arXiv:2512.04069v2 Announce Type: replace
Abstract: Vision Language Models (VLMs) demonstrate strong qualitative visual understanding, but struggle with metrically precise spatial reasoning required for embodied applications. The agentic paradigm promises that VLMs can use a wide variety of tools that could augment these capabilities, such as depth estimators, segmentation models, and pose estimators. Yet it remains an open challenge how to realize this vision without solely relying on handcrafted prompting strategies or enforcing fixed, predefined tool pipelines that limit VLMs' ability to discover optimal tool-use patterns. Reinforcement Learning could overcome this gap, but has so far been limited to reasoning with a single visual tool due to the large search space in multi-tool reasoning. We introduce Double Interactive Reinforcement Learning (DIRL), a two-phase training framework where VLMs learn to coordinate multiple tools through interactive exploration and feedback. In the teaching phase, we combine demonstrations from a single tool specialist trained via interactive RL with traces from a frontier model using all tools. In the exploration phase, the model further refines multi-tool coordination through continued RL. Our model, SpaceTools, with tool-augmented spatial reasoning ability, achieves state-of-the-art performance on spatial understanding benchmarks (RoboSpatial-Home, BLINK, BOP-ASK) and demonstrates reliable real-world manipulation using a 7-DOF robot as a tool. DIRL provides substantial improvements over the vanilla SFT (+12% on RoboSpatial) and RL (+16% on RoboSpatial) baselines. Project page: https://spacetools.github.io/.
Science Journals
arXiv:2511.01938v3 Announce Type: replace
Abstract: Grokking is a puzzling phenomenon in neural networks where full generalization occurs only after a substantial delay following the complete memorization of the training data. Previous research has linked this delayed generalization to representation learning driven by weight decay, but the precise underlying dynamics remain elusive. In this paper, we argue that post-memorization learning can be understood through the lens of constrained optimization: gradient descent effectively minimizes the weight norm on the zero-loss manifold. We formally prove this in the limit of infinitesimally small learning rates and weight decay coefficients. To further dissect this regime, we introduce an approximation that decouples the learning dynamics of a subset of parameters from the rest of the network. Applying this framework, we derive a closed-form expression for the post-memorization dynamics of the first layer in a two-layer network. Experiments confirm that simulating the training process using our predicted gradients reproduces both the delayed generalization and representation learning characteristic of grokking.
arXiv:2606.00913v1 Announce Type: cross
Abstract: Multi-arm bandit algorithms are increasingly used in online platforms, clinical trials, and social science experiments, but valid statistical inference on their performance remains an open challenge. After deploying bandits, a natural question is whether one can construct a confidence interval for its mean reward and assess whether it reliably outperforms a baseline policy. The total reward achieved in any single bandit deployment is random, and deploying a bandit twice on the same population typically yields different reward trajectories due to stochastic rewards. Standard statistical inference methods cannot be used because bandit algorithms introduce complex dependencies in the collected data, which violate the i.i.d. assumption underlying many classical approaches. Moreover, existing inference methods for adaptively collected data only apply to estimands that do not depend on the data-collection algorithm (such as the mean reward under a fixed action). We propose Bandit Simulation for Inference (BSI), a framework that fits a simulator of the bandit environment from observed data--either on-policy or off-policy--and uses it to estimate the mean reward under any evaluation policy, including adaptive blackbox algorithms. BSI formally propagates uncertainty in the estimated simulator parameters into the confidence interval construction. Furthermore, for BSI to be valid, it requires only weak exploration assumptions on the behavior policy and avoids importance weighting. We prove that BSI yields asymptotically valid confidence intervals, and demonstrate empirically that it maintains nominal coverage in settings where standard off-policy evaluation methods fail.
arXiv:2606.00643v1 Announce Type: cross
Abstract: Physics-Informed Neural Networks (PINNs) often train slowly or fail to converge on challenging partial differential equations (PDEs), a behavior recently linked to severely ill-conditioned loss landscapes inherited from the underlying differential operator. We study PINNs augmented with a pointwise data-fidelity term, added at a few points in the domain to the standard residual and boundary losses. We show that this supervision term acts as an operator-level preconditioner: for suitable weights, our comparison bounds guarantee a substantially smaller condition number than under the standard PINN loss, independently of how the pointwise labels are obtained. For a broad class of PDEs admitting a Feynman-Kac (FK) representation, we generate such labels by Monte Carlo averages of the FK functional, resulting in what we call ``FK-PINNs", and using the excess risk decomposition approach, we derive non-asymptotic $L^2(\Omega)$-error bounds for FK-PINNs with $\tanh$ activation trained by finitely many steps of gradient descent. Along the way, we establish pseudo-dimension bounds for first- and second-order derivatives of $\tanh$ neural networks, which are of independent interest and, to the best of our knowledge, new. Numerical experiments on Poisson, Schr\"odinger, mean exit time, and committor problems corroborate the theory, and show that FK-PINNs can successfully solve PDEs for which standard PINNs exhibit severe failure modes.
arXiv:2509.24808v2 Announce Type: replace
Abstract: Explaining why a language model produces a particular output requires local, input-level explanations. Existing methods uncover global capability circuits (e.g., indirect object identification), but not why the model answers a specific input query in a particular way. We introduce query circuits, which directly trace the information flow inside a model that maps a specific input to the output. Unlike surrogate-based approaches (e.g., sparse autoencoders), query circuits are identified within the model itself, resulting in more faithful and computationally accessible explanations. To make query circuits practical, we address two challenges. First, we introduce Normalized Deviation Faithfulness (NDF), a robust metric to evaluate how well a discovered circuit recovers the model's decision for a specific input, and is broadly applicable to circuit discovery beyond our setting. Second, we develop sampling-based methods to efficiently identify circuits that are sparse yet faithfully describe the model's behavior. Across benchmarks (IOI, arithmetic, MMLU, and ARC), we find that there exist extremely sparse query circuits within the model that can recover much of its performance on single queries. For example, a circuit covering only 1.3% of model connections can recover about 60% of performance on an MMLU questions. Overall, query circuits provide a step towards faithful, scalable explanations of how language models process individual inputs. The project page is at https://tony10101105.github.io/query-circuit/.
arXiv:2503.07154v3 Announce Type: replace
Abstract: Generative pre-training is often framed through a false dichotomy between autoregressive models for discrete signals and diffusion models for continuous signals. We argue that the dichotomy is false because it conflates model family, data representation, training objective, and inference procedure. Autoregression is an inference procedure that expands a sequence through normalized conditional draws, while diffusion is a refinement procedure that repeatedly revises an existing state. The more useful contrast is therefore not autoregressive versus diffusion, but discrete tokens learned with cross-entropy versus continuous tokens learned with diffusion-style objectives, together with the inference algorithms used to sample from them. From this perspective, algorithmic progress should prioritize inference-time efficiency along two axes: sequence expansion and state refinement. We advocate designing the inference procedure before the training objective, because a training method cannot compensate for an inference map that omits necessary arguments or imposes an incorrect factorization. We illustrate this principle through a target-time limitation of DDIM-style samplers, a joint-distribution limitation of multi-token prediction, and recent flow-map and few-step distillation methods that directly parameterize long-range inference moves.
arXiv:2605.29539v2 Announce Type: replace
Abstract: Vision-language foundation models have shown promising zero-shot generalization for Cross-Domain Few-Shot Object Detection (CD-FSOD). However, they face two critical challenges in fine-tuning: insufficient support set utilization due to sparse single-instance annotations, and severe overfitting under extremely limited target-domain samples. To address these issues, this paper proposes GiPL, an efficient two-branch training framework. In the first branch, we design an iterative pseudo-label self-training paradigm, which performs zero-shot inference on the support set to generate reliable pseudo-annotations, fuses them with ground-truth labels, and iteratively optimizes the model to fully exploit support set data. In the second branch, we introduce generative data augmentation pipeline using large vision-language models, which synthesizes domain-aligned, multi-object annotated images to enrich training samples and suppress overfitting. Extensive experiments on three challenging CD-FSOD datasets (RUOD, CARPK, CarDD) under 1/5/10-shot settings demonstrate that GiPL consistently outperforms state-of-the-art methods with significant performance gains. Code is available at \href{https://github.com/z-yaz/CDiscover}{CDiscover}.
arXiv:2503.07325v2 Announce Type: replace
Abstract: Understanding and certifying the behavior of modern deep neural networks remains a fundamental challenge in reliable machine learning. We introduce a new class of data-dependent generalization bounds that apply directly to trained models, without any modification. In particular, we present an exactly computable bound that is non-vacuous across all evaluated networks, including ImageNet-scale models with 600M parameters. This this is the first work showing that meaningful generalization guarantees are achievable even for large, unaltered deep networks.
Our approach reveals that generalization is governed by the interaction between the trained model and the geometry of the data distribution. We decompose the generalization error into two interpretable components: a distributional complexity term, capturing how the data mass is distributed across the input space, and local model-behavior terms, capturing the network's behavior within individual regions. This joint dependence identifies where and why generalization gaps arise. Empirically, some components of our bound are highly predictive of the true test error, and the bound tightens when the partition aligns with the intrinsic data geometry, highlighting data-dependent local regularity as a key driver of generalization.
arXiv:2606.00574v1 Announce Type: cross
Abstract: The Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will map sources in multiband colour--variability space. We present a prototype coherence-based framework for astrobiology and technosignature searches, in which candidates are treated as structured departures from natural astrophysical manifolds rather than isolated photometric outliers. We illustrate the framework with three simulated cases: five Kuiper Belt Object (KBO) surface/activity states, a grid of 649 synthetic exoplanet spectra with vegetation-red-edge-like (VRE) perturbations, and 500 synthetic multiband light curves, each projected into LSST-like observable space and analysed through colour geometry, chromatic variability, and cross-band coherence. Key results include a full-colour Mahalanobis distance $D\approx5.1$ for the weak-coma KBO state (${\sim}5\sigma$ in the five-dimensional colour vector), an indicative VRE coherence threshold at $f_{\rm crit}\approx0.13$, and an idealised stacking forecast reaching $5\sigma$ under optimistic assumptions. We show, using a small Gaia~DR3 stellar sample, that stellar colour and photometric stability may inform the prioritisation of Galactic regions for applying such coherence diagnostics.
arXiv:2504.20852v2 Announce Type: replace
Abstract: Data-driven machine learning (ML) models, such as FuXi, exhibit notable limitations in forecasting typhoon intensity and structure. This study presents a comprehensive evaluation of FuXi-SHTM, a hybrid ML-physics model, using all 2024 western North Pacific typhoon cases. The FuXi-SHTM hybrid demonstrates clear improvements in both track and intensity forecasts compared to the standalone SHTM, FuXi, and ECMWF HRES models. Compared to FuXi alone, FuXi-SHTM reduces typhoon track forecast errors by 16.5% and 5.2% at lead times of 72 h and 120 h, respectively, and reduces intensity forecast errors by 59.7% and 47.6%. Furthermore, FuXi-SHTM simulates cloud structures more realistically compared to SHTM, and achieves superior representation of the 10-m wind fields in both intensity and spatial structure compared to FuXi and SHTM. Increasing the resolution of FuXi-SHTM from 9 km to 3 km further enhances intensity forecasts, highlighting the critical role of the resolution of the physical model in advancing hybrid forecasting capabilities.
arXiv:2510.21372v2 Announce Type: replace
Abstract: Transformer-based models have advanced NLP, yet Hebrew still lacks a RoBERTa encoder that is trained at scale and released in both base and large variants. We present HalleluBERT, a RoBERTa-based encoder family trained from scratch on 49.1~GB of deduplicated Hebrew web text and Wikipedia using a Hebrew-specific byte-level BPE vocabulary. On native Hebrew benchmarks for named entity recognition (BMC, NEMO) and sentiment classification (SMCD), HalleluBERT outperforms monolingual and multilingual baselines, and yields the highest unweighted mean score across the three benchmarks. We release model weights and tokenizer under the MIT license to support reproducible Hebrew NLP research.
arXiv:2606.02237v1 Announce Type: new
Abstract: Distribution Matching Distillation (DMD) compresses pretrained diffusion models into efficient few-step generators by aligning their noised distributions across all scales. In principle, such distribution-level supervision remains agnostic to specific noise-data pairings of the teacher; this provides the student the freedom to remap latent noise, a behavior consistently observed in low-dimensional settings. Surprisingly, we find that in high-dimensional settings, distilled students spontaneously reproduce the original noise-data pairings of the teacher, a phenomenon we term copying. We demonstrate that copying is neither a byproduct of adversarial objectives nor a result of teacher memorization. Instead, our evidence suggests that copying is an emergent property arising from the limited geometric freedom of the student model during high-dimensional distillation.
arXiv:2603.27459v3 Announce Type: replace
Abstract: Arc-standard derivations over projective dependency trees can be interpreted as the incremental construction of lexicalized ordered trees with contiguous yields. Each \textsc{shift}, \textsc{leftarc}, and \textsc{rightarc} transition corresponds to a deterministic tree update, and the resulting ordered tree uniquely determines the dependency arcs introduced by the derivation. We show that this representation is not an arbitrary encoding: a single-headed dependency tree admits such a contiguous ordered representation if and only if it is projective. The proposal is therefore derivational rather than conversion-based, since the ordered object is defined over the transition sequence itself rather than obtained by transforming a completed dependency graph. This gives a tree-theoretic interpretation of arc-standard parsing, in which projective dependency derivations implicitly construct recoverable constituency-style ordered trees. For non-projective inputs, the interpretation can be used through pseudo-projective lifting and inverse decoding. A small implementation study confirms that the mapped derivations are executable in an existing neural transition-based parser.
arXiv:2606.02523v1 Announce Type: new
Abstract: Suicide memes are memes used to express suicide-related thoughts or comment on suicide-related issues. Suicide memes are increasingly common on social media, yet remain poorly understood and potentially harmful. There is an urgent need to better understand their characteristics and to develop appropriate content moderation strategies that limits users' exposure to potentially harmful content. Currently, the absence of annotated datasets of suicide memes remains a key barrier to developing and evaluating automated moderation approaches. In this paper, we introduce FigSIM, the first dataset designed for fine-grained analysis of suicide memes. The dataset consists of 1049 memes, each annotated for (1) fine-grained suicide severity levels, (2) figurative phenomena (e.g., metaphors), and (3) suicide-related content (e.g., suicide method depiction). We benchmark 16 unimodal and multimodal models across three tasks: figurative language, suicide severity, and suicide-related content detection. Overall, FigSIM demonstrates that suicide memes pose unique challenges for both modeling and content moderation. Analysis revealed biases, such as underprediction of higher suicide severity levels, especially for figurative memes. The dataset (including splits used for analyses) is publicly available. Content Warning: This paper contains suicide-related content that may be triggering.
arXiv:2510.01800v3 Announce Type: replace
Abstract: Academic regulation advising is essential for helping students interpret and comply with institutional policies, yet building effective systems requires domain specific regulatory resources. To address this challenge, we propose REBot, an LLM enhanced advisory chatbot powered by CatRAG, a hybrid retrieval reasoning framework that integrates retrieval augmented generation with graph based reasoning. CatRAG unifies dense retrieval and graph reasoning, supported by a hierarchical, category labeled knowledge graph enriched with semantic features for domain alignment. A lightweight intent classifier routes queries to the appropriate retrieval modules, ensuring both factual accuracy and contextual depth. We construct a regulation specific dataset and evaluate REBot on classification and question answering tasks, achieving state of the art performance with an F1 score of 98.89%. Finally, we implement a web application that demonstrates the practical value of REBot in real world academic advising scenarios.
arXiv:2606.02134v1 Announce Type: new
Abstract: Deep neural networks achieve strong performance on many supervised learning tasks but remain vulnerable to adversarial perturbations. Neural network verification provides mathematically rigorous robustness guarantees, yet at substantial computational cost. To mitigate this, certified training techniques optimise for verifiable robustness during training, typically inducing a trade-off between natural and certified accuracy controlled by method-specific hyperparameters. Because these metrics are inherently conflicting, the common practice of reporting a single configuration is problematic: it can mislead conclusions about overall performance and prevents unbiased assessments of the state of the art. We address this by evaluating certified training methods via Pareto front comparisons over the natural--certified accuracy trade-off. To enable fair, method-agnostic comparisons, we perform efficient automated multi-objective hyperparameter optimisation to identify a set of Pareto-optimal configurations for each method. This approach often uncovers substantial undertuning in previously reported configurations, yielding superior performance and establishing a new state of the art. Leveraging these fronts, we present the first comprehensive multi-objective comparison of certified training approaches, showing that prior advancements are less pronounced than assumed and revealing previously unreported performance complementarities.
arXiv:2606.01443v1 Announce Type: new
Abstract: A central difficulty in training Joint-Embedding Predictive Architectures (JEPAs) is preventing representation collapse. LeJEPA addresses this by enforcing an isotropic Gaussian target on the embeddings via Sketched Isotropic Gaussian Regularization (SIGReg). This target is in tension with the manifold hypothesis, which expects embeddings to concentrate on a low-dimensional subset of the ambient space. We propose \emph{UR-JEPA}, which targets a uniformly $n$-rectifiable measure of local tangent dimension $n$ at small scales, realized through a Gaussian-kernel smoothed Carleson-type square function $\mathcal{L}^{\text{CGLT}}$, with a complementary Jones $\beta$-number formulation. On Inet10, UR-JEPA($\mathcal{L}^{\text{CGLT}}$) attains $0.9141 \pm 0.0014$ for a $+0.83$\,pp gain over LeJEPA($\mathcal{L}^{\text{SIGReg}}$) with $\sim 30\%$ lower seed standard deviation; on matched-recipe Galaxy10~SDSS, a single-seed ImageNet-$100$ run, and a $3$-seed EuroSAT remote-sensing run, the two methods lie in the same peak-accuracy band at convergence, with UR-JEPA retaining its lower-seed-variance signature. On EuroSAT the in-domain pair is competitive at $96.0$ to $96.1\%$ with large remote-sensing foundation-model transfer at a $25\times$ smaller backbone. The distinction is geometric: direct visualization of the projector output distribution shows that on all four datasets UR--JEPA($\mathcal{L}^{\text{CGLT}}$) produces a global PCA spectrum with a $4$ to $5$ order-of-magnitude drop at index $\sim 20$ to $25$ out of $D = 32$, while LeJEPA's spectrum is near-flat (top-to-bottom ratio at most $3.6$). Per-dimension marginals are simultaneously near-Gaussian for both methods (mean Shapiro-Wilk $W \in [0.992, 0.996]$) as a Diaconis-Freedman consequence. At matched accuracy the two regularizers therefore yield structurally distinct projected representations.
arXiv:2504.04718v2 Announce Type: replace
Abstract: Recent studies have demonstrated that test-time compute scaling effectively improves the performance of small language models (sLMs). However, prior research has mainly examined test-time compute scaling with an additional larger model as a verifier, leaving verification by sLMs underexplored. In this work, we investigate whether sLMs can reliably verify the output candidates under test-time scaling. We find that even with knowledge distillation from larger verifiers, sLMs struggle with verification tasks requiring memorization, such as numerical calculations and fact-checking. To address this limitation, we propose Tool-integrated verification (T1), a two-stage framework that first filters candidates with external tools and then uses an sLM for final verification, offloading memorization-heavy steps to tools such as a code interpreter. Within T1, we prove that offloading to external tools reduces the memorization burden on sLMs and improves test-time scaling performance. Experiments on the MATH benchmark demonstrate that, with T1, a Llama-3.2 1B model under test-time scaling outperforms the significantly larger Llama-3.1 8B model. Moreover, T1 improves the verification accuracy of both process reward models (PRMs) and critic models. Our findings highlight the potential of tool integration to substantially improve the verification abilities of sLMs.
arXiv:2603.27446v2 Announce Type: replace
Abstract: This paper investigates the nonlinear dynamics and phase transitions in power packet network connected with routers, conceptualized as macroscopic information-ratchets. In the emerging paradigm of cyber-physical energy systems, the interplay between stochastic energy fluctuations and the thermodynamic cost of control information defines fundamental operational limits. We first formulate the dynamics of a single router using a Langevin framework, incorporating an exponential cost function for information acquisition. Our analysis reveals a discontinuous (first-order) phase transition, where the system adopts a strategic abandon of regulation as noise intensity exceeds a critical threshold $D_c$. This transition represents a fundamental information-barrier inherent to autonomous energy management. Here, we extend this model to network configurations, where multiple routers are linked through diffusive coupling, sharing energy between them. We demonstrate that the network topology and coupling strength significantly extend the bifurcation points, with collective resilient behaviors against local fluctuations. These results provide a rigorous mathematical basis for the design of future complex communication-energy network, suggesting that the stability of proposed systems is governed by the synergistic balance between physical energy flow and the thermodynamics of information exchange. It will serve to design future complex communication-energy networks, including internal energy management for autonomous robots.
arXiv:2605.26444v2 Announce Type: replace
Abstract: The massive vocabulary sizes of large language models, often exceeding 100k tokens, impose a computational bottleneck on the final linear projection layer during speculative decoding. Existing vocabulary pruning solutions rely on static or coarsely-grained sub-vocabularies that necessitate large active sizes ($\sim$30k) to maintain draft quality. We propose NanoSpec, a novel training-free approach that breaks this trade-off by dynamically constructing a minimalist, context-aware active vocabulary for each generation step. Leveraging the inherent temporal locality of language generation, NanoSpec achieves high coverage while slashing the average vocabulary size by over $40\times$ (to $<$3k tokens) without requiring any auxiliary trained parameters. To realize the theoretical benefits of such high sparsity on modern hardware, we introduce a system-algorithm co-design that overcomes the inefficiencies of sparse memory access through asynchronous gathering and GPU-resident state management. As a complementary plug-and-play module, NanoSpec cuts draft time by an average of 51.6\%, delivering a $1.17$-$1.29\times$ end-to-end speedup over the state-of-the-art speculative decoding methods EAGLE-2 and EAGLE-3 across 7 tasks and outperforming complex training-based pruning baselines.
arXiv:2604.02878v2 Announce Type: replace
Abstract: In Global Navigation Satellite System (GNSS)-denied underwater environments, individual unmanned underwater vehicles (UUVs) suffer from unbounded dead-reckoning drift, making collaborative navigation (CN) crucial for accurate state estimation. However, the severe communication delay inherent in underwater acoustic channels poses serious challenges to real-time state estimation. Traditional filters, such as Extended Kalman Filters (EKFs) or Unscented Kalman Filters (UKFs), usually block the main control loop while waiting for delayed data, or effectively discard Out-of-Sequence Measurements (OOSMs), resulting in serious drift. To address this, we propose an Asynchronous Two-Speed Kalman Filter (TSKF) enhanced by a novel projection mechanism, which we term Variational History Distillation (VHD). The proposed architecture decouples the estimation process into two parallel threads: a fast-rate thread that utilizes Gaussian Process (GP) compensated dead reckoning to guarantee high-frequency real-time control, and a slow-rate thread dedicated to processing asynchronously delayed collaborative information. By introducing a Finite-Length Circular State Buffer (FLCSB), the algorithm applies delayed measurements to their corresponding historical states, and utilizes a VHD-based projection to fast-forward the correction to the current time without computationally heavy recalculations. Simulation results demonstrate that the proposed TSKF maintains a trajectory error comparable to computationally intensive batch-optimization methods under severe delays (up to 30\,s). Executing in sub-millisecond time, it significantly outperforms standard EKF/UKF. The results demonstrate an effective control, communication, and computing (3C) co-design that significantly enhances the resilience of autonomous marine automation systems.
arXiv:2606.00347v1 Announce Type: cross
Abstract: We study empirical $L_p$ moments of a random vector $\pmb\varphi$ based on its i.i.d.\ copies $\pmb\varphi^1,\ldots,\pmb\varphi^m$, that is, $\frac1m\sum_{j=1}^m |\langle \pmb\varphi^j,y\rangle|^p$. Our main result is a new estimate for the expected uniform deviation \[ \mathbb{E}\sup_{y\in D}\biggl| \frac1m\sum_{j=1}^m |\langle \pmb\varphi^j,y\rangle|^p -\mathbb{E}|\langle \pmb\varphi,y\rangle|^p \biggr| \] over an arbitrary index set $D$. The proof is based on a new bound for Talagrand's $\gamma$-functional, sharper than the standard Dudley-type entropy estimate. We then apply this estimate to the following two problems.
First, for $p>2$, we study Marcinkiewicz-type discretization of $L_p$ norms on an $N$-dimensional subspace $X_N\subset B(\Omega)$ of bounded functions on a probability space $(\Omega,\mu)$. We obtain bounds in terms of the norm of the embedding $
(X_N,\|\cdot\|_{L_p(\mu)})\hookrightarrow B(\Omega). $
In particular, we prove that when this norm is of order $N^{1/p}$ and \[ m \ge C(p)\, N\log N\,(\log\log N)^{p-1}, \] then $m$ random samples suffice to approximate the $L_p(\mu)$ norm uniformly on $X_N$ by the sampled discrete $L_p$ norm. This substantially improves the previously known bound in this setting $
m \ge C(p)\, N(\log N)^{\min\{p,3\}}, $
and is optimal up to the factor $(\log\log N)^{p-1}$ in the random-sampling setting.
Second, for $1\le p<2$, we obtain an $L_p$ analogue of the restricted isometry property via random sampling for bounded orthogonal systems and, more generally, for $N$-element systems $\mathcal D_N$ satisfying a Riesz-type condition. We prove that when \[ m \ge C(p)\, s\log N\,(\log s)^2\,\log\log s, \] then $m$ random samples suffice to guarantee an $L_p$ restricted isometry-type property uniformly over the class of all $s$-sparse functions generated by $\mathcal D_N$.
arXiv:2606.00286v1 Announce Type: cross
Abstract: Quenched disorder in the environment can fundamentally alter transport dynamics in both active and passive systems. We explore how disordered arrays of filaments govern the distribution of intermittently moving particles which switch between diffusive and processive transport. Motivated by the mixed-polarity arrangements of parallel microtubules observed in mammalian dendrites, we show that such arrays tend to result in localization of particles at regions of convergent filament orientation. In the rapid attachment-detachment limit, the disordered system can be described by a noisy one-dimensional effective energy landscape, whose structure is approximated by a random walk. The depth and width of wells on this landscape are expressed as a function of the transport kinetics and system geometry. Localization is shown to be strongest at intermediate run-lengths, where biased transport persists long enough to sense the quenched filament polarity but not so long as to facilitate escape from local traps. These results demonstrate robust localization of particles moving on random filament networks, highlighting the emergent spatial organization that arises from an interplay of active transport and quenched disorder.
arXiv:2606.00255v1 Announce Type: cross
Abstract: The work leading to this thesis focuses on assessing and extending quantum theories in order to explore and test their implications across various regimes -- including thermodynamics, semiclassical and quantum gravity scenarios, and the in principle detectable predictions of such theories. The general motivation stems from a basic desire to understand the world form its very foundations. For instance, how can we bridge the gap between what we observe or `perceive' and the fundamental quantum nature in our theories. In particular, this work originated from the search to a better understanding of the nature of time according to our physical theories and the common perception that it invariably `flows' to the future, or, in other words, why do we observe distinct natural processes evolving asymmetrically in time? These motivations led to three distinct, yet interconnected and successful, lines of research, presented here in three separate parts: I. On Possible Detections within Physical Theories; II. On Explaining the Approach to Thermodynamic Equilibrium; and III. Relativistic Collapse Theories and a Self-Consistent Model of Semiclassical Gravity.
arXiv:2606.02080v1 Announce Type: new
Abstract: Biological image analysis increasingly demands integration across heterogeneous tools, programming environments, and domain knowledge that few researchers can command simultaneously. We present Agentic-J, a containerised, multi-agent AI assistant, primarily for ImageJ/Fiji that enables biologists to specify analysis tasks in natural language, from nuclei segmentation and cell tracking to multi-condition quantification. The agent generates executable scripts organised into a documented project structure, so every analysis decision is traceable and the workflow can be reproduced or shared. The specialised sub-agents handle plugin management, code generation, debugging, quality assurance, and statistical reporting. In this paper we introduce the system's design, demonstrate real biological microscopy image analysis workflows, and detailed the technical implementation.