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01.
arXiv (CS.CV) 2026-06-16

DLWM: Diverse Latent World Models for Efficient Multimodal Reasoning

Reasoning capabilities of multimodal large language models (MLLMs) have improved considerably in recent years. Existing approaches typically rely on explicit chain-of-thought or continuous latent-space trajectories to enhance multi-step reasoning. However, these methods generally assume that an input admits a single latent interpretation and unfold reasoning along a fixed path or under a uniform computation budget. In real-world multimodal settings, visual observations are often subject to occlusion, blur, viewpoint variation, or semantic ambiguity, giving rise to multiple plausible interpretations. A uniform reasoning strategy not only limits the model's ability to explore multiple hypotheses but also incurs high memory usage and rollout cost. We present DLWM (Diverse Latent World Models), a multimodal reasoning framework that combines latent-space reasoning with reinforcement learning. First, we construct a set of diverse latent world hypotheses in continuous latent space, each capturing a different plausible interpretation of the visual input, and unfold latent reasoning independently on each hypothesis. An orthogonality-based diversity regularizer explicitly prevents hypothesis collapse. Second, we formulate the latent reasoning process as a resource-constrained sequential decision problem and introduce a resource-aware reinforcement learning policy that adaptively allocates computation across hypotheses, dynamically deciding whether to expand, terminate, or merge reasoning paths, thereby substantially reducing memory footprint and improving rollout efficiency. Experiments on multiple multimodal reasoning benchmarks demonstrate that DLWM outperforms existing methods by 2-5 points in accuracy while reducing memory usage by 24%.

02.
arXiv (CS.LG) 2026-06-19

Predicting Mergeability of Parameter-Efficient Fine-Tuning Updates

arXiv:2606.19549v1 Announce Type: new Abstract: Low-rank adaptation (LoRA) makes it cheap to train many domain- and task-specific language model adapters, but whether two adapters can be merged is usually discovered only after both have been fully trained and evaluated. This late feedback is costly: adapters that are strong in isolation can interfere destructively once their updates are combined. We ask whether this outcome can be anticipated. We formalize adapter mergeability as the degree to which an adapter preserves its single-task utility after merging, and show that it can be forecast from signals measured in the first few percent of training – chiefly how the low-rank updates and their gradients align across tasks and how much they disturb shared representations. We package these signals into MergeProbe, a lightweight predictor that estimates pairwise and set-level retention and turns the estimate into a concrete decision: merge directly, reweight, prune, or route. On MERGE-PEFT, a five-domain benchmark spanning math, code, science, instruction following, and safety, MergeProbe attains the best average and worst-case retention among strong interference-aware merge baselines while adding far less deployment overhead than full task routing. This turns LoRA merging from a post-hoc engineering step into an anticipatory measurement problem.

03.
arXiv (CS.CL) 2026-06-16

Bridging the Usability Gap: Lessons from Interpreting Studies for Machine Interpreting Design

Machine interpreting (MI), the live, real-time branch of speech translation, has achieved remarkable progress on standard benchmarks, with some systems approaching human parity on textual fidelity. Yet the user experience remains far inferior to interpreter-mediated communication, revealing what we term the accuracy illusion: systems that appear accurate on paper but fail in practice to support smooth, goal-oriented interaction. This paper defines MI as a distinct subfield of speech translation, with its own characteristics and the need for evaluation methods grounded in communicative effectiveness rather than isolated fidelity metrics. Drawing on insights from interpreting studies, we identify critical dimensions of professional interpreting practice that are overlooked by current systems, and consolidate them into three interdependent design priorities for future MI: agency (context-sensitive initiative and repair), grounding (multimodal and discourse-level situational awareness), and experience (adaptive improvement through real interaction). Together, these priorities chart a path toward closing the usability gap and enabling systems that can sustain authentic multilingual communication in real time.

04.
arXiv (CS.LG) 2026-06-16

Transformers Learn the Mestre-Nagao Heuristic

arXiv:2606.15036v1 Announce Type: new Abstract: We train a two-layer transformer encoder to classify rational elliptic curves $E/\mathbb{Q}$ of conductor $\leq 10000$ as either rank 0 or rank 1 from the first 128 normalized Frobenius traces. We achieve >99% accuracy on both classes, and accuracy is essentially unchanged on test curves with no isogeny or quadratic-twist relative in the training set. We then apply techniques from mechanistic interpretability such as attention analysis, linear probing, activation patching, logit attribution, and neuron-level circuit analysis to reverse-engineer the algorithm the (centroid in function space) model learned. We find that a sparse circuit of 20 out of 512 layer-1 MLP neurons is sufficient for rank prediction under a linear probe with an AUROC of 0.992 at plateau, implementing a push-pull detector architecture of rank-0 and rank-1 detectors with a one-sided readout. However, we notice that the model has sub-optimal readout problems indicating a mismatch in rank-order between the readout pathway and the discriminative circuit. Critically, the learned input weights of the top discriminating neuron match the Mestre-Nagao sum heuristic weights $\log(p)/(p\cdot \log{B})$ with a Spearman coefficient $r = 0.997$ and Pearson coefficient $r = 0.952$: the model has learnt a result from analytic number theory from the Frobenius trace data alone. We additionally find that all 50 independently trained models concentrate CLS attention on prime positions at 2-50$\times$ the rate of composite positions. The CLS embedding encodes $\log{L(E,1)}$ with $R^2 = 0.962\pm 0.011$ across the 50 models (after controlling for the conductor). Activation patching analysis reveals that attention weights are dissociated from causal information flow. Additionally, the 50 solutions from training are near-identical in function space (with pairwise agreement $>$98.8%) despite large weight space barriers.

05.
arXiv (CS.AI) 2026-06-16

AIRMap: AI-Generated Radio Maps for Wireless Digital Twins

arXiv:2511.05522v4 Announce Type: replace-cross Abstract: Accurate, low-latency channel modeling is essential for real-time wireless network simulation and digital-twin applications. Traditional modeling methods like ray tracing are however computationally demanding and unsuited to model dynamic conditions. In this paper, we propose AIRMap, a deep-learning framework for ultra-fast radio-map estimation, along with an automated pipeline for creating the largest radio-map dataset to date. AIRMap uses a single-input U-Net autoencoder that processes only a 2D elevation map of terrain and building heights. Trained on 1.2M Boston-area samples and validated across four distinct urban and rural environments with varying terrain and building density, AIRMap predicts path gain with under 4 dB RMSE in 4 ms per inference on an NVIDIA L40S-over 100x faster than GPU-accelerated ray tracing based radio maps. A lightweight calibration using just 20% of field measurements reduces the median error to approximately 5%, significantly outperforming traditional simulators, which exceed 50% error. Integration into the Colosseum emulator and the Sionna SYS platform demonstrate near-zero error in spectral efficiency and block-error rate compared to measurement-based channels. These findings validate AIRMap's potential for scalable, accurate, and real-time radio map estimation in wireless digital twins.

06.
arXiv (CS.AI) 2026-06-24

IPO Finance Agent: Evaluation of LLM Financial Analysts beyond Finance Agent v2, with Automated Rubric Generation – the Case of the SpaceX (SPCX) IPO

arXiv:2606.23032v2 Announce Type: replace Abstract: Finance Agent v2 (by Vals AI) has emerged as the reference benchmark for evaluating both Anthropic Claude and OpenAI ChatGPT frontier language models on financial tasks. However, it narrowly deals with periodic reporting from publicly traded companies (SEC 10-K and 10-Q filings), and its agentic harness relies on naive, unenriched chunk retrieval. Neither the task design nor the retrieval approach addresses the distinct challenges of IPO due diligence. SEC S-1 filings combine historical financial statements, governance structures, pro forma and common-control accounting treatments, capital-formation narratives, and underwriting-sensitive risk disclosures within substantially longer documents than typical periodic filings. That is why we introduce IPO Finance Agent, which extends the Finance Agent v2 framework along two directions: task domain and retrieval architecture. During our experiments, the original Finance Agent v2 harness basically failed to deliver any output related to the SpaceX S-1 filing, due to document length. We therefore had to improve the agentic harness with contextual retrieval, a more realistic and industry-standard approach for long documents. We also built a dataset of 1,000 IPO-diligence questions, and publicly release 70 questions on the SpaceX (SPCX) S-1 filing to support reproducibility, while the remainder are held private to guard against benchmark contamination. In addition, we introduce an evaluator-optimizer pipeline to automatically generate evaluation rubrics for the benchmark: candidate facts are extracted from model answers, consolidated into draft criteria, then automatically audited for omissions, hallucinations, mistiered items, and redundancy, with LLM feedback driving iterative repair, targeted enrichment, and deduplication. Human experts only review final rubrics before deployment. Results show that the best-performing evaluated model, Alibaba Qwen 3.7 Max, reaches 79.4% accuracy at 0.30 USD per query, and the most cost-efficient model on the resulting Pareto frontier, Xiaomi MiMo-2.5 Pro, reaches slightly lower accuracy (76.8%) at 0.05 USD per query. Both exceed the current Finance Agent v2 leaderboard ceiling-Google Gemini 3.5 Flash at 57.9% for 2.51 USD per querywhile undercutting even FABv2's cheapest entry (MiniMax M3: 48.3% at 0.32 USD) on cost-efficiency. Code and data are released on GitHub: https://github.com/benstaf/ipoagent

07.
arXiv (CS.LG) 2026-06-11

Minimal surfaces, Knots, and Neural Networks

arXiv:2605.26234v2 Announce Type: replace-cross Abstract: A recent conjecture by Joel Fine posits a relationship between the coefficients of the HOMFLY polynomial of a knot $K$ in the 3-sphere $S^3$, and the signed count of minimal surfaces in hyperbolic 4-space $\mathrm{H}^4$ meeting the sphere at infinity at $K$, with prescribed genus and self-intersection number. In this paper, we develop a novel machine learning framework based on Physics-Informed Neural Networks (PINNs) to solve the minimal surface equation in hyperbolic space. We utilise this framework to test Fine's Conjecture by constructing near-minimal surfaces bounding various families of knots in $S^3$. Furthermore, we develop an algorithmic method to find self-intersections and compute their sign. For every knot analysed, the computationally discovered minimal surfaces and their self-intersection numbers perfectly align with the predictions of Fine's Conjecture, providing empirical evidence for it.

08.
arXiv (CS.AI) 2026-06-12

An Embodied Simulation Platform, Benchmark, and Data-Efficient Augmentation Framework for Wet-Lab Robotics

arXiv:2606.12936v1 Announce Type: cross Abstract: Wet-lab robots can improve the reproducibility, throughput, and safety of biomedical experiments, but scaling their learning requires customizable simulators for safe and reproducible task generation, open editable laboratory assets, and efficient pipelines that turn limited demonstrations into usable training data. We present Pipette, an embodied simulation platform, benchmark, and data-efficient augmentation framework for wet-lab robot learning. Pipette releases over 43 open-source and re-editable wet-lab assets, together with an extensible asset-building pipeline. A key component of Pipette is its simulation-based data augmentation pipeline, replaying human demonstrations in simulation, applies lighting, camera, speed, and action perturbations, and filters generated episodes with automatic task success checks, rapidly expanding usable training data from limited manual demonstrations. We further introduce an 11-task wet-lab embodied benchmark covering sample handling, culture-ware manipulation, device operation, and precision placement. With only 30 demonstrations per task, ACT achieves 65.5% average success rate, while simulation augmentation improves SmolVLA from 44.1% to 74.7% and {\pi}0 from 40.4% to 46.5%, validating the effectiveness of Pipette for data-efficient VLA training and evaluation. Pipette also supports natural-language-driven scene construction and task registration, lowering the barrier for non-expert users to define new wet-lab robotic tasks.

09.
arXiv (math.PR) 2026-06-17

The Erdős-Hajnal High-Girth Subgraph Conjecture Holds in the Polynomial Chromatic-Sparsity Regime

作者:

arXiv:2606.17901v1 Announce Type: cross Abstract: For a graph $G$ put $h_r(G)=\max{\chi(H):H\subseteq G,\operatorname{girth}(H)\ge r}.$ Erdős and Hajnal asked whether $h_r(G)\to\infty$ as $\chi(G)\to\infty$, for every fixed $r\ge4$. We prove this in every fixed polynomial edge-density regime: for all $r\ge4$, $k\ge2$, $P,C>0$, there is $M=M_{r,k}(P,C)$ such that $\chi(G)\ge M,\ e(G)\le C\chi(G)^P\Longrightarrow h_r(G)\ge k.$ Quantitatively, after replacing $P$ by $P\vee2$ and $C$ by $C\vee2$, $M_{r,k}(P,C)\le \exp!\left(O_{r,k}\bigl((P+2+\log(C\vee2))^2\bigr)\right),$ and consequently the same conclusion holds throughout the quasi-polynomial range $e(G)\le \exp\bigl(C_0(\log\chi(G))^a\bigr),\ 1 < a < 3/2,$ for all sufficiently large $\chi(G)$. In each fixed polynomial-density regime we also obtain $f_{P,C}(k,r)\le k^{O_{r,P,C}(1)}.$ The proof combines a chromatic-defect random extraction lemma, compact and near-quadratic sparse-core bases, and a peeling/thinning bootstrap increasing the admissible edge exponent by $1/(r-1)$. We also prove structural saturation results for possible counterexamples, including Moore-strength exact-cycle packings and quadratic saturation in projected colour-pair space. Finally, writing $h_r^{\mathrm f}(G)=\max{\chi_{\mathrm f}(H):H\subseteq G,\operatorname{girth}(H)\ge r},$ we develop a fractional random-extraction framework based on Mohar-Wu preservation. We prove sufficient cheap-cycle-killing criteria and verify them for several structured families, including clique-organised families, line graphs of incidence graphs of equal-order generalized quadrangles and generalized hexagons, and the Bohman-Keevash tracking-time triangle-free-process graph. We also isolate a density-free obstruction that any proof using this fractional surgery route must overcome.

10.
bioRxiv (Bioinfo) 2026-06-16

DMcloud: Macromolecular Structure Modeling Using Local Structure Fitting for Medium to Low Resolution cryo-EM maps

Cryogenic electron microscopy (cryo-EM) has become an essential experimental approach in structural biology for determining macromolecular structures. When the resolution of a cryo-EM map is worse than approximately 5[A], fitting known or predicted molecular models into the map becomes a common strategy for interpretation. However, accurately fitting biomolecular models into cryo-EM maps, particularly for large macromolecular complexes, remains challenging when the input structure models contain errors or are in a conformation different from that represented in the map. Here, we present DMcloud, a method for local structure fitting of proteins and nucleic acids in cryo-EM maps. Instead of forcing an entire input model into the map, DMcloud divides input structures into local regions, identifies regions that are supported by the density, removes unsupported regions, and assembles the retained regions into a final model. We benchmarked DMcloud on 176 cryo-EM maps, including intermediate and high-resolution maps that include proteins, DNAs, or RNAs. For EM maps in the 5.0-10.0 [A] and 2.5-5.0 [A] resolution ranges, DMcloud achieved average sequence modeling coverage of 0.49 and 0.70, respectively. For DNA/RNA maps, DMcloud achieved an average sequence coverage of 0.75. Across all datasets, DMcloud consistently outperformed existing methods in model accuracy, map-model correlation, and modeling coverage.

11.
arXiv (CS.LG) 2026-06-19

Linear Mode Connectivity under Data Shifts for Deep Ensembles of Image Classifiers

arXiv:2511.04514v2 Announce Type: replace Abstract: The phenomenon of linear mode connectivity (LMC) links several aspects of deep learning, including training stability under noisy stochastic gradients, the smoothness and generalization of local minima (basins), the similarity and functional diversity of sampled models, and architectural effects on data processing. In this work, we experimentally study LMC under data shifts and identify conditions that mitigate their impact. We interpret data shifts as an additional source of stochastic gradient noise, which can be reduced through small learning rates and large batch sizes. These parameters influence whether models converge to the same local minimum or to regions of the loss landscape with varying smoothness and generalization. Although models sampled via LMC tend to make similar errors more frequently than those converging to different basins, the benefit of LMC lies in balancing training efficiency against the gains achieved from larger, more diverse ensembles. Code and supplementary materials are available at https://github.com/DLR-KI/LMC. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.

12.
arXiv (CS.CV) 2026-06-16

Rel-Zero: Harnessing Patch-Pair Invariance for Robust Zero-Watermarking Against AI Editing

Recent advancements in diffusion-based image editing pose a significant threat to the authenticity of digital visual content. Traditional embedding-based watermarking methods often introduce perceptible perturbations to maintain robustness, inevitably compromising visual fidelity. Meanwhile, existing zero-watermarking approaches, typically relying on global image features, struggle to withstand sophisticated manipulations. In this work, we uncover a key observation: while individual image patches undergo substantial alterations during AI-based editing, the relational distance between patch pairs remains relatively invariant. Leveraging this property, we propose Relational Zero-Watermarking (Rel-Zero), a novel framework that requires no modification to the original image but derives a unique zero-watermark from these editing-invariant patch relations. By grounding the watermark in intrinsic structural consistency rather than absolute appearance, Rel-Zero provides a non-invasive yet resilient mechanism for content authentication. Extensive experiments demonstrate that Rel-Zero achieves substantially improved robustness across diverse editing models and manipulations compared to prior zero-watermarking approaches.

13.
arXiv (quant-ph) 2026-06-16

Non-Markovianity-based ultrasensitive parameter estimation

arXiv:2211.05142v2 Announce Type: replace Abstract: Accurate parameter estimation is a central task in quantum metrology and sensing, where quantum resources can provide precision beyond classical limits. In realistic settings, however, system-environment interactions lead to decoherence, reducing these strategies to their classical counterparts. Noise is typically classified as Markovian or non-Markovian, with the latter often preserving quantum coherence longer and thus supporting better metrological performance. Still, the absence of noise is generally considered ideal. In this work, we uncover a striking reversal: certain non-Markovian environments not only outperform Markovian ones - including their quantum Cramér-Rao bounds - but can also surpass the entirely noiseless case. We demonstrate these findings numerically for an all-optical setup, which is experimentally feasible and can be extended to other physical platforms. In general, our results open new avenues for noise-assisted quantum metrology beyond conventional limits.

14.
arXiv (CS.LG) 2026-06-16

Whole-Brain Connectomic Graph Model Enables Whole-Body Locomotion Control in Fruit Fly

arXiv:2602.17997v3 Announce Type: replace Abstract: Animals perform coordinated whole-body movements under the control of neural systems shaped by brain-wide connectivity. The mapping of the whole-brain neural connections, or the connectomes, provides a natural graph for modeling sensorimotor information flow, yet its potential as a neural controller for embodied agents remains largely unexplored. Here, we introduce the Fly-connectomic Graph Model, which directly instantiates the whole-brain connectome of an adult Drosophila as a graph-structured neural controller for movements of a simulated biomechanical fruit fly via deep reinforcement learning. We achieve stable performance across diverse locomotion tasks, as well as better sample efficiency compared to both graph and non-graph baselines. Our results demonstrate a biologically informed way towards effective control policy design by translating whole-brain wiring principles into actionable architectural priors, while also improving the interpretability through dynamic information flow. This work also highlights the potential to bridge neuromechanics with embodied intelligence by providing a computational platform for investigating the sensorimotor transformation underlying animal behavior and a paradigm to advance the development of more nature-aligned intelligent systems.

15.
Nature (Science) 2026-06-10

Mutation-dependent responses to sleep and exercise in clonal haematopoiesis

Clonal haematopoiesis (CH) activates inflammation and increases the risk of atherosclerosis1,2. Whether lifestyle alters CH clone expansion or the phenotypic programming of CH mutant cells, thereby affecting atherosclerosis, is unknown. Here, in humans and mice and across mutations in Jak2, Tet2, Trp53 and Dnmt3a, we demonstrate mutation-dependent responses to sleep and exercise in CH and show that mutant cells are uniquely sensitive to lifestyle. In two human datasets, moderate-to-vigorous physical activity was associated with lower prevalence of non-DNMT3A-driven CH. In atherogenic mice with Jak2V617F or Tet2 loss of function (LOF), but not Trp53 LOF or Dnmt3aR878H CH, uninterrupted sleep or exercise curtails clone expansion. In CH with the Jak2V617F mutation, sleep and exercise reduces clone expansion by selectively reprogramming mutant, but not cohabitant wild type, haematopoietic progenitor cells towards antiproliferative and metabolically healthy phenotypes by tempering bone marrow macrophage–haematopoietic progenitor cell IL-1β signalling. Sleep or exercise also lessens Jak2V617F-driven, Tet2 LOF-driven and Trp53 LOF-driven, but not Dnmt3aR878H-driven, atherosclerosis by locally reprogramming mutant vascular macrophages, independent of peripheral clone dynamics. In Jak2V617F, but not adjacent wild type, aortic macrophages, uninterrupted sleep blunts CLEC4E-dependent inflammasome activation, consequently diminishing lesions. Exercise, meanwhile, activates PAC1+ neurons in the locus coeruleus, raising the levels of peripheral noradrenaline, which signals through adrenergic receptor β2 (ADRβ2) whose expression is preserved by exercise in Jak2V617F, but not cohabitant wild type, aortic macrophages, selectively repressing their inflammatory programming and atherosclerosis. Our findings establish that healthy lifestyles gene-specifically diminish CH and selectively reprogram mutant haematopoietic progenitor cells and macrophages to maintain cardiovascular health. Sleep and exercise can slow clonal haematopoiesis and limit mutant cell-driven atherosclerosis.

16.
arXiv (quant-ph) 2026-06-19

QMCtwin: Master-Equation Simulation of Syndrome Statistics Beyond Pauli Noise

arXiv:2606.19848v1 Announce Type: new Abstract: As quantum error correction moves toward large-scale experimental implementations, decoder performance increasingly depends on how faithfully hardware noise is translated into syndrome statistics. Standard stabilizer workflows achieve scalability by replacing device dynamics with stochastic Pauli or detector-error models, but this compression can discard coherent phase information, nonunital drift, continuous-time effects of always-on couplings, and correlations generated by simultaneous Hamiltonian and dissipative evolution. Here we present QMCtwin, a sign-problem-suppressed quantum Monte Carlo framework for master-equation simulation of QEC circuits, and apply it to a full syndrome-extraction round of a distance-$7$ rotated surface code with $97$ physical qubits. The open-system model includes realistic superconducting-device noise mechanisms such as relaxation, pure dephasing, coherent gate miscalibration, residual $ZZ$ crosstalk, and drive-qubit detuning. By directly estimating syndrome observables from the QMC-generated stochastic density matrix estimator, we compare the master-equation dynamics with their Pauli-twirled Clifford simulation counterparts. QMCtwin predicts syndrome-extraction biases and correlations between syndromes and proxies of logical-string-parity that are absent or strongly suppressed in the stochastic Pauli description. We introduce information-theoretic diagnostics that further quantify how information concerning syndromes versus string-parity proxies differs between the realistic master-equation simulation and the corresponding Pauli-twirled model. These results show that QMC-based master-equation digital twins can expose noise features hidden by conventional Pauli/Clifford noise models and provide a practical path toward more accurate decoder-facing syndrome models.

18.
arXiv (CS.AI) 2026-06-19

How Do Instructions Shape Speech? Cross-Attention Attribution for Style-Captioned Text-to-Speech

arXiv:2606.20532v1 Announce Type: new Abstract: Style-captioned text-to-speech systems use natural language to control voice characteristics, but how individual words influence acoustic output remains unclear. Understanding this is critical for diagnosing failure modes and improving controllability in expressive TTS. We propose cross-attention attribution for speech diffusion models, adapting the DAAM framework to the speech domain for the first time, and apply it to CapSpeech-TTS. Our method extracts per-token heatmaps across 25 layers and 24 ODE steps. We analyze 3,600 (style caption, text transcript) combinations comprising 120 style captions conditioning the generation of 30 text transcripts each, revealing how caption tokens shape waveforms. Results show: (1) style tokens have lower temporal variance than content/function tokens, confirming global conditioning; (2) style attention correlates with F0 and energy; (3) style conditioning peaks in early steps and deep layers; (4) attention entropy reaches its minimum at layer 17, co-occurring with the style importance peak, indicating maximal network selectivity at the most style-critical stage. This is the first study of how natural language influences cross-attention in speech diffusion models

19.
arXiv (CS.LG) 2026-06-16

Stochastic-Dimension Frozen Sampled Neural Network for High-Dimensional Gross-Pitaevskii Equations on Unbounded Domains

arXiv:2604.09361v4 Announce Type: replace Abstract: This paper introduces the Stochastic-Dimension Frozen Sampled Neural Network (SD-FSNN), a novel computational framework for solving high-dimensional Gross-Pitaevskii equation (GPE) on unbounded domain. The proposed method circumvents the curse-of-dimensionality that plagues traditional discretizations and the computational bottlenecks of gradient-based neural network solvers through a synergistic combination of techniques. First, a prescribed Gaussian envelope encodes the far-field decay of the wavefunction, enabling a space-time separation where the spatial approximation is handled by a frozen, single-hidden-layer neural network with data-driven sampled features. This yields a gradient-free formalism where spatial derivatives are analytically precomputed and time-dependence is evolved via reduced ODEs. Second, a stochastic-dimension sampler provides a conditionally unbiased estimate of the spatial operator by evaluating only a small subset of spatial dimensions at each time step, essentially reducing computational and memory costs. Discrete conservation laws are also enforced, ensuring long-term stability. Extensive numerical experiments on GPE in up to 1000 dimensions demonstrate that SD-FSNN achieves significantly higher accuracy and efficiency compared to state-of-the-art methods, including PINNs, randomized feature methods, and tensor-network approaches. The results confirm that SD-FSNN effectively mitigates the Kolmogorov $n$-width barrier for frozen-basis models on structured solution manifolds.

20.
arXiv (math.PR) 2026-06-11

Integrated expectile-based measures of inequality

arXiv:2606.12333v1 Announce Type: cross Abstract: Expectiles provide a class of asymmetric location functionals that incorporate the magnitude of deviations and admit a natural geometric interpretation. Building on their structural consistency with the convex stochastic order, this paper introduces a family of integrated expectile functionals for measuring risk, dispersion, and inequality. The proposed functionals admit analytical representations as integrals of expectiles across asymmetry levels. For a distinguished subclass of these constructions, a geometric representation is available: the resulting quantities can be expressed as weighted areas of star-shaped sets encoding the distributional asymmetry of a random variable. This approach yields a new class of expectile-based inequality indices, constituting a natural counterpart to classical Gini-type measures while preserving desirable monotonicity and consistency properties. Empirical counterparts are derived in closed form and admit explicit decompositions over finite samples. The framework extends naturally to multivariate settings through directional expectile constructions, leading to measures capable of capturing genuinely joint forms of multivariate dispersion and inequality.

21.
arXiv (CS.LG) 2026-06-11

Understanding Sample Efficiency in Predictive Coding

arXiv:2605.11911v2 Announce Type: replace Abstract: Predictive Coding (PC) is an influential account of cortical learning. Much of recent work has focused on comparing PC to Backpropagation (BP) to find whether PC offers any advantages. Small scale experiments show that PC enables learning that is more sample efficient and effective in many contexts, though a thorough theoretical understanding of the phenomena remains elusive. To address this, we quantify the efficiency of learning in BP and PC through a metric called ``target alignment'', which measures how closely the change in the output of the network is aligned to the output prediction error. We then derive and empirically validate analytical expressions for target alignment in Deep Linear Networks. We show that learning in PC is more efficient than BP, which is especially pronounced in deep, narrow and pre-trained networks. We also derive exact conditions for guaranteed optimal target alignment in PC and validate our findings through experiments. We study full training trajectories of linear and non-linear models, and find the predicted benefits of PC persist in practice even when some assumptions are violated. Overall, this work provides a mechanistic understanding of the higher learning efficiency observed for PC over BP in previous works, and can guide how PC should be parametrised to learn most effectively.

22.
arXiv (CS.AI) 2026-06-17

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning

arXiv:2606.17513v1 Announce Type: cross Abstract: Neural operators provide fast surrogates for PDEs but their deterministic predictions limit their use in tasks requiring uncertainty quantification (UQ), especially under geometric variability. Existing approaches primarily model uncertainty in network parameters, largely overlooking the geometry-aware representations learned by the operator itself. We propose REEF-GP (Residual on Embedded Features Gaussian Process), a post-hoc UQ framework that fits a GP to the residuals of a frozen neural operator whose internal embeddings define the kernel feature space. Rather than learning a separate feature map, REEF-GP adapts the operator's intrinsic coordinate-feature representations to construct geometry-aware uncertainties. To ensure stability and scalability on unstructured domains, REEF-GP incorporates spectral-normalized projections, heteroscedastic geometry-aware noise, and efficient subset-based training that avoids restrictive low-rank approximations. Across five PDE benchmarks with varying geometries, REEF-GP preserves predictive accuracy while achieving calibrated uncertainty estimates competitive with deep ensembles but at a fraction of their cost. Our approach remains robust under geometric distribution shift, with uncertainty concentrating in physically meaningful regions (e.g., shock fronts). Our results demonstrate that accurate and scalable post-hoc UQ for neural operators can be achieved directly in their learned feature space, offering a practical alternative to parameter-centric approaches.

23.
arXiv (CS.CV) 2026-06-11

Finding Sparse Subnetworks in One Training Cycle via Progressive Magnitude-Based Pruning

Neural network pruning reduces model size by removing less important parameters while aiming to preserve predictive performance. Although the Lottery Ticket Hypothesis (LTH) shows that sparse subnetworks can match dense networks when trained from suitable initializations, its iterative pruning procedure requires multiple complete training cycles. This work evaluates progressive magnitude-based pruning as a single-cycle alternative. The method gradually increases sparsity during training using a linear schedule and updates pruning masks based on active weight magnitudes. We conduct systematic experiments on CIFAR-10 and MNIST across ResNet, VGG-style, and LeNet architectures, comparing the proposed method with representative iterative and initialization-based pruning baselines, including LTH, SNIP, and GraSP. On CIFAR-10, the method achieves 95.12\% accuracy on ResNet-18 at 72.9\% sparsity, compared with 90.5\% reported for LTH. At extreme sparsity, it achieves 93.13\% accuracy on a VGG-like architecture at 97\% sparsity, compared with approximately 92.0\% for SNIP, and 93.44\% accuracy on VGG-19 at 97.97\% sparsity, compared with 92.19\% for GraSP at 98\% sparsity. A sparsity-accuracy analysis on ResNet-18 further shows that accuracy remains within 0.1 percentage points of the dense baseline across 70–85\% sparsity. These results indicate that progressive magnitude-based pruning provides an effective single-cycle approach for neural network sparsification under the evaluated settings.

24.
arXiv (CS.CV) 2026-06-16

Disagreement-Based Cross-Model Routing for Implicit Video Question Answering

We study multiple-choice video question answering on the ImplicitQA benchmark, where the correct answer is never explicitly shown but must be inferred from off-screen events, line-of-sight cues, causal structure, and cross-shot spatial layout. On this benchmark a single frontier video LLM already operates near its accuracy ceiling, and we observe that conventional self-consistency strategies – majority voting across repeated samples of the same model – can hurt rather than help, because the model's errors on hard questions are correlated. We propose disagreement-based cross-model routing, a pure inference-time procedure that requires no labels and no training. We triple-sample a native-video model (Gemini 3.1 Pro Preview) at temperature zero, exploit the genuine sample-to-sample variance of its video-processing pipeline to identify the roughly 20% subset of questions where the three samples disagree, and route only that subset to a second model from a different family (Claude Opus 4.8) that consumes uniformly sampled frames with adaptive thinking. On the 1001-question validation set with public ground truth – our main evaluation – the method improves AvgAcc by +1.43 over the best single sample of the primary model, with per-category gains concentrated on Motion & Trajectory (+5.49), Inferred Counting (+3.45), and Vertical Spatial Reasoning (+1.82) – the categories most dependent on cross-shot reference resolution. The same pipeline applied to the held-out 172-question CVPR 2026 ImplicitQA challenge test set achieves 82.03 AvgAcc / 79.71 MacroAvgAcc (+1.81 over the best single sample of the primary model), confirming the validation result on an independent split.

25.
arXiv (CS.AI) 2026-06-17

Catastrophic Forgetting is Low-Rank: A Function-Space Theory for Continual Adaptation

arXiv:2606.18024v1 Announce Type: cross Abstract: Catastrophic forgetting in continual adaptation is usually studied through parameter drift, replay, or distillation, but these views do not identify which output-space directions are vulnerable. We give a function-space account in the NTK regime: new-task training induces old-task prediction drift through the cross-task kernel, yielding a closed-form predictor for the forgetting vector before any new-task gradient step. In frozen-backbone linear-head PEFT-CL, where the model is linear in the trainable parameters, the predictor is exact up to numerical precision; for nonlinear adapters/full fine-tuning, it is a local NTK approximation. The same expression reveals that forgetting concentrates in a small number of old-task NTK eigenmodes and under frozen linear heads gives a Kronecker scaling rule for the vulnerable rank. These results clarify the relation to prior NTK-overlap theory, explain why parameter-space regularizers can miss output-space interference, and motivate a targeted spectral regularizer.