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

SMEPilot: Characterizing and Optimizing LLM Inference with Scalable Matrix Extensions

arXiv:2606.16332v1 Announce Type: cross Abstract: Modern CPUs increasingly integrate matrix extensions, such as Arm Scalable Matrix Extension (SME), that provide high-throughput matrix execution within the CPU. For LLM inference, however, these units are not a universal replacement for conventional CPU cores: prefill, decode, attention, and KV-cache operations expose different arithmetic intensities, vector behavior, and layout requirements, while SME units and CPU cores still compete for shared memory bandwidth. This paper studies this mismatch through a roofline-based characterization of SME-enabled CPUs and uses the resulting model to guide operator-level execution choices. We present SMEPilot, an LLM inference engine that selects CPU-only, SME-only, or cooperative SME+CPU execution for each operator shape. SMEPilot partitions matrix work across SME and CPU cores at tile granularity, overlaps SME-suitable matrix stages with CPU-suitable vector stages in attention, and maintains layout state so packed tensor representations are reused rather than repeatedly rebuilt on critical paths. Across Llama-3.2-3B, Qwen3-4B, and Qwen3-30BA3B on phone, PC, and server platforms, SMEPilot improves end-to-end inference performance by up to 3.94$\times$.

02.
arXiv (CS.CL) 2026-06-16

LoLA: Low-Rank Linear Attention With Sparse Caching

The per-token cost of transformer inference scales with context length, preventing its application to lifelong in-context learning. Linear attention is an efficient alternative that maintains a constant memory footprint, even on infinite context lengths. While this is a potential candidate for lifelong learning, it falls short in memory capacity. In this paper, we propose LoLA, a training-free augmentation to linear attention that boosts associative recall. LoLA distributes past key-value pairs from context into three memory systems: (i) recent pairs in a local sliding window cache; (ii) difficult-to-memorize pairs in a sparse, global cache; and (iii) generic pairs in the recurrent hidden state of linear attention. We show through ablations that our self-recall error metric is crucial to efficiently manage long-term associative memories. On pass-key retrieval tasks, LoLA improves the base model's performance from 0.6% to 97.4% accuracy. This is achieved with a 4.6x smaller cache than Llama-3.1 8B on 4K context length. LoLA also outperforms other 1B and 8B parameter subquadratic models on zero-shot commonsense reasoning tasks.

03.
arXiv (CS.LG) 2026-06-19

SEAGAN: domain-Specific and Edge-Aware Graph Attention Network for Dynamic Plant Processes

arXiv:2606.19623v1 Announce Type: new Abstract: Graph neural networks (GNNs) provide a flexible framework for learning from scientific data linked through physical, biological, or functional relationships. One promising domain is plant physiology, where measured responses often arise from multiple interacting processes whose exact separation remains difficult even with manual intervention. In plant physiology, a key example is the A-Ci curve, which relates net CO2 assimilation rate (Anet) to leaf intercellular CO2 concentration (Ci) and is used to estimate photosynthetic parameters in leaf and crop-canopy models. However, reliable estimation requires identifying the active biochemical limitation state at each curve point, which remains a major source of uncertainty. Here, we formulate limitation-state identification along A-Ci curves as a graph-based node classification problem, with curve points as nodes. Domain-specific graph representations are created using distance-based k-nearest-neighbor (kNN) and auxiliary-signal-guided (ASG) connectivity, with edge attributes encoding pairwise relations. The framework was evaluated against conventional learning baselines, graph-based architectures, and an automated fitting-based benchmark. Results on a large synthetic dataset with known ground-truth limitation states show that graph-based models improve classification, particularly near biochemical transition regions. The best-performing configuration, SEAGAN (domain-Specific and Edge-Aware Graph Attention Network for Dynamic Plant Processes), integrates process-aware node features, edge attributes, kNN connectivity, and graph attention with weighted cross-entropy loss, achieving an F1-score of 0.857 and an accuracy of 0.882. The results show that representing A-Ci curves as graphs improves biochemical limitation-state analysis, with edge-aware attention over local kNN neighborhoods providing the most effective strategy.

04.
arXiv (CS.LG) 2026-06-11

FlexiBrain: Resolution-Agnostic Voxel-Level Encoding for Native fMRI

arXiv:2606.11500v1 Announce Type: cross Abstract: The success of large-scale deep learning models in neuroscience is fundamentally constrained by severe data heterogeneity. Native fMRI data aggregated from diverse sources exhibit substantial variation in both spatial and temporal resolutions. Consequently, most existing frameworks rely on lengthy, rigid preprocessing pipelines that enforce uniformity across datasets. This practice introduces two critical limitations: (1) potential degradation of subject-specific anatomical information; (2) significant computational overhead, often requiring hours of processing per subject. Here, we propose FlexiBrain, a resolution-agnostic voxel-level encoding framework for native fMRI based on Mamba-JEPA. FlexiBrain defines patch sizes in real-world physical units and employs a dynamic patch resizing, thereby bypassing destructive spatial standardization while enabling direct ingestion of data in native space. We instantiate the framework using an efficient Mamba-JEPA backbone to model high-dimensional 4D fMRI signals. Across five diverse downstream neuroscience tasks, FlexiBrain consistently outperforms recent state-of-the-art methods, achieving gains of up to 12 percentage points without external data augmentation. Importantly, FlexiBrain functions as a seamless plug-in module, substantially reducing preprocessing costs and accelerating the development of robust voxel-level fMRI foundation models. Code is available at https://github.com/OneMore1/FlexiBrain.

05.
medRxiv (Medicine) 2026-06-11

Ferritin across long-term conditions in England: cross-sectional primary care study

Background Iron deficiency (ID) is a readily treatable condition once identified. Ferritin is the primary diagnostic marker, but cut-offs vary and inflammation complicates interpretation in patients with long-term conditions (LTCs). Aim To describe ferritin distribution and the prevalence of threshold-defined low ferritin in adults with and without LTCs in primary care. Design and setting Cross-sectional observational study using routinely collected electronic health records from a national primary care database in England (1st January 2015 to 31st December 2021). Method Adults with >1 ferritin test in Clinical Practice Research Datalink (CPRD) Aurum were included. LTCs were identified using validated primary-care code lists. Outcomes included ferritin distribution and threshold-defined ID prevalence using World Health Organization (WHO) (

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

Latent Thought Flow: Efficient Latent Reasoning in Large Language Models

arXiv:2606.16222v1 Announce Type: new Abstract: Large Language Models (LLMs) increasingly rely on intermediate reasoning, yet explicit Chain-of-Thought (CoT) suffers from a linguistic space bottleneck: each thought must be decoded into tokens, causing high inference overhead. Latent reasoning moves deliberation into continuous space, but existing methods mostly learn deterministic or reward-maximizing paths, lacking a principled way to allocate probability across trajectories with different correctness and costs. We propose Latent Thought Flow (LTF), which models reasoning as variable-length continuous trajectories and trains a sampler to match a reward-induced posterior over answer quality and computation cost. We instantiate this with a continuous GFlowNet using stochastic latent transitions. To handle sparse answer supervision, we introduce an Entropy-Weighted Subtrajectory Balance objective for intermediate rewards and a reference-prior regularizer to anchor exploration. Experiments under finetuning and transfer learning settings show that LTF outperforms explicit CoT and latent reasoning baselines, improving accuracy by 9.5% while reducing reasoning length by 27.2% on average compared with strong latent reasoning baselines.

07.
medRxiv (Medicine) 2026-06-11

Neighborhood socioeconomic status associated with post-stroke cognitive impairment: a retrospective cohort study

Background: Late complications after stroke (LCAS), including cognitive symptoms, impact quality of life and recovery. It is not known if neighborhood-level measures of socioeconomic status (SES) influence LCAS. This study assessed associations between SES measures, including neighborhood income inequality (Gini) and area deprivation index (ADI), and cognitive symptoms after acute ischemic stroke (AIS) in a hospital leveraging active surveillance of LCAS. Methods: This retrospective cohort study included 512 patients hospitalized with AIS at Tufts Medical Center with subsequent follow-up (between zero and three months or between three and twelve months) in the Stroke Clinic from 1/1/2018 - 12/31/2022. Using ZIP code data, patients were characterized as low Gini (low inequality) and high ADI (high deprivation) (Gini = 5) by state medians. These variables were combined, indicating patients who were living in both a low Gini and high ADI neighborhood to evaluate the effects of living in a homogeneously deprived area. There were 206 and 281 patients in the low Gini and high ADI groups respectively. 140 patients lived in a low Gini and high ADI neighborhood. The multivariable logistic analysis assessed the likelihood of cognitive symptoms, adjusting for age, race, ethnicity, sex, NIH Stroke Scale (NIHSS), thrombolysis, active LCAS surveillance, poverty, and ADI-Gini combination. Results: There were no associations between high ADI (OR: 1.03, 95% CI: 0.67 ? 1.57) or low Gini (OR: 1.74, 95% CI: 0.98 ? 3.07) alone and cognitive symptoms after AIS. However, the combined variable demonstrated increased likelihood of cognitive symptoms in the high ADI-low Gini group (OR: 1.82, 95% CI: 1.08 ? 3.06). Conclusions: This study suggests that individuals living in homogeneously deprived neighborhoods report higher likelihood of cognitive symptoms after AIS. Further studies with increased power are needed to investigate the underlying causes of these disparities and to develop interventions to reduce these complications.

09.
arXiv (CS.LG) 2026-06-12

Distribution-Agnostic Robust Trajectory Optimization via Chance-Constrained Reinforcement Learning

arXiv:2606.13605v1 Announce Type: cross Abstract: This paper presents a distribution-agnostic robust trajectory-optimization framework based on chance-constrained reinforcement learning. The uncertainty is represented here through initial conditions and process noise, with the only requirement being that it can be sampled. A deterministic nominal trajectory is first computed offline, and reinforcement learning is then used only to robustify that baseline through a structured affine closed-loop correction law comprising a feedforward control adjustment and time-varying feedback gains. Probabilistic feasibility is enforced empirically through rollout-based upper-tail quantiles, while terminal dispersion is regulated through covariance-feasibility penalties. The framework is assessed on two materially different trajectory design problems. The flagship case study is a three-dimensional multi-impulse Earth-Mars transfer, where the learned policy is benchmarked against a recent robust trajectory-optimization reference under Gaussian uncertainty and then evaluated under bounded uniform uncertainty and under process disturbances not seen during training. The second case study is a stochastic atmospheric pinpoint rocket landing problem, used to assess portability to a short-horizon continuous-thrust setting with drag, mass depletion, and glide-slope constraints. The results show that the proposed framework can remain competitive in upper-tail fuel cost while preserving probabilistic feasibility, and that the same robustification scaffold can be carried across heterogeneous spacecraft trajectory planning problems without redesign of its core stochastic-control structure.

10.
PLOS Computational Biology 2026-06-17

Machine learning-driven identification of virulence determinants in <i>Borrelia burgdorferi</i> associated with human dissemination

by Hoa Thanh Nguyen, Catherine A. Brissette Lyme disease, the most common tick-borne infectious disease in the United States, presents with highly variable clinical outcomes, ranging from localized erythema migrans to severe disseminated complications affecting the heart, joints, and nervous system. The bacterial determinants underlying this phenotypic variation remain largely unknown, limiting our ability to predict disease progression and optimize treatment strategies. Here, we applied machine learning (ML) approaches to identify specific amino acid residues within surface-exposed virulence factors that predict human dissemination phenotypes. Utilizing the published whole genome sequences from 299 clinical Borrelia burgdorferi isolates collected from the United States and Slovenia over a 30-year period (1992–2021), we extracted and characterized translated amino acid sequences (variants) of seven known virulence factors (BB_0406, BBK32, DbpA, OspA, OspC, P66, and RevA). Protein variants were classified based on their association with disseminated versus localized infections using clinical metadata. Cramér’s V analysis revealed possible strong associations between dissemination phenotypes and five adhesins: BBK32, DbpA, OspC, P66, and RevA. We developed ML models using five algorithms with multiple feature selection strategies, achieving robust predictive performance for DbpA, OspC, and RevA variants (all performance metrics > 0.7). Feature importance analysis identified 57, 29, and 42 key predictive residues for DbpA, OspC, and RevA, respectively. Notably, B-cell epitope prediction revealed significant enrichment of ML-identified residues within predicted epitope regions for OspC (11 overlapping residues, OR = 3.57, p = 0.006) and RevA (12 overlapping residues, OR = 2.37, p = 0.048), suggesting these residues may influence immune recognition and bacterial persistence. This study establishes the first computational framework linking Borrelia protein sequence variants to clinical dissemination phenotypes, providing molecular insights into Lyme disease pathogenesis that may inform the development of improved diagnostics and therapeutic targets.

11.
arXiv (quant-ph) 2026-06-11

A saturation-absorption rubidium magnetometer with multilevel optical Bloch-equation modeling for intermediate-to-high fields

arXiv:2601.09115v2 Announce Type: replace Abstract: We present SASHMAG (Saturated Absorption Spectroscopy High-field MAGnetometer), an atomic sensor designed for precision magnetic-field measurements in the intermediate-to-high field regime ($>0.2\,T$) using Rubidium-87 ($^{87}Rb$). The sensor operates in the hyperfine Paschen-Back regime, where the hyperfine and Zeeman interactions decouple, and utilizes counter-propagating pump-probe configuration in Faraday geometry to resolve isolated, Doppler-free Zeeman transitions. To interpret the resulting spectra in this strongly field-dependent regime, we developed a comprehensive multilevel optical Bloch-equation model solved explicitly in the uncoupled $\ket{m_I, m_J}$ basis, capturing state mixing and nonlinear saturation dynamics. This model reproduces measured spectra at sub-Doppler resolution and is consistent with analytical expectations for power broadening and thermal Doppler scaling. Magnetic field estimation is performed using a physics-constrained optimization routine that infers the magnetic field by minimizing the residual between experimentally extracted line centers and calculated transition frequencies from the field-dependent Hamiltonian. We demonstrate magnetic field retrieval from $0.2\,T$ to $0.4\,T$ with a precision of $\pm 0.0017 \,T$). Furthermore, the validated simulation establishes a foundation for generating synthetic training datasets, paving the way for autonomous, Machine Learning-enhanced magnetometry in applications ranging from MRI to fusion reactors.

12.
arXiv (math.PR) 2026-06-12

Fourier Dimensions of Mandelbrot Cascades under Minimal Integrability

Authors:

arXiv:2606.08703v2 Announce Type: replace Abstract: This note announces exact Fourier dimension formulas for canonical Mandelbrot cascade measures under the minimal Kahane Peyriere integrability condition and records the canonical b adic extension on cubes. In the dyadic interval setting, the theorem is proved in a balanced vector weight model allowing dependence between sibling weights. Almost surely on non extinction, the Fourier, energy, and L2 dimensions all equal the energy exponent. The scalar specialization gives the canonical Mandelbrot Kahane Fourier dimension formula under the minimal integrability condition. On the circle, the endpoint formula is given by the endpoint lower local dimension exponent. For the b adic Mandelbrot cascade on cubes, the Fourier dimension is the minimum of 2 and the energy exponent, with the universal Fourier barrier at dimension two providing the high dimensional obstruction.

13.
arXiv (CS.LG) 2026-06-15

Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise

arXiv:2512.14967v2 Announce Type: replace Abstract: We present a novel numerical method for solving McKean–Vlasov forward–backward stochastic differential equations (MV–FBSDEs) with common noise, combining Picard iterations, elicitability and deep learning. The key innovation involves elicitability to derive a pathwise loss function, enabling efficient training of neural networks to approximate both the backward process and the conditional expectations arising from common noise, without requiring computationally expensive nested Monte Carlo simulations. The mean-field interaction term is parameterized via a recurrent neural network trained to minimize an elicitable score, while the backward process is approximated through a hybrid feedforward and recurrent network representing the decoupling field. We validate the algorithm on a systemic-risk inter-bank borrowing and lending model, where analytical solutions exist, demonstrating accurate recovery of the true solution. We further extend the model to quantile-mediated interactions, showcasing the flexibility of the elicitability framework beyond conditional means or moments. Finally, we apply the method to a non-stationary Aiyagari–Bewley–Huggett economic growth model with endogenous interest rates, illustrating its applicability to complex mean-field games without closed-form solutions.

14.
bioRxiv (Bioinfo) 2026-06-11

Hyper3D-lite: count-preserving representation auditing for long-read multi-contact genome data

Authors:

Long-read and single-molecule sequencing technologies are rapidly increasing molecule-level data, with platforms such as Oxford Nanopore, PacBio HiFi, and Roche sequencing-by-expansion advancing at different technology readiness levels. In the specific context of Pore-C and HiPore-C multi-contact chromatin-conformation assays, long-read multi-contact 3D genome assays preserve molecule-level contact context, but common downstream pairwise projections can expand one multi-contact molecule into many pair records. This creates a representation problem: apparent contact evidence can increase through the counting frame before biological interpretation begins. Hyper3D-lite addresses this problem as a representation-first audit tool for read-to-fragment-style long-read multi-contact inputs. It compares all-pair projection with CPB, a count-preserving statistical accounting reference point, and separates broad software outputs from conservative higher-order candidate calls.

15.
arXiv (CS.LG) 2026-06-17

Public transit gains and spatially uneven travel demand changes after NYC congestion pricing

arXiv:2606.17530v1 Announce Type: cross Abstract: New York City implemented the nation's first cordon-based congestion pricing program in January 2025, providing an opportunity to evaluate how system-wide urban mobility responds to large-scale pricing interventions. Because such policies generate spillovers across modes and locations, credible control groups are difficult to construct. We address this challenge using time series foundation models to generate probabilistic counterfactual demand forecasts with calibrated uncertainty. Applying this framework to bus, subway, and aggregate trip volume data, we find that post-policy bus and subway ridership increased significantly relative to expected no-policy demand, while overall travel demand decreased modestly. The effects are spatially heterogeneous: while reductions in overall travel demand are concentrated within the Congestion Relief Zone, transit gains extend beyond Manhattan's core. Socio-demographic analyses further reveal uneven adaptation across neighborhoods, highlighting spatial equity implications. Our framework provides a scalable approach for the uncertainty-aware evaluation of system-wide urban interventions when clean control groups are unavailable.

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

DeepForestVisionV2: Ecology-Driven Taxonomy Expansion for Camera-Trap Monitoring in African Tropical Forests

Camera-trap monitoring in African tropical forests increasingly extends beyond closed-canopy interiors to riverbanks, clearings, and park edges. Among available open tools for African forest camera-trap classification, DeepForestVision is the only one providing a matched offline workflow for both photographs and videos, and previous work showed that it outperformed other available baselines on a comparable benchmark. However, it was designed for closed-canopy, ground-level forest interiors and uses a 35-class prediction space that becomes too coarse when deployments encounter arboreal primates, birds, semi-aquatic taxa, or human-associated confounders such as livestock. We present DeepForestVisionV2, an ecology-driven expansion from 35 to 64 prediction classes (61 animal classes plus human, vehicle, and blank) designed to address three recurrent deployment gradients: vertical stratification, scene openness, and anthropogenic interfaces. DeepForestVisionV2 retains the same offline workflow and is trained on 1,535,010 photographs and 243,354 videos from multi-country African tropical-forest projects. Evaluation combines a cross-country cropped-photo validation set, used to assess robustness across sites and camera-trap settings, with three held-out Uganda video benchmarks spanning the targeted gradients. On the validation set, DeepForestVisionV2 reaches 0.86 accuracy, 0.82 macro-F1, and 0.81 balanced accuracy. On the deployment benchmarks, it preserves or improves baseline accuracy despite its harder classification task, while increasing the number of identified taxa from 22 to 29 in forest-interior videos and from 4 to 9 at riverbanks. In the park-edge use case, it raises accuracy from 0.62 to 0.86 and reduces false alarms from 11 to 0. These results show that DeepForestVisionV2 materially improves field utility while preserving robustness across sites, habitats, and camera-trap settings.

17.
arXiv (CS.CL) 2026-06-15

Towards Direct Latent-Space Synthesis for Parallel Branches in LLM-Agent Workflows

Large language models increasingly serve as execution engines for agentic systems, yet they still consume context through a sequential text interface. This creates a mismatch with modern structured agent workflows, in which independent branches explore subtasks, retrieve evidence, or generate candidate solutions before a final synthesis step. Existing systems typically merge these branches by concatenating their textual outputs, which discards the parallel structure and incurs redundant prefill computation. In this work, we introduce Parallel-Synthesis, a plug-and-play framework that enables a synthesizer to directly consume the KV caches produced by parallel worker agents. Parallel-Synthesis combines a cache mapper that calibrates independently generated branch caches with a fine-tuned synthesizer adapter that enables generation from this non-sequential cache interface. We train Parallel-Synthesis using data that exposes the synthesizer to parallel cache contexts, teaches aggregation across cached branches, and distills reasoning behavior from standard text-concatenation-based synthesis. Across nine downstream datasets spanning math, science QA, code generation, GAIA, and multi-agent database diagnosis, Parallel-Synthesis matches or outperforms text-based synthesis on seven datasets and remains close on the other two. It also reduces time-to-first-token by 2.5x-11x, suggesting that direct cache-based synthesis is a promising interface for more native and efficient synthesis over parallel agent branches.

18.
arXiv (quant-ph) 2026-06-16

Conditions for Unitarity in Timeless Quantum Theory

arXiv:2504.01579v3 Announce Type: replace Abstract: Quantum timeless approaches solve the problem of time by recovering the usual unitary evolution of quantum theory relative to a clock in a stationary quantum Universe. For some Hamiltonians of the Universe, such as those including an interaction term with the clock, the dynamics is substantially altered and can be non-unitary. This work derives necessary and sufficient conditions for the relative dynamics to be unitary and finds the general form of the unitary evolution operator. A physical interpretation of these conditions is given in terms of the clock's rate. Unitary dynamics is associated with rates that are constant in time and independent of the clock's internal structure.

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

Protein Design with Agent Rosetta: A Case Study for Specialized Scientific Agents

arXiv:2603.15952v2 Announce Type: replace Abstract: Large language models (LLMs) are capable of emulating reasoning and using tools, creating opportunities for autonomous agents that execute complex scientific tasks. Protein design provides a natural testbed: although machine learning (ML) methods achieve strong results, these are largely restricted to canonical amino acids and narrow objectives, leaving unfilled need for a generalist tool for broad design pipelines. We introduce Agent Rosetta, an LLM agent paired with a structured environment for operating Rosetta, the leading physics-based heteropolymer design software, capable of modeling non-canonical building blocks and geometries. Agent Rosetta iteratively refines designs to achieve user-defined objectives, combining LLM reasoning with Rosetta's generality. We evaluate Agent Rosetta on design with canonical amino acids, matching specialized models and expert baselines, and with non-canonical residues – where ML approaches fail – achieving comparable performance. Critically, prompt engineering alone often fails to generate Rosetta actions, demonstrating that environment design is essential for integrating LLM agents with specialized software. Our results show that properly designed environments enable LLM agents to make scientific software accessible while matching specialized tools and human experts.

20.
arXiv (CS.AI) 2026-06-16

OSGuard: A Benchmark for Safety in Computer-Use Agents

arXiv:2606.15034v1 Announce Type: new Abstract: Computer-use agents are increasingly evaluated by whether they complete realistic desktop and web tasks. However, task success alone can miss failures in which an agent reaches the nominal goal through an unsafe shortcut. We introduce OSGuard, a dual-granularity benchmark suite for evaluating safety in computer-use agents under benign, unchanged user instructions. OSGuard contains an action-level benchmark for local guardrail decisions and a risk-augmented execution suite for end-to-end evaluation. The action-level benchmark consists of contextualized proposed actions labeled as allowed, unrelated, or unsafe, each judged relative to the original instruction and current interface state. The execution suite contains manually constructed OSWorld-derived task variants in which the original task remains achievable, but the environment is modified to introduce latent hazards such as destructive overwrites, etc. Each variant is paired with augmented evaluators that retain the original task-success criterion while adding explicit state-based safety invariants, allowing us to distinguish safe completions from unsafe completions that satisfy the nominal task objective. Our experimental results on OSGuard show that current multimodal guardrails can perform well on isolated action judgments, while risk-augmented execution exposes remaining gaps between local oversight and reliable end-to-end safety. This dual-granularity design enables more precise diagnosis of whether models can both recognize unsafe proposed actions and improve full-task safety when deployed as guardrails.

21.
arXiv (CS.LG) 2026-06-19

The Token Is a Group Element: On Lie-Algebra Attention over Matrix Lie Groups

arXiv:2606.20547v1 Announce Type: new Abstract: We place the attention token on the group: a token is an element $g_i$ of a matrix Lie group $G$ – a bare transformation, with no feature payload and no external action $\rho(g)$ carrying it. To our knowledge this is the first attention construction whose tokens are bare matrix Lie group elements: their score is the closed-form algebra norm of the relative pose rather than a learned kernel, and it reaches the affine full-frame groups that every irrep- or surjective-exp-based method must exclude. We call it Lie-Algebra Attention. Once tokens are group elements, the rest follows with none of the usual representation-theoretic machinery. The relative geometry of a pair is canonical, $g_i^{-1} g_j$, so the pairwise invariant $w_{ij} = \log(g_i^{-1} g_j)$ is intrinsic rather than designed; equivariance under the diagonal $G$-action is tautological, and the cocycle condition holds automatically. The attention score is the negative squared algebra norm, $s_{ij} = -\|\log(g_i^{-1} g_j)\|_\lambda^2/\tau$: the canonical proximity kernel under a block-weighted Frobenius inner product, with no irreducible representations, spherical harmonics, Clebsch-Gordan products, or learned kernel. The construction applies to any matrix Lie group on a chosen logarithm chart containing the relative poses, including the non-compact non-abelian affine groups with scale and shear that no vector-token attention method reaches: neither the irrep tradition nor surjective-exp methods. Three sequence-completion experiments, on SE(2), SO(3), and Aff(2), bear this out: the closed-form score matches a learned MLP kernel on the same invariant and outperforms it on SE(2), using 50 to 80x fewer score parameters, while a vector-token baseline breaks invariance by five to twelve orders of magnitude.

22.
arXiv (quant-ph) 2026-06-19

Mitigating Trotter Errors via Post-Processed Symmetry Restoration

arXiv:2606.20242v1 Announce Type: new Abstract: Quantum simulation is a powerful tool for exploring complex quantum many-body systems such as condensed matter physics and gauge theories. Trotterization, which approximates the ideal time evolution operator by decomposing it into a sequence of local gate operations, is one of the most widely used quantum simulation algorithms. However, such Trotterized implementations generally fail to preserve the symmetries of the target Hamiltonian during compilation. As a result, they can drive quantum states out of symmetrically allowed subspaces, leading to unphysical dynamics and symmetry-violating algorithmic errors. In this work, we propose a symmetry-based Trotter error mitigation protocol using classical post-processing. By applying symmetry transformations to the initial state or interleaving them between discrete Trotter layers, and then averaging an ensemble of the resulting measurement outcomes via classical post-processing, our method systematically projects out the symmetry-violating components of the Trotter error while leaving the ideal dynamics unchanged. Importantly, this framework naturally accommodates non-local spatial symmetries and anti-unitary operations such as time reversal, which are difficult or impossible to implement directly with hardware-native quantum gates. We benchmark our protocol on the one-dimensional XY model and the one-dimensional Schwinger model. In the XY model, enforcing reflection symmetry suppresses the leading-order Trotter error, whereas in the Schwinger model, interleaving gauge transformations between Trotter layers enables gauge-twirling effectively to reduce unphysical violations of local Gauss's law. These results demonstrate that symmetry-based post-processing provides a depth-preserving route to substantially improving the fidelity of Trotterized quantum simulations on near-term devices.

23.
arXiv (CS.AI) 2026-06-19

Too long; didn't solve

arXiv:2604.07593v2 Announce Type: replace Abstract: Mathematical benchmarks consisting of a range of mathematics problems are widely used to evaluate the reasoning abilities of large language models, yet little is known about how their structural properties influence model behaviour. In this work, we investigate two structural length variables, prompt length and solution length, and analyse how they relate to model performance on a newly constructed adversarial dataset of expert-authored mathematics problems. We find that both prompt and solution lengths correlate positively with increased model failure across models. We also include a secondary, exploratory analysis of cross-model disagreement. Under a difficulty-adjusted normalised analysis, both variables retain weak negative associations with realised model separation, slightly stronger for prompt length. Overall, our main robust finding is that structural length is linked to empirical difficulty in this dataset.

24.
arXiv (math.PR) 2026-06-18

Geometric obstructions to Lipschitz transport between weighted Hessian $\mathrm{CD}(\kappa,\infty)$ manifolds

arXiv:2606.11085v2 Announce Type: replace Abstract: We construct a weighted Riemannian manifold $(\mathbb R^2,g,\mu)$ satisfying $\mathrm{CD}(1/2,\infty)$, the curvature-dimension condition, with the following property: if $\gamma$ denotes a centered Gaussian measure on $\mathbb R^2$, then there is no Lipschitz map $T:(\mathbb R^2,\|\cdot\|) \to (\mathbb R^2,g)$ satisfying $T_\#\gamma=\mu$. Building on this, we prove a Weyl-type asymptotic law for the eigenvalues of the weighted Laplacian $-\Delta_{g,\mu}$ and show that they are asymptotically negligible when compared to the eigenvalues of $-\Delta_{\gamma}$. These results give strong counterexamples to two questions of E. Milman and complement the recent counterexample of Aryan.

25.
arXiv (CS.LG) 2026-06-16

A Validated LBM Dataset and Pipeline for Surrogate Modeling of Turbulent 3D Obstructed Channel Flows

arXiv:2606.16765v1 Announce Type: new Abstract: Evaluating neural operators for 3D turbulent flow requires validated datasets with physical benchmarks. We present a reproducible pipeline generating training data for 3D channel flows around generated geometries at Re=1,000-10,000. Our lattice Boltzmann solver with cumulant collision operators is rigorously verified against experimental measurements (Strouhal number, drag coefficients, turbulent fluctuations) with comprehensive grid convergence studies at resolution 1024x512x512. Building upon an established framework, this validated pipeline enables standardized surrogate model comparison. We outline planned systematic evaluation of Fourier Neural Operator and U-Net variants on forecasting, super-resolution, and error correction tasks, using physics-informed metrics to assess turbulent energy cascade representation. Future work will compare computational efficiency between numerical solvers and neural surrogates, exploring practical application. We seek community feedback on our validation approach, planned benchmark methodology, and evaluation priorities for neural operators in turbulent flows.