announce Type: cross
Abstract: AI for scientific discovery is entering an agentic era, where protein-engineering systems are expected to prioritize future wet-lab experiments rather than merely fit static measurements. We introduce TadA-Bench, a million-variant wet-lab replay benchmark from 31 TadA directed-evolution rounds for future-round discovery toward agentic protein engineering. TadA-Bench preserves the campaign chronology and defines a fixed-data replay task: given earlier experimental rounds, models rank variants that appear only in later rounds. It provides aligned DNA, RNA, and protein views, and uses Seq2Graph, a graph-based label-unification pipeline, to reconcile noisy enrichment measurements into consistent cross-round activity labels. Random-split controls show strong interpolation, but future-round ranking and finite-budget candidate selection are much weaker. Controlled analyses suggest that evolutionary coverage is more informative than local data density, positioning TadA-Bench as a reproducible wet-lab replay substrate for future-round discovery toward agentic protein engineering; the data and code are released on Hugging Face and GitHub.
arXiv:2606.02596v1 Announce Type: new
Abstract: The curvature exponent $\alpha$ in $h_k \propto \sigma_k^\alpha$ -- governing how Hessian eigenvalues scale with gradient singular values -- varies systematically across layer types ($\alpha \approx 2$ for convolutions, $\approx 1$ for transformer attention, $< 1$ for MLP up-projections). Why? We prove the Spectral Alignment Decomposition: $\alpha = 2 + d\log\Phi_k / d\log\sigma_k$, where $\Phi_k$ measures alignment between Kronecker factor eigenbases and gradient singular directions. This reduces "why does $\alpha$ vary?" to a geometric question we answer for LayerNorm, residual connections, and softmax heads. The decomposition implies a spectral transfer identity $s = \alpha\gamma$ linking curvature exponent, effective gradient rank-decay $\gamma$, and Hessian decay exponent $s$. The identity is algebraic; its empirical content is that $\alpha$ and $\gamma$, fit on independent data (HVPs vs. SVD), recover $s$ to ~2% median error across 93 layers, five architectures, and three datasets -- with no free parameters. A zeta-function bound on participation ratio shows curvature concentrates onto effectively one direction per layer. As a proof of concept, we derive the architecture-adaptive preconditioner $T(\sigma;\alpha)$ and show that Spectral Newton -- implementing $T$ in the gradient singular basis -- outperforms AdamW on vision benchmarks where $\alpha \approx 2$.
arXiv:2606.03690v1 Announce Type: new
Abstract: Integrated sensing and communication (ISAC) has emerged as a promising key technology for future wireless networks, enabling the efficient coordination of sensing and communication functions within limited resources. This work investigates a secure ISAC system assisted by an uncrewed aerial vehicle (UAV). By incorporating the extended Kalman filter (EKF), the proposed system is capable of delivering communication services to legitimate users while simultaneously jamming eavesdroppers and performing joint prediction and tracking of the trajectories of both legitimate and illegitimate users. Considering practical constraints such as {sensing beamwidth}, transmit power, and UAV's propulsion energy consumption, the secrecy rate is maximized through the joint design of transmit beamforming and UAV trajectory. To tackle the resulting highly non-convex optimization problem, an efficient iterative algorithm is developed by integrating block coordinate descent, successive convex approximation, and EKF, thereby yielding a high-quality suboptimal solution. Extensive simulation results validate the superior performance of the proposed scheme compared to benchmarks.
arXiv:2606.03689v1 Announce Type: new
Abstract: Survival Analysis (SA) is a statistical framework that models the time span until some event of interest occurs. Widely used in several domains, including healthcare and churn prediction, a central challenge in its applicability stems from the time of the event being partially observed or \emph{right-censoring}.
Tabular Foundation Models (TFM) have attracted significant interest in recent years due to their ability to perform prediction tasks in a single forward pass, requiring no dataset-specific parameter fitting. Despite their success, their application to prediction tasks on time-to-event data remains difficult due to right censoring. In this work, we present a training-free method to survival regression by leveraging TFMs to both predict the time of the event and iteratively impute right-censored data.
Our method uses a TFM to construct an Accelerated Failure Time (AFT) model requiring no training beyond fitting a single scalar parameter. Subsequently, by building on the Buckley-James estimator, we introduce a non-parametric in-context estimator for right-censored data. Our experiments on standard survival analysis benchmarks show that our method is competitive with several parametric and semi-parametric survival regression models that require training, including Cox regression and parametric AFT models.
arXiv:2605.08747v4 Announce Type: replace
Abstract: Standard embodied evaluations do not independently score whether an agent correctly commits to task completion at episode closure, a capacity we call terminal commitment. Behaviorally distinct failures--never completing the task, completing it but failing to stop, and reporting success without sufficient evidence--collapse into the same benchmark failure. We introduce VIGIL, an evaluation framework that makes terminal commitment independently measurable. Under VIGIL's default protocol, agents observe only egocentric RGB, receive no action-success signals, and must end each episode with a semantic report checked deterministically against hidden world state. This yields two separate scores: world-state completion (W) and benchmark success (B), where B additionally requires a correct terminal report. This decoupling makes four outcome categories distinguishable: missed execution, post-attainment drift, unsupported commitment, and verified success. Across 20 models on 1,000 frozen episodes, systems with comparable W differ by up to 19.7 pp in B: one model converts achieved states into correct reports, while another with near-identical execution drifts past the goal without closing. An action-feedback intervention further tests the separation: execution-oriented signals improve W broadly, yet commitment failures persist in models that do not already ground terminal reports in the achieved state. VIGIL provides a protocol that makes terminal commitment independently visible and scorable.
arXiv:2507.10419v3 Announce Type: replace
Abstract: We propose LoRA-MCL, a training scheme that extends next-token prediction in language models with a method designed to decode diverse, plausible sentence continuations at inference time. Traditional language modeling is an intrinsically ill-posed problem: given a context, multiple futures may be equally plausible. Our approach leverages Multiple Choice Learning (MCL) and the winner-takes-all loss to efficiently handle ambiguity through Low-Rank Adaptation. We provide a theoretical interpretation of applying MCL to language modeling, assuming the data is generated from a mixture of distributions. We illustrate the proposed approach using mixtures of Markov chains. We then demonstrate with experiments on audio and visual captioning, as well as machine translation, that our method achieves high diversity and relevance in generated outputs. We release the code for applying LoRA-MCL to a wide range of language models.
arXiv:2512.17575v2 Announce Type: replace
Abstract: We present an analytical model for the frequency response of a gas microbubble oscillating near a spherical inclusion of arbitrary size and mechanical nature (rigid, fluid, or viscoelastic) immersed in a viscous compressible fluid. The model considers both radial and nonspherical oscillations in the linear regime and predicts how their resonance frequencies and oscillation amplitudes are altered by the bubble size, material properties, and distance to the nearby sphere. As a key application, we demonstrate that scanning the frequency response of a bubble near a viscoelastic object, such as an erythrocyte-like particle mimicking a biological cell, offers a way to recover its mechanical properties through inverse modeling, opening new possibilities for high-resolution elastography at the microscale.
arXiv:2602.10949v2 Announce Type: replace-cross
Abstract: Effective initialization in deep networks requires an understanding of random neural networks. In this work, a rigorous probabilistic analysis of deep bias-free random Leaky ReLU networks is provided. We prove a Law of Large Numbers and a Central Limit Theorem for the logarithm of the norm of network activations, establishing that, as the number of layers increases, their growth is governed by a parameter called the Lyapunov exponent. This parameter characterizes a sharp phase transition between vanishing and exploding activations, and we calculate the Lyapunov exponent explicitly for Gaussian or orthogonal weight matrices. Our results reveal that standard methods, such as He initialization or orthogonal initialization, do not guarantee activation stability for deep networks of low width. Based on these theoretical insights, we propose a novel initialization method, referred to as Lyapunov initialization, which sets the Lyapunov exponent to zero and thereby ensures that the neural network is as stable as possible, leading empirically to improved learning.
arXiv:2605.29663v2 Announce Type: replace
Abstract: Ground robots often carry payloads, implements, or other attachments that turn their effective footprint into complex, non-convex shapes. Navigating safely through clutter then requires reasoning about this true geometry, yet most local planners simplify it with convex or inflated proxies and rasterize sensor data into occupancy grids or distance fields. Both choices eliminate feasible motions when clearance is comparable to the footprint geometry. We present EXACT-MPPI, a training-free local navigation framework that maps local point-cloud observations and sparse guidance directly to motion commands, without any intermediate map representation. The framework embeds an analytic, exact signed-distance evaluator into a Model Predictive Path Integral (MPPI) controller. The footprint is represented as a simple polygon for general convex or concave planar shapes, with a rectangle-cover specialization for faster evaluation of rectilinear footprints, enabling footprint-aware collision costs without convex decomposition, inflation, or learned encoders. During each MPPI rollout, observed obstacle points are transformed into the predicted body frame and evaluated against the footprint. All operations are batched in JAX, leveraging GPU parallelism for real-time receding-horizon control. Experiments show that EXACT-MPPI accelerates batched distance evaluation over a learned point-to-robot baseline, preserves feasible motion where convex-footprint planners fail, and remains robust under dense static and moving obstacles. The same framework deploys on differential-drive, Ackermann, omnidirectional, and hybrid-mode platforms by changing only the footprint description and motion model without per-platform training. Pairing exact footprint geometry with sampling-based predictive control thus offers a practical, training-free path to footprint-aware local navigation across diverse robots.