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01.
arXiv (CS.CL) 2026-06-19

HydraHead: From Head-Level Functional Heterogeneity to Specialized Attention Hybridization

The quadratic complexity of attention poses a critical bottleneck for long-context processing, spurring interest in hybrid attention designs. Most open-source hybrid models adopt a layer-wise strategy. Yet, prior work has noted the inherent difficulty of integrating Linear Attention (LA) with Full Attention (FA), suggesting that the design space of attention hybridization remains underexplored. To probe this space, we conduct interpretability analysis and observe that layers exhibit block-wise functional similarity, while individual heads within the same layer display distinct functional specialization despite sharing input features. This head-level heterogeneity suggests that the head dimension provides a natural and principled granularity for fusing heterogeneous attention signals. Building on this insight, we introduce HydraHead, a novel architecture that hybridizes FA and LA along the head axis. HydraHead features two key innovations: (1) an interpretability-driven selection strategy that identifies retrieval-critical heads and preserves FA only for them, and (2) a scale-normalized fusion module that reconciles the distributional gap between FA and LA head outputs. By leveraging a three-stage transfer pipeline with parameter reuse and distillation, we achieve high-performance hybrid models with minimal training overhead. Under a unified training setup, HydraHead outperforms other hybrid designs in long-context tasks while maintaining strong general reasoning. With interpretability-driven head selection, it matches a 3:1 layer-wise hybrid's long-context performance at a 7:1 LA-to-FA ratio. Crucially, trained on only 15B tokens, HydraHead achieves over 69% improvement over the baseline at 512K context length, approaching Qwen3.5, a leading model of comparable size with a native context length of 256K. This highlights the significant scaling potential of head-level hybridization.

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

Combining Retrieval-Augmented Text Generation with LLMs for Reading Content Recommendations

arXiv:2606.14817v1 Announce Type: cross Abstract: This work presents the design, implementation, and evaluation of a system for generating personalized reading content using Large Language Models (LLMs) combined with Retrieval-Augmented Generation (RAG). The proposed architecture consists of four modules: Input, RAG, Generation, and Judging and enables users to specify both a question and a target reading content complexity. RAG is employed to retrieve relevant information from the Internet, enriching and grounding the content produced by three modern LLMs: Meta LLaMA 4 Scout, LLaMA 3.1 8B Instant, and Google Gemma2 9B. Reading materials are generated using three prompting strategies (Chain-of-Thought, zero-shot, and few-shot), and the LLM-as-a-Judge module automatically evaluates answer quality and alignment with the desired readability level. Experimental results show that RAG consistently improves system performance across all models and prompting techniques, increasing relevance and particularly groundedness by up to 26-35 percentage points. Overall, the findings demonstrate that the RAG-augmented architecture effectively produces reading content tailored to user queries and desired textual complexity.

03.
arXiv (quant-ph) 2026-06-17

Robust Spin Splitting and Strain-Controlled Optical Response in Monolayer CrC2N4 for Valleytronic and Optoelectronic Applications

arXiv:2606.17329v1 Announce Type: cross Abstract: Monolayer CrC2N4 recently emerged as a promising two-dimensional semiconductor, yet its spin-orbit-coupled (SOC) physics and strain-tunable optical response remained largely unexplored. Here, we investigated the electronic, valley, charge-transfer, and optical properties of pristine and biaxially strained monolayer CrC2N4 using first-principles calculations. The monolayer exhibited a direct band gap at the K/K' valleys. SOC produced valley contrasting out-of-plane spin polarization, yielding a moderate valence band spin splitting of 51.9 meV and a small conduction band spin splitting of 1.7 meV. Orbital-resolved analysis showed that the edge states were mainly governed by Cr-d and N-p hybridization, while Bader analysis indicated polar-covalent bonding through charge transfer toward N atoms. Biaxial strain in the range of -4% to +4% tuned the band gap from 1.987 to 1.421 eV and drove an indirect-to-direct gap transition near -1% strain. Tensile strain enhanced the Berry curvature and red-shifted the optical response toward the visible-near-infrared region. These results suggested monolayer CrC2N4 as a promising platform for strain-engineered valleytronic and optoelectronic device applications.

04.
arXiv (CS.CV) 2026-06-15

$\mu_0$: A Scalable 3D Interaction-Trace World Model

World models that capture how actions induce physical change enable scalable robot learning without reliance on embodiment-specific action labels. Pixel-space video models provide broad visual priors but expend model capacity on dense appearance reconstruction, while direct action models require embodiment-specific labels that hinder scalability. We present $\mu_0$, a scalable world model based on 3D traces. Rather than predicting dense pixels or directly modeling actions, $\mu_0$ forecasts smooth 3D trajectories for salient interaction points such as objects, tools, hands, and contact regions, yielding a compact, embodiment-agnostic motion interface. To enable training from diverse video sources, our TraceExtract system automatically extracts 3D supervision by selecting keypoints, constructing globally aligned traces, and associating motion segments with hierarchical language captions. This TraceExtract supervision pretrains $\mu_0$ by combining a pretrained vision-language backbone with a modular trace expert, which represents each query via B-spline control points and predicts future traces. Experiments show that $\mu_0$ outperforms baselines in both 2D and 3D trace prediction, including trace prediction models and tokenized VLM methods. Because $\mu_0$ is frozen and reusable, it can be paired with action experts for downstream robot embodiments. Despite action-free pretraining, the resulting trace-conditioned policies achieve performance competitive with VLA models pretrained with action supervision, such as $\pi_0$. These results establish 3D traces as a scalable and transferable representation for cross-embodiment manipulation.

05.
arXiv (CS.LG) 2026-06-19

Multimodal Concept Bottleneck Models

arXiv:2606.19882v1 Announce Type: cross Abstract: Concept Bottleneck Models (CBMs) enhance the interpretability of deep learning networks by aligning the features extracted from images with natural concepts. However, existing CBMs are constrained in their ability to generalize beyond a fixed set of predefined classes and the risk of non-concept information leakage, where predictive signals outside the intended concepts are inadvertently exploited. In this paper, we propose Multimodal Concept Bottleneck Model (MM-CBM) to address these issues and extend CBMs into CLIP. MM-CBM utilizes dual Concept Bottleneck Layers (CBLs) to align both the image and text embeddings into interpretable features. This allows us to perform new vision tasks like zero-shot classification or image retrieval in an interpretable way. Compared to existing methods, MM-CBM achieves up to 51.26% accuracy improvement on average across four standard benchmarks. Our method maintains high accuracy, staying within ~5% of black-box performance while offering greater interpretability.

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

Online LLM Selection via Constrained Bandits with Time-Varying Demand

arXiv:2606.17489v1 Announce Type: cross Abstract: Large Language Models (LLMs) are increasingly deployed in edge-cloud inference systems to handle diverse user tasks with heterogeneous accuracy, latency, and cost profiles. Selecting the appropriate LLM for each incoming task is critical for ensuring service quality and efficient resource utilization. However, model heterogeneity, stochastic and unknown performance characteristics, and time-varying task demands make static selection strategies inadequate. Real-world deployments often impose hard resource budgets such as monetary expenditure limits, along with soft service-level requirements such as latency guarantees. These constraints introduce additional challenges for online decision-making. We formulate this problem as a constrained stochastic bandit learning task, where the learner sequentially selects models under both packing-type (hard) and covering-type (soft) constraints, while adapting to time-varying task demand. The learner operates without access to the underlying reward, cost, or latency distributions and must rely on partial feedback. We develop a novel online learning algorithm that leverages confidence-bound estimates and demand predictions to balance reward maximization with long-term constraint satisfaction. We provide theoretical guarantees showing sublinear regret and sublinear covering constraint violations compared to an offline benchmark with full information. Experimental results on synthetic workloads demonstrate the effectiveness and robustness of our approach in dynamic, resource-constrained environments.

07.
arXiv (CS.CV) 2026-06-12

Fully Distributed Multi-View 3D Tracking in Real-Time

Multi-camera tracking with overlapping fields of view typically relies on centralized fusion, which creates computational bottlenecks that prevent deployment at scale. We present MV3DT, a fully distributed framework for real-time multi-view 3D tracking that achieves accurate identity propagation and occlusion recovery through peer-to-peer coordination, eliminating the need for central aggregation. Each camera node executes a lightweight modular pipeline comprising monocular 3D perception, distributed multi-view association, and collaborative fusion via lightweight messaging. MV3DT achieves 94.3% IDF1 and 93.3% MOTA on WILDTRACK, competitive with state-of-the-art centralized methods, while demonstrating superior scalability by sustaining 30 FPS on 100 cameras with less than 10 ms inter-camera latency and only 2.2% communication overhead. MV3DT operates in a zero-shot regime given camera calibrations, requiring no scene-specific learning and making it directly deployable in new environments. These results establish MV3DT as a practical solution for real-time multi-view tracking in large-scale overlapping camera networks.

08.
arXiv (CS.AI) 2026-06-11

Rule Taxonomy and Evolution in AI IDEs: A Mining and Survey Study

arXiv:2606.12231v1 Announce Type: cross Abstract: The adoption of AI-powered Integrated Development Environments (AI IDEs) has introduced "Rules" as a novel software artifact, allowing developers to persistently inject project-specific constraints and architectural guidelines into the context of Large Language Models (LLMs). Despite their role in aligning AI behavior with developer intent, the taxonomy, evolution, and practical impact of these rules remain largely unexplored. To bridge this gap, we conducted a mixed-methods empirical study on AI IDE rules. By mining 83 open-source projects and extracting 7,310 rules, we established a comprehensive taxonomy comprising 5 primary and 25 secondary categories. We then triangulated these artifacts with survey responses from 99 practitioners. Our analysis identified a contrast between developer priorities and actual configurations: while practitioners rate architectural constraints as highly important, rule files in repositories primarily consist of low-level workflow and code formatting constraints. Furthermore, our analysis of 1,540 rule evolution events revealed that rules are updated frequently. Repository data further indicate that rule evolution is primarily driven by constructive context expansions (29.17%) and enrichments (26.59%). In contrast, surveyed developers reported modifying rules primarily to correct AI errors (77.78%), typically by adding new negative constraints rather than editing existing ones. Finally, an artifact compliance assessment of 160 rule evolution events revealed that updating rules significantly improves the adherence of software artifacts, with the average artifact compliance rate increasing by 22.99% (from 49.14% to 72.13%) following an update. Our study provides empirical insights that can help developers optimize prompting strategies and guide tool builders in designing automated conflict-detection and context-management mechanisms for AI IDEs.

09.
arXiv (CS.AI) 2026-06-19

PrototypeNAS: Rapid Design of Deep Neural Networks for Microcontroller Units

arXiv:2603.15106v2 Announce Type: replace Abstract: Enabling efficient deep neural network (DNN) inference on edge devices with different hardware constraints is a challenging task that typically requires DNN architectures to be specialized for each device separately. To avoid the huge manual effort, one can use neural architecture search (NAS). However, many existing NAS methods are resource-intensive and time-consuming because they require the training of many different DNNs from scratch. Furthermore, they do not take the resource constraints of the target system into account. To address these shortcomings, we propose PrototypeNAS, a zero-shot NAS method to accelerate and automate the selection, compression, and specialization of DNNs to different target microcontroller units (MCUs). We propose a novel three-step search method that decouples DNN design and specialization from DNN training for a given target platform. First, we present a novel search space that not only cuts out smaller DNNs from a single large architecture, but instead combines the structural optimization of multiple architecture types, as well as optimization of their pruning and quantization configurations. Second, we explore the use of an ensemble of zero-shot proxies during optimization instead of a single one. Third, we propose the use of Hypervolume subset selection to distill DNN architectures from the Pareto front of the multi-objective optimization that represent the most meaningful tradeoffs between accuracy and FLOPs. We evaluate the effectiveness of PrototypeNAS on 12 different datasets in three different tasks: image classification, time series classification, and object detection. Our results demonstrate that PrototypeNAS is able to identify DNN models within minutes that are small enough to be deployed on off-the-shelf MCUs and still achieve accuracies comparable to the performance of large DNN models.

10.
arXiv (CS.LG) 2026-06-15

Equivariant Representation Learning via Class-Pose Decomposition

arXiv:2207.03116v4 Announce Type: replace Abstract: We introduce a general method for learning representations that are equivariant to symmetries of data. Our central idea is to decompose the latent space into an invariant factor and the symmetry group itself. The components semantically correspond to intrinsic data classes and poses respectively. The learner is trained on a loss encouraging equivariance based on supervision from relative symmetry information. The approach is motivated by theoretical results from group theory and guarantees representations that are lossless, interpretable and disentangled. We provide an empirical investigation via experiments involving datasets with a variety of symmetries. Results show that our representations capture the geometry of data and outperform other equivariant representation learning frameworks.

11.
arXiv (CS.AI) 2026-06-16

OmniMouse: Scaling properties of multi-modal, multi-task Brain Models on 150B Neural Tokens

arXiv:2604.18827v2 Announce Type: replace-cross Abstract: Scaling data and artificial neural networks has transformed AI, driving breakthroughs in language and vision. Whether similar principles apply to modeling brain activity remains unclear. Here we leveraged a dataset of 3.1 million neurons from the visual cortex of 73 mice across 323 sessions, totaling more than 150 billion neural tokens recorded during natural movies, images and parametric stimuli, and behavior. We train multi-modal, multi-task models that support three regimes flexibly at test time: neural prediction, behavioral decoding, neural forecasting, or any combination of the three. OmniMouse achieves state-of-the-art performance, outperforming specialized baselines across nearly all evaluation regimes. We find that performance scales reliably with more data, but gains from increasing model size saturate. This inverts the standard AI scaling story: in language and computer vision, massive datasets make parameter scaling the primary driver of progress, whereas in brain modeling – even in the mouse visual cortex, a relatively simple system – models remain data-limited despite vast recordings. The observation of systematic scaling raises the possibility of phase transitions in neural modeling, where larger and richer datasets might unlock qualitatively new capabilities, paralleling the emergent properties seen in large language models. Code available at https://github.com/enigma-brain/omnimouse.

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

DC-Motion: Decoupling Semantics and Details via Discrete-Continuous Tokens for Human Motion Generation

Text-to-motion generation requires synthesizing physically realistic dynamics that strictly follow complex and long-horizon textual instructions. Existing approaches rely on homogeneous representation spaces that may fail to capture the hierarchical nature of human motion, with diffusion models struggling at compositional semantic reasoning and AR models sacrificing fine-grained physical details due to quantization. To solve it, we introduce DC-Motion, a factorized generative framework designed to explicitly decouple semantics and details via discrete-continuous tokens. A Discrete-Continuous VAE (DC-VAE) first decomposes motion into discrete tokens for semantics and continuous residuals for fine-grained dynamics. Then, a masked AR model predicts the discrete structure from text, and a lightweight residual diffusion model recovers the continuous physical details. Extensive experiments demonstrate that DC-Motion effectively improves the capability to follow complex instructions. By effectively balancing semantic controllability and physical realism, our approach offers a highly adaptable modeling paradigm for human motion generation. On both HumanML3D and KIT-ML datasets, DC-Motion achieves state-of-the-art performance, delivering the best FID for motion realism and R-precision for text alignment.

13.
arXiv (CS.AI) 2026-06-12

Mental-R1: Aligning LLM Reasoning for Mental Health Assessment

arXiv:2606.13176v1 Announce Type: new Abstract: Mental health problems such as anxiety, depression, and suicide remain urgent global challenges, where timely and accurate assessment is critical for effective intervention. Recently, large language models have been explored for mental health assessment. However, existing general-purpose post-training methods do not align with the cognitive processes of human assessment, which may lead to unreliable reasoning outcomes. To bridge this gap, we propose Cognitive Relative Policy Optimization (CRPO), a reinforcement learning framework tailored for the mental health domain. CRPO extends group relative policy optimization by integrating stage-dependent uncertainty modeling into the policy optimization process. Specifically, we introduce a stage-wise entropy regularization mechanism that encourages broad exploration in early reasoning phases and progressively enforces confident decision-making in later stages, mimicking the human cognitive shift from uncertainty to certainty. In addition, inspired by cognitive appraisal theory, we formalize cognitive reasoning stages, thereby guiding theory-grounded interpretable inference. Experiments on 8 mental health datasets show that CRPO achieves an average improvement of 10.4 percentage points in weighted F1-score over the best reinforcement learning baseline. Furthermore, the CRPO-trained model Mental-R1 demonstrates clear advantages compared with existing large language models on reasoning-intensive cases, suggesting that CRPO enhances reasoning capabilities for mental health assessment.

14.
arXiv (quant-ph) 2026-06-16

Lattice surgery for near-term experimental logical qubit entanglement creation in planar architectures

arXiv:2606.15190v1 Announce Type: new Abstract: In the era of early fault-tolerant quantum computing, basic demonstrations of entanglement operations between a few logical qubits are at the frontier of recent developments in quantum computing. In this work, we describe in detail, at both the logical and physical qubit levels, a logical teleportation protocol between two surface code logical qubits based on lattice surgery. We address several aspects of the teleportation protocol pertinent to superconducting qubit architectures. We explore the modularity constraints in the number and location of stabilizer readouts and compare variants of the teleportation protocol in this regard. Additionally, we investigate potential performance improvements related to in-sequence decision logic and the optimal size of the interface region between two surface code patches on a superconducting chip. Based on our simulations, we show possible near-term improvements in lattice surgery protocols that facilitate fault-tolerant quantum computing in superconducting circuit architectures.

15.
arXiv (CS.CV) 2026-06-11

SDQM: Synthetic Data Quality Metric for Object Detection Dataset Evaluation

The performance of machine learning models depends heavily on training data. The scarcity of large-scale, well-annotated datasets poses significant challenges in creating robust models. To address this, synthetic data generated through simulations and generative models has emerged as a promising solution, enhancing dataset diversity and improving the performance, reliability, and resilience of models. However, evaluating the quality of this generated data requires an effective metric. We introduce the Synthetic Dataset Quality Metric (SDQM) to assess data quality for object detection tasks without requiring model training to converge. This metric enables more efficient generation and selection of synthetic datasets, addressing a key challenge in resource-constrained object detection tasks. In our experiments, SDQM demonstrated a strong correlation with the mean average precision (mAP) scores of YOLO11, a leading object detection model, whereas previous metrics only exhibited moderate or weak correlations. In addition, it provides actionable insights into improving dataset quality, minimizing the need for costly iterative training. This scalable and efficient metric sets a new standard for evaluating synthetic data. The code for SDQM is available at https://github.com/ayushzenith/SDQM

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

Towards Advanced Mathematical Reasoning for LLMs via First-Order Logic Theorem Proving

Large language models (LLMs) have shown promising first-order logic (FOL) reasoning capabilities with applications in various areas. However, their effectiveness in complex mathematical reasoning involving multi-step FOL deductions is still under-researched. While LLMs perform competitively on established mathematical reasoning benchmarks, they struggle with multi-step FOL tasks, as demonstrated by Deepseek-Prover-V2-7B's low accuracy (4.2%) on our proposed theorem proving dataset. This issue arises from the limited exploration of diverse proof strategies and the potential for early reasoning mistakes to undermine entire proofs. To address these issues, we propose DREAM, a self-adaptive solution that enhances the Diversity and REAsonability of LLMs' generation strategies. DREAM incorporates an Axiom-Driven Strategy Diversification mechanism to promote varied strategic outcomes and a Sub-Proposition Error Feedback to help LLMs reflect on and correct their proofs. Our contributions include pioneering advancements in LLMs' mathematical reasoning through FOL theorem proving, introducing a novel inference stage solution that improves performance by 0.6% to 6.4%, and providing a curated dataset of 447 mathematical theorems in Lean 4 format for evaluation.

17.
arXiv (CS.LG) 2026-06-16

IBAD: Interpretable Behavioral Anomaly Detection on Human Mobility Data

arXiv:2606.16023v1 Announce Type: new Abstract: Human mobility appears highly diverse, yet much of a person's daily mobility can be explained by a small set of recurring behavioral templates, such as commuting, school-centered activities, caregiving, nightlife, or errand patterns. We present \texttt{IBAD} (\underline{I}nterpretable \underline{B}ehavioral \underline{A}nomaly \underline{D}etection), a framework that learns interpretable daily mobility templates and represents each individual as a distribution over mixtures of these templates. Rather than focusing on specific locations, IBAD characterizes activities that individuals perform across locations. This approach first discovers global behavioral templates using Latent Dirichlet Allocation (LDA), then employs a hierarchical self-supervised model to learn normal behavior of individuals from their soft behavioral templates. We also introduce a splicing benchmark that creates controlled behavioral mismatches between an individual's historical profile and injected mobility patterns. Experiments on real-world and synthetic datasets show that daily behavior can be effectively decomposed into a small number of interpretable templates. Crucially, we show that the learned behavioral archetypes transfer across distinct geographic and demographic contexts. Furthermore, IBAD maintains a robust competitive performance across all settings. For reproducibility purposes, the code is accessible at ~\href{https://github.com/USC-InfoLab/IBAD}{https://github.com/USC-InfoLab/IBAD}.

18.
arXiv (CS.CL) 2026-06-18

SFT Overtraining Predicts Rank Inversion via Entropy Collapse Under RLVR

The standard heuristic of selecting the SFT checkpoint with the highest pass@1 for GRPO can fail when SFT compresses the rollout distribution. For binary rewards, the expected within group advantage variance is $p(1{-}p)(g{-}1)/g$; when early GRPO drives $p$ below $p^*(g)$, most groups have identical rewards and provide no group relative signal. We study SFT depth ladders for Qwen2.5-Coder-3B and DeepSeek-Coder-6.7B. We test Qwen2.5-Coder-3B across five depths and three seeds, and DeepSeek-Coder-6.7B across four matched depths and three seeds. On Qwen, pre RL pass@1 rises with SFT depth, but peak GRPO pass@10 falls from $0.806$ to $0.481$ (3 seed mean, $n{=}20$); pre RL entropy is positively associated with the GRPO outcome ($\rho{=}{+}0.69$). On DeepSeek, pass@1 remains far above $p^*(8){=}0.083$, and GRPO outcomes compress rather than invert. A two stage diagnostic, combining pre RL entropy triage with an early GRPO entropy monitor, flags high risk checkpoints and can stop failing runs early. Simple KL to reference regularisation and label smoothing variants do not rescue the collapsed Qwen checkpoint in our setting, suggesting the failure is not a trivial GRPO hyperparameter artefact.

19.
Science (Express) 2026-04-23

Structural N- and O-glycans revealed by high-resolution cryo-EM analysis of tubular mastigonemes | Science

Authors: Unknown Author

The chemical complexity and non-templated biosynthesis of glycans have posed significant challenges for establishing sequence-structure relationships. Here we report cryo-EM structures of tubular mastigonemes from a golden alga species, Ochromonas danica , in which a large number of N- and O-glycans are resolved at 1.8-2.2 Å resolution. Beyond high-mannose and complex N-glycans, we identify a non-canonical N-glycan on the Ala- Asn -Asp (A N D) motif. The surface spikes comprise dense O-glycans coating PSXX tetrapeptide repeats, with two glycans linked on trihydroxylated proline and one on serine per repeat. In addition to various types of sugars and their covalent modifiers, water molecules (>10% of resolved volume) and cations are clearly resolved and mediate the structural assembly. Our study establishes a framework for investigating glycan folding in high-order biological assemblies.

20.
arXiv (CS.AI) 2026-06-11

On the Geometry of On-Policy Distillation

arXiv:2606.07082v2 Announce Type: replace-cross Abstract: On-policy distillation (OPD) is increasingly used to improve large language model reasoning, but its training dynamics remain poorly understood. We characterize the trajectory of OPD updates in parameter space and compare it with supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR). A suite of parameter-space diagnostics consistently places OPD in a relaxed off-principal regime: compared with SFT, its updates affect fewer weights and avoid principal directions more strongly, while compared with RLVR, they remain less tightly constrained. Beyond this static localization, OPD exhibits subspace locking: its cumulative updates rapidly enter a narrow low-dimensional channel. Constraining training to the update subspace formed early in training preserves OPD performance but substantially degrades SFT, indicating that the locked subspace is functionally sufficient for OPD. Control experiments further show that sparsifying the update tokens and shifting rollout generation off-policy preserve the rank dynamics, whereas mixing the OPD objective with RLVR changes them. Overall, these results suggest that OPD is not merely an intermediate point between SFT and RLVR, but induces its own update geometry in parameter space.

21.
arXiv (quant-ph) 2026-06-15

Stab-QRAM: A Clifford-Only Quantum Oracle for Affine Boolean Data

arXiv:2509.26494v3 Announce Type: replace Abstract: Oracle-based quantum algorithms require coherent evaluation of classical functions on superposed inputs, and in fault-tolerant architectures this cost is dominated by non-Clifford gates: generic lookup constructions incur $T$-counts that grow with the data size. Here we show that affine Boolean functions $f(\mathbf{x})=A\mathbf{x}+\mathbf{b}$ over $\mathbb{F}_2$ – the algebraic core of parity checks, linear feedback shift registers, and cipher linear layers – are exactly the functions admitting computational-basis-preserving Clifford oracles, and we develop this correspondence into Stab-QRAM, a compiler mapping a specification $(A,\mathbf{b})$ to an ancilla-free circuit of CNOT and $X$ gates with zero $T$-count. Via K\"{o}nig's edge-coloring theorem, the compiled schedule provably attains the minimum depth for its gate set. Case studies spanning Simon-type oracles, block-encodings of $X$-type coset operators, and syndrome extraction for CSS codes show one compiler serving the algorithm, primitive, and error-correction layers of the quantum stack.

22.
arXiv (CS.LG) 2026-06-16

Probabilistic Signature Inversion: Learning Conditional Distributions from Truncated Signatures

arXiv:2606.15332v1 Announce Type: new Abstract: The signature transform is a principled feature map for continuous-time paths, valued for its uniqueness and universality. Recovering a path from its truncated signature is, however, structurally ill-posed because the truncated signature map is not injective. We therefore reframe truncated signature inversion as a probabilistic problem – learning the conditional distribution of a path given its truncated signature – and adopt a signature-conditioned flow matching model as a practical estimator. This probabilistic formulation elucidates the fundamental difficulty of inversion: Bayes reconstruction error quantifies the irreducible uncertainty remaining after conditioning on a statistic. We derive the Bayes-optimal error under linear statistics, obtaining a closed form for log-GBM and numerically tractable formulas for log-fBM and OU, yielding a concrete theoretical baseline for model validation. This baseline upper-bounds the Bayes error under truncated-signature conditioning, since truncated signatures provide richer information than linear statistics. Experiments show that empirical reconstruction errors under linear-statistics conditioning faithfully align with the theory-derived baseline, while errors decrease when the statistic is replaced with truncated signatures. Moreover, generated paths faithfully recover the conditioning signature while preserving key distributional and temporal structures, indicating that the estimator is well-calibrated to the target conditional distribution. Together, these results establish a well-posed probabilistic framework for truncated-signature inversion, with applicability demonstrated on real financial data beyond the parametric process families covered by theory.

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

From Correspondence to Actions: Human-Like Multi-Image Spatial Reasoning in Multi-modal Large Language Models

While multimodal large language models (MLLMs) have made substantial progress in single-image spatial reasoning, multi-image spatial reasoning, which requires integration of information from multiple viewpoints, remains challenging. Cognitive studies suggest that humans address such tasks through two mechanisms: cross-view correspondence, which identifies regions across different views that correspond to the same physical locations, and stepwise viewpoint transformation, which composes relative viewpoint changes sequentially. However, existing studies incorporate these mechanisms only partially and often implicitly, without explicit supervision for both. We propose Human-Aware Training for Cross-view correspondence and viewpoint cHange (HATCH), a training framework with two complementary objectives: (1) Patch-Level Spatial Alignment, which encourages patch representations to align across views for spatially corresponding regions, and (2) Action-then-Answer Reasoning, which requires the model to generate explicit viewpoint transition actions before predicting the final answer. Experiments on three benchmarks demonstrate that HATCH consistently outperforms baselines of comparable size by a clear margin and achieves competitive results against much larger models, while preserving single-image reasoning capabilities.

25.
Nature (Science) 2026-06-10

Gene ancestries reveal diverse microbial associations during eukaryogenesis

The origin of eukaryotes remains a central enigma in biology1. Continuing debates agree on the pivotal role of a symbiosis between an alphaproteobacterium and an Asgard archaeon2,3. However, the nature, timing and contributions of other potential bacterial partners4–6 and the role of interactions with viruses7–9 remain contentious. To address these questions, we used advanced phylogenomic approaches and comprehensive datasets spanning the known diversity of cellular life and viruses. Our analysis provided a revised reconstruction of the last eukaryotic common ancestor (LECA) proteome, in which we traced the phylogenetic origin of each protein family. We found compelling evidence for multiple waves of horizontal gene transfer from diverse bacterial donors, with some likely to have preceded mitochondrial endosymbiosis. We inferred plausible traits of the major donors and their functional contributions to the LECA. Our findings support a contribution of horizontal gene transfers to shaping the proteomes of pre-LECA ancestors and suggest a facilitating role of Nucleocytoviricota viruses. Taken together, our results suggest that ancient eukaryotes may have originated within complex microbial ecosystems through a succession of diverse associations that left a footprint of horizontally transferred genes. Phylogenomic reconstruction of the proteome of the last eukaryotic common ancestor sheds light on the origin of eukaryotes, indicating an important role of horizontal transfer of genes from diverse bacterial and viral donors.