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01.
bioRxiv (Bioinfo) 2026-06-10

HOMED enables hierarchical and multimodal optimization of DNA methylation deconvolution across tissues

Cellular heterogeneity is a major confounder in bulk DNA methylation data for epigenome-wide association studies. Existing reference-based DNAm deconvolution methods often ignore hierarchies among related cell types and may generalize poorly across datasets due to limited variability in reference profiles. We developed HOMED (Hierarchically Optimized Methylation Deconvolution), a framework that integrates cell-lineage hierarchies, single-cell RNA sequencing-guided deconvolution, and paired bulk RNA-seq/DNAm data for CpG signature optimization. Across simulated and real peripheral blood mononuclear cell, lung, and placental datasets, HOMED consistently yielded the highest PCCs and lowest RMSEs, outperforming existing scRNA-seq-guided DNAm deconvolution methods, improving accuracy, resolution, and cross-tissue generalizability.

02.
arXiv (CS.CV) 2026-06-11

i1: A Simple and Fully Open Recipe for Strong Text-to-Image Models

Diffusion models have consistently driven progress in text-to-image generation. However, it is challenging to attribute recent progress to specific modeling and data choices: state-of-the-art open-weight models provide limited ablations, and do not disclose their training data and full training details. The research community needs fully open (weights, data, and code) models as a foundation for further research; yet existing fully open models still fall significantly short of leading models in performance. In this project, we conduct a systematic investigation of the modeling and data design choices in text-to-image diffusion training and inference with 300+ controlled experiments totaling 700K+ TPU v6e hours. Our experiments highlight several empirical findings (e.g., equal weighting is a strong default for mixing curated datasets) and simple design decisions (e.g., larger text encoder adapters improve performance with minimal added parameters) for training strong models. Guided by these insights, we train i1, a 3B-parameter text-to-image diffusion model using only publicly available datasets. i1 is competitive with leading models on five representative benchmarks (GenEval, DPG, PRISM, CVTG-2K, and LongText), and outperforms the best existing fully open model by 29.5 absolute percentage points on average. We provide the i1 checkpoints, training and inference code, and the data processing pipeline. Together, our findings and the i1 recipe establish a practical foundation for future open research in text-to-image diffusion models. Our code is available at https://github.com/zlab-princeton/i1.

03.
arXiv (quant-ph) 2026-06-12

Non-Hermitian skin effect induced by spatial noncommutativity

arXiv:2606.12961v1 Announce Type: new Abstract: In all known schemes for the non-Hermitian skin effect, the non-Hermitian ingredient that drives the skin localization, whether asymmetric hopping or gain and loss, is invariably introduced by hand as an independent model parameter along the skin direction. Here we show that when two spatial coordinates do not commute, the skin effect can break free of this paradigm: a gain-loss potential applied along one coordinate automatically generates non-reciprocity along the other through the coordinate noncommutativity, driving all eigenstates to pile up exponentially at a boundary. We term this phenomenon the noncommutative skin effect. The inverse skin length is proportional to the noncommutativity parameter and is given by an analytic formula, exact in the thermodynamic limit and verified by exact diagonalization of lattice models; the reflection symmetry of the imaginary potential furnishes an exact criterion for the presence or absence of the effect, valid rigorously for finite-size systems. For a sinusoidal imaginary potential, the skin direction of all eigenstates flips collectively at parameter points fixed purely by geometry. Because the flip point is independent of the potential strength, the reversal constitutes a zero-crossing measurement scheme intrinsically robust against systematic errors, from which the noncommutativity parameter can be extracted directly. The qualitative transition of the eigenstates from uniform to exponentially localized renders the effect a nonperturbative probe of spatial noncommutativity, and the Peierls-phase structure of its lattice model is in principle accessible to cold-atom synthetic dimensions, photonic resonators, and topolectrical circuits.

04.
arXiv (CS.CV) 2026-06-24

Agentic Collaborative Cognition for Zero-Shot 3D Understanding

Recent advancements have explored agentic zero-shot 3D understanding by reformulating it as video keyframe understanding with Multimodal Large Language Models (MLLMs). However, existing methods face an intrinsic bottleneck due to the finite observation perspectives inherent in videos and the implicit perception of 3D scenes. In this paper, we propose a collaborative multi-agent framework that assigns a Planning Agent to handle high-level viewpoint planning and supplement novel perspectives, and a Perception Agent to explicitly summarize the 3D scene into a structured holistic cognitive map. Specifically, Planning Agent first analyzes this cognitive map to determine query-relevant viewpoints and supplements missing critical perspectives to ensure comprehensive observation. Subsequently, Perception Agent documents object-level attributes from these views by assigning consistent instance identifiers across viewpoints, thereby integrating fragmented observations into the holistic cognitive map. In parallel, it provides feedback to filter out mismatched candidate objects and guide subsequent viewpoint planning. Through this closed-loop iterative process, two agents collaboratively figure out candidates until Perception Agent determines that sufficient information has been captured to complete the task. Extensive experiments demonstrate that our method achieves state-of-the-art performance on 6 benchmarks, with improvements of 11.1\% Acc@0.5 on ScanRefer, 14.6 BLEU-1 on 3D-assisted dialog, and 2.1 EM on SQA3D.

05.
arXiv (CS.AI) 2026-06-11

DecompSR: A dataset for decomposed analyses of compositional multihop spatial reasoning

arXiv:2511.02627v3 Announce Type: replace Abstract: We introduce DecompSR, decomposed spatial reasoning, a large benchmark dataset (over 5m datapoints) and generation framework designed to analyse compositional spatial reasoning ability. The generation of DecompSR allows users to independently vary several aspects of compositionality, namely: productivity (reasoning depth), substitutivity (entity and linguistic variability), overgeneralisation (input order, distractors) and systematicity (novel linguistic elements). DecompSR is built procedurally in a manner which makes it is correct by construction, which is independently verified using a symbolic solver to guarantee the correctness of the dataset. DecompSR is comprehensively benchmarked across a host of Large Language Models (LLMs) where we show that LLMs struggle with productive and systematic generalisation in spatial reasoning tasks whereas they are more robust to linguistic variation. DecompSR provides a provably correct and rigorous benchmarking dataset with a novel ability to independently vary the degrees of several key aspects of compositionality, allowing for robust and fine-grained probing of the compositional reasoning abilities of LLMs.

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

Exploring Feature Extraction Technique Parameters for Acoustic Gunshot Classification

arXiv:2606.19568v1 Announce Type: cross Abstract: Acoustic gunshot detection is a problem with applications across civilian public safety, military operations, and wildlife conservation, yet the field lacks a rigorous exploration of feature extraction techniques with a focus on generalization to realistic data. The mixed effectiveness of commercial gunshot detection and classification systems indicates an open problem that is not adequately addressed by the current literature. In this paper, we present a systematic investigation of common feature extraction techniques using a dataset of 23,000 gunshot recordings across 85 firearms and 21 calibers. We benchmark three feature extraction techniques with 12 total unique parameter sets using ResNet-18. Our results demonstrate that using the correct feature extraction technique can improve top-1 accuracy by up to 20%, and utilizing the correct parameters for a given feature extraction technique can improve that value by up to 4.7%.

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

MP3: Multi-Period Pattern Pre-training forSpatio-Temporal Forecasting

arXiv:2606.13119v1 Announce Type: cross Abstract: Spatio-Temporal forecasting is crucial in diverse fields, such as transportation, climate, and energy. Urban spatio-temporal data exhibits temporal mirage: similar short-window inputs have divergent future trends, and vice versa. Existing spatio-temporal graph neural networks (STGNNs) cannot effectively identify such mirages. We argue that the core reason lies in the short-window inputs that have incomplete period observation, heterogeneous global spatial correlation, and cross-period superposition causality. To bridge this gap, we develop a novel Multi- Period Pattern Pre-training (MP3), a plug-and-play pre-training plugin for distinguishing temporal mirages. MP3 presents two core innovations: (1) The multi-period pattern learning is designed to learn multi-period patterns from long time series. Specifically, multi-period temporal modeling leverages edge convolution to identify different multi-period patterns. Multi-period spatial modeling uses a bottleneck project and a global memory bank to capture heterogeneous global spatial relations efficiently. Cross-period pattern interaction employs a causality-enhanced Transformer to capture dependencies across different period patterns. (2) This plugin can seamlessly integrate into existing STGNN backbones to strengthen their forecasting performance. The experiment on five STGNN baselines across five real-world datasets (including a large-scale dataset CA) verify the effectiveness, superior scalability and strong adaptability of MP3, which brings consistent and robust performance improvements across all evaluated baselines. On average, MP3 reduces the MAE 4.7% and the RMSE 5.0%. The code can be available at https://github.com/YAN-outlook/MP3.

08.
arXiv (quant-ph) 2026-06-24

Spectrally engineered collinear type-0 SPDC source with enhanced spectral brightness for entanglement distribution

arXiv:2606.24036v1 Announce Type: new Abstract: Entangled photon sources with high spectral brightness are important resources for photonic quantum information processing, particularly in quantum communication and quantum networking where usable photon flux of entangled photons is often constrained by channel loss and source inefficiency. Here, we demonstrate a spectrally engineered type-0 spontaneous parametric down-conversion (SPDC) source with enhanced spectral brightness for entanglement distribution. By pumping a 30-mm ppKTP crystal with an ultra-narrowband laser slightly detuned from degeneracy, photon-pair generation is concentrated into a narrow spectral bandwidth while retaining the strong nonlinear interaction of type-0 phase matching. The source produces a coincidence rate of 44.6 kHz corresponding to a detected spectral brightness of 0.507 MHz/mW/nm. We further integrate the source into a Sagnac interferometer to generate polarization-entangled photon pairs and demonstrate entanglement distribution through a 2.56 km free-space round-trip channel. Our results show that spectral engineering provides a practical route to compact, spectrally bright entangled-photon sources for quantum communication applications.

09.
arXiv (CS.LG) 2026-06-16

PhysGuard: Fisher-Guided Gradient Projection for Sim-to-Real Neural PDE Surrogates

arXiv:2606.16602v1 Announce Type: new Abstract: Neural operator models trained on simulation data often lose accuracy when applied to experimental measurements due to the sim-to-real gap. Standard fine-tuning with limited real data can reduce this gap, but it may also damage the core physics-relevant representations learned during pretraining. Although knowledge-preserving adaptation has been widely investigated in vision or language tasks, it remains unclear whether these methods are suitable for neural operators whose architectures and protected knowledge are fundamentally different. Neural operators need to preserve core-scale physical structures rather than semantic or visual features. We propose PhysGuard, a physics-preserving framework for accurate sim-to-real adaptation of neural operators. Specifically, PhysGuard uses the empirical Fisher Information Matrix computed on simulation data to identify physics-critical parameter directions, then restricts fine-tuning updates to directions that do not interfere with them. A layer-wise Gram-matrix formulation makes this efficient for models with millions of parameters, while an adaptive threshold automatically determines the protected subspace size. A spectral probe experiment shows that the dominant Fisher directions are strongly associated with low-frequency output structures. Experiments on benchmark across four neural operator architectures and different physical systems show that PhysGuard performs strongly on most evaluation metrics compared to baselines. The benefits are most evident under severe domain shift, where it reduces low-frequency error by up to 32\% compared to standard fine-tuning while maintaining adaptability. Our code is available at https://github.com/ZhouChaunge/PhysGuard.

10.
arXiv (math.PR) 2026-06-17

Limit theorems for descents and inversions of shelf-shuffles

arXiv:2510.00343v2 Announce Type: replace Abstract: We prove central limit theorems for the number of descents and inversions of permutations produced by shelf-shuffles. These are a model for casino card shuffling machines. We show the asymptotic normality of the number of descents in two limiting regimes depending on the ratio of cards to shelves. On the other hand, we study the inversions by employing a modification of the techniques from Islak's analysis of the statistics of riffle shuffles. In particular, we obtain a bound for the rate of convergence for inversions that is independent of the number of shelves.

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

Physics-conforming Latent Twins

arXiv:2606.15053v1 Announce Type: new Abstract: Surrogate models are central to scientific machine learning, where they enable fast prediction, simulation, inference, and control for complex physical systems. For time-dependent problems, however, accurate interpolation of training trajectories is not sufficient: reliable surrogates should also respect the conservation laws, invariants, admissibility conditions, and dissipative structures that give those trajectories physical meaning. We introduce Physics-conforming Latent Twins, a framework for learning latent surrogate solution operators whose dynamics satisfy selected physical principles by design. The method builds on the Latent Twin formulation by jointly learning an encoder, a decoder, and a latent flow map between arbitrary time-indexed states, while constraining the latent dynamics to preserve or dissipate prescribed structural quantities. We develop a constraint-transfer viewpoint that connects physical structure in the original state space with compatible constraints in latent space, and prove structure-preservation bounds showing how latent enforcement improves control of physical defects after decoding. We also derive algebraic conditions for latent flow maps that preserve linear and quadratic invariants or enforce dissipative inequalities. Numerical experiments on representative ODE and PDE benchmarks demonstrate improved constraint satisfaction, structural fidelity, and qualitative long-time behavior while maintaining accurate surrogate prediction.

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

Clipping Makes Distributed and Federated Asynchronous SGD Robust to Stragglers

arXiv:2606.13287v1 Announce Type: new Abstract: In modern machine learning, parallelization of training is an important strategy for increasing scale. Asynchronous stochastic gradient descent (ASGD), which maximizes the utilization of available hardware by avoiding waiting for slow workers. However, with constant step sizes, the convergence of ASGD is nonetheless affected negatively by slow workers due to large delays in updates. At the same time, it has been empirically observed in asynchronous training of deep learning models that gradient clipping "stabilizes" training. In this work, we provide a theoretical justification for this behavior, as we show that clipping removes the dependence of the maximum delay in the oracle complexity. We employ a sub-Weibull model of gradient noise which generalizes sub-Gaussian and sub-exponential distributions to more heavy-tailed distributions, motivated by empirical observations in deep learning. We show convergence in expectation, and the first time in asynchronous optimization, convergence with high probability.

13.
medRxiv (Medicine) 2026-06-19

Rumination as a cognitive vulnerability factor in perinatal bereavement: evidence from the CARING study

Purpose. Perinatal loss is associated with a high risk of persistent psychological distress, including prolonged grief, depression, anxiety, and post-traumatic stress symptoms. Cognitive processes such as rumination may play a crucial role in maintaining and amplifying distress following loss, yet their specific contribution in perinatal bereavement remains underexplored. Methods. The CARING (Cognitive Analysis and Rumination INvestigation in perinatal Grief) study employed a cross-sectional design involving 298 parents who experienced perinatal loss within the previous five years. Participants completed an anonymous online survey including measures of depressive rumination (Ruminative Response Scale, RRS), angry rumination (Anger Rumination Scale, ARS), perinatal grief (Perinatal Grief Scale, PGS), general psychopathology (SCL-90), and post-traumatic stress symptoms (NSESSS). Non-parametric analyses were conducted to examine associations between rumination patterns and psychological outcomes. Results. Higher levels of rumination were significantly associated with greater perinatal grief, depressive and anxiety symptoms, and post-traumatic stress. Depressive rumination showed consistently stronger associations with all outcomes compared to angry rumination. Participants presenting both depressive and angry rumination exhibited the highest levels of grief intensity, psychological distress, and PTSD symptoms, suggesting a graded relationship between rumination patterns and severity of distress. Rumination levels were not significantly associated with gestational age at loss or with having received psychological support. Conclusions. Rumination, particularly in its depressive form, appears to function as a transdiagnostic cognitive vulnerability factor in perinatal bereavement. These findings highlight rumination as a potential target for early screening and tailored psychological interventions aimed at reducing long-term distress following perinatal loss.

14.
arXiv (CS.CV) 2026-06-12

Language-Guided Abstraction for Visual Reasoning

The Abstraction and Reasoning Corpus (ARC) is viewed as a critical avenue to Artificial General Intelligence (AGI), as it enables models to learn abstract transformation rules from few-shot examples and then generalize to new tasks. However, prevalent ARC methodology is either pure language or vision-only (i.e., VARC). The former depends heavily on LLMs, consuming billions of parameters. The latter often struggles to capture high-level semantics, leading to overfitting on pixel-level patterns. To bridge this gap, we propose L-VARC, a novel framework that enhances visual reasoning via a language-guided Learning Using Privileged Information (LUPI) branch. Specifically, we design a Semantic Compression Module by feeding a unified, task-agnostic prompt into DeepSeek-V3. In this way, the raw LARC (a crowd-sourced language description dataset) can be substantially refined and structured, fitting with the context length constraint of standard text encoders (e.g., CLIP). Moreover, we design a Cross-Attention Projector to align visual features with semantic embeddings, aiming to guide the training of the ARC model. Notably, the LUPI branch is taken in the training process and will be discarded during inference, thereby yielding a lightweight model with a mere 18 million parameters. Extensive experiments demonstrate that our L-VARC effectively leverages linguistic priors to boost visual reasoning and outperforms state-of-the-art. Ablation studies further confirm the contribution of the two new designs towards the L-VARC framework. The code is available at https://github.com/GZHU-DVL/L-VARC.

15.
arXiv (quant-ph) 2026-06-16

Quantum Illumination with Symmetry-Constrained Random Unitaries

arXiv:2606.15586v1 Announce Type: new Abstract: Quantum illumination provides a quantum advantage in detecting weakly reflecting objects embedded in a noisy environment, even when environmental noise destroys most of the initial entanglement. We investigate this advantage using Haar-random probe states constrained to symmetry-resolved subspaces. Employing tools from quantum channel discrimination and asymptotic hypothesis testing, we derive the discrimination exponents associated with Haar-random probe ensembles and identify the role of symmetry in determining their performance. We show that typical states drawn from fixed-charge sectors achieve the same asymptotic quantum-illumination advantage as maximally entangled probes. In particular, we show that the effective thermal-noise suppression and the corresponding Chernoff exponent are governed by the dimension of the accessible symmetry sector. Our results reveal that the operational resource underlying quantum illumination can be generalized from fine-tuned structure of a specific probe state to the existence of a large symmetry-protected correlation subspace. These findings establish a direct connection between quantum illumination, symmetry-resolved typicality, and quantum channel discrimination, and demonstrate that near-optimal quantum hypothesis testing resources can emerge naturally from generic many-body quantum states constrained by conservation laws.

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

Latent Visual States for Efficient Multimodal Reasoning

The integration of visual evidence has significantly enhanced the capabilities of large multimodal models. However, this integration predominantly relies on generating discrete outputs (etc., code or box coordinates) to invoke external tools, a process that introduces rigid dependencies and substantial latency. To overcome these limitations, we propose {EVA} (LatEnt Visual StAtes), a novel framework that natively generates continuous latent visual representations. These internal representations manifest as an adaptive sequence of Latent\_slot tokens, serving as intermediate visual thoughts during the reasoning process. These Latent\_slot tokens are then trained end-to-end with the discrete text tokens. This co-optimization, notably, causes extreme policy deviation in the 'transition window' following the Latent\_slot tokens. We develop D-GSPO (Decouple-GSPO) to target this root cause by decoupling the optimization of latent and discrete components. To support SFT, we construct EVA-230K, a high-quality text-image interleaved CoT dataset encompassing a diverse range of real-world scenes, documents, charts and OCR tasks. Extensive experiments across multiple benchmarks confirm that EVA achieves significant performance gains while enhancing inference efficiency.

17.
arXiv (quant-ph) 2026-06-11

An Introduction to the Foundations and Interpretations of Quantum Mechanics

arXiv:2603.09818v2 Announce Type: replace Abstract: This article surveys a selection of key conceptual and interpretational developments in quantum mechanics, tracing the theory from its foundational postulates to contemporary discussions of measurement, nonlocality, and the emergence of classicality. Beginning with the structure of Hilbert space and the postulates governing state evolution and measurement, the epistemic stance of the Copenhagen interpretation and its modern reformulations are examined. The Einstein-Podolsky-Rosen argument, Bell's theorem, and Hardy's paradox are then discussed as probes of locality and realism, alongside the deterministic but explicitly nonlocal de Broglie-Bohm theory. The measurement problem and the implications of contextuality are analyzed in relation to objective collapse models, which introduce new physical dynamics to account for definite outcomes. Finally, the role of decoherence in the suppression of interference and the emergence of classical behavior is explored, together with the interpretational frameworks of many-worlds and consistent histories. This material aims to provide a coherent introductory overview of how several of the most prominent interpretations address the central concern of what quantum mechanics tells us about the nature of physical reality.

18.
arXiv (CS.LG) 2026-06-15

Smoothing Dark Areas in Molecular Latent Diffusion

arXiv:2606.13955v1 Announce Type: new Abstract: Latent diffusion is a promising framework for scalable 3D molecular generation, but it requires a latent space that remains smooth, valid, and navigable beyond posterior samples. Existing molecular VAEs, however, are typically learned through reconstruction-based objectives, which do not guarantee such a latent space. We show that this leads to dark areas: regions of latent space that are reachable during diffusion sampling but decode to disconnected or chemically invalid molecules. Unlike in image generation, molecular decoding requires strict structural and chemical precision, so even small latent perturbations can produce catastrophic failures. We therefore propose TopVAE, a topology-optimized VAE that reduces dark areas by making the decoder internalize structural and chemical constraints during training, eliminating the need for test-time chemical correction. TopVAE greatly improves off-posterior robustness, and when paired with a standard DiT, achieves $77\%$ lower FCD-3D on QM9, the highest V&C, $52\%$ lower FCD-3D on GEOM-Drugs, and $1.29{\times}$ more stable and connected molecules on zero-shot scaffold inpainting.

19.
arXiv (CS.LG) 2026-06-17

Edge Flow: A Tractable and Predictive Continuous-Time Model for Gradient Descent at the Edge of Stability

Authors:

arXiv:2606.18080v1 Announce Type: new Abstract: Gradient descent in deep learning may operate at the edge of stability (EoS), a regime in which the largest eigenvalue of the loss Hessian hovers near the stability threshold $2/\eta$, where $\eta$ is the learning rate. Classical analysis tools such as gradient flow and the descent lemma do not apply here, motivating the search for a continuous-time model valid at EoS. We propose Edge Flow, a system of three coupled ordinary differential equations that provides a tractable, faithful, and predictive model of gradient descent dynamics at EoS. Edge Flow decomposes the dynamics into a center, an oscillation direction, and an oscillation magnitude. The center follows a modified gradient flow on a symmetrized loss; the direction tracks a top eigenvector of the Hessian via Rayleigh quotient dynamics; and the magnitude grows or decays exponentially depending on whether the sharpness exceeds or falls below the threshold $2/\eta$. Crucially, sharpness stabilization emerges from the coupled dynamics via a self-stabilization feedback loop. Discretizing Edge Flow only requires two gradient evaluations and one Hessian–vector product at each iteration. We demonstrate empirically that Edge Flow tracks the dynamics of gradient descent at least as faithfully as previously proposed continuous-time EoS models, while in addition resolving the oscillation of the sharpness at the onset of EoS, and that it provides a principled framework for understanding and mitigating instabilities in this regime.

20.
arXiv (CS.CV) 2026-06-19

HY-WU (Part I): An Extensible Functional Neural Memory Framework and An Instantiation in Text-Guided Image Editing

Foundation models are transitioning from offline predictors to deployed systems expected to operate over long time horizons. In real deployments, objectives are not fixed: domains drift, user preferences evolve, and new tasks appear after the model has shipped. This elevates continual learning and instant personalization from optional features to core architectural requirements. Yet most adaptation pipelines still follow a static weight paradigm: after training (or after any adaptation step), inference executes a single parameter vector regardless of user intent, domain, or instance-specific constraints. This treats the trained or adapted model as a single point in parameter space. In heterogeneous and continually evolving regimes, distinct objectives can induce separated feasible regions over parameters, forcing any single shared update into compromise, interference, or overspecialization. As a result, continual learning and personalization are often implemented as repeated overwriting of shared weights, risking degradation of previously learned behaviors. We propose HY-WU (Weight Unleashing), a memory-first adaptation framework that shifts adaptation pressure away from overwriting a single shared parameter point. HY-WU implements functional (operator-level) memory as a neural module: a generator that synthesizes weight updates on-the-fly from the instance condition, yielding instance-specific operators without test-time optimization.

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

Leverage Is Not Reach: A Control-Window Law for Single-Neuron Steering in Language Models

Authors:

Aligned language models gate behaviors such as refusal and language routing through sparse feed forward neurons, yet no theory predicts when a single neuron intervention controls a behavior coherently rather than collapsing the output. We develop a budget normalized control window framework for single neuron steering. A dose along one write direction reduces to one control coordinate: the alignment between the residual stream and the write, driven along a universal saturation curve in units of a coherence budget set by the residual norm divided by the write norm. Coherent control exists when a behavior trigger lies below the collapse ceiling. The same coordinate governs benign mode switches and refusal; the ceiling follows from weights and one generic forward pass, while triggers are measured at rollout. On fifteen held out neurons, the predicted ceiling has mean absolute error 0.14, about 0.07 in bulk layers, and the committed open or closed verdict holds on eleven against a ten of fifteen majority baseline. Closed cases expose three failure modes rather than violations: collapse before trigger, too little depth to propagate, or a normalization that caps how far one neuron can push. The law explains why local gradient attribution anti predicts control: true controllers write off the readout axis and carry a near zero first order gradient. A forward only contrastive screen made precise by the window recovers controllers that attribution misses. On refusal, the hardest case, intervention success is typed, not scalar: coherent bypass and strict actionable reach separate, so a neuron can flip refusal in fluent, on task text with no actionable content, and genuine actionable reach appears only for three of six audited Llama pivots and only at later rollout horizons. Single neuron steering is therefore a budgeted, typed audit of controllability rather than a fixed dose anecdote.

22.
arXiv (quant-ph) 2026-06-24

Perfect State Transfer on Quotient Graphs in Shunt Decomposition-Based Quantum Walks

arXiv:2606.24440v1 Announce Type: cross Abstract: This paper investigates perfect state transfer (PST) in discrete-time quantum walks constructed via the shunt decomposition method. The walks are defined on a graph $G$ and its associated quotient graph $G/\pi$, induced by an equitable partition $\pi$. Through the shunt decomposition of $G$, we derive an explicit relation between the shift operator of the parent graph $G$ and that of its quotient graph $G/\pi$. We construct a reflection operator based on the characteristic matrix, which establishes a connection between the transition operator of the parent graph and that of its lower-dimensional quotient graph. We then prove that PST occurs on $G$ if and only if it occurs on $G/\pi$. Furthermore, we express the unitary evolution operator of the quotient graph in terms of Chebyshev polynomials of the first kind, from which we derive explicit criteria for PST. As an application, we establish PST on the cycle graph $C_{n}$ at time $k = n/2$, and lift the result to the parent graph $C_{2n}$ via the equitable partition $\pi$. We further show that if an equitable partition $\pi$ of $G$ induces a quotient isomorphic to $K_n^{\circlearrowleft}$, the complete digraph on $n$ vertices with a loop at every vertex, then PST occurs at step $k = n$, and the walk is periodic at $k = 2n$. This framework is applied to two families of graphs, which are the complete bipartite digraph $K_{n,n}^{\rightleftharpoons}$ and the circulant graph $\operatorname{Circ}(2n, S)$, where $S$ consists of all odd residues modulo $2n$ and $n = 2^s$ for some $s \geq 1$, establishing PST in their respective line digraphs. Collectively, these results also answer the question posed by Godsil and Zhan concerning which shunt decompositions or embeddings of a graph admit PST.

23.
arXiv (quant-ph) 2026-06-11

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data

arXiv:2601.13467v2 Announce Type: replace Abstract: Using the spinless Haldane model, we study the witness-filtered Berry curvature, quantum geometric tensor, and quantum Fisher information on the gapped strata of the parameter space and evaluate them through the Fukui-Hatsugai-Suzuki discretization. The filtered quantities isolate the part of the geometric response carried by sublattice coherence: they suppress contributions from regions where the occupied Bloch state is locally A/B-separable and emphasize regions where curvature and coherence coexist. We derive exact lattice identities, reconstruction formulas for the curvature-weighted coherence, and bounds relating the filtered quantum geometric tensor and quantum Fisher information to single-particle mode entanglement. Across the gap-closing stratum, the quantized response changes admit a natural description in terms of Hecke modifications. We elicit a corresponding Langlands viewpoint – not as a full correspondence, but as an organizational principle and as the mathematical shadow of these physical geometric constructions.

24.
arXiv (CS.CV) 2026-06-19

DiffMath: Symbol- and Graph-Aware Latent Diffusion Transformer for Handwritten Mathematical Expression Generation

Handwritten Mathematical Expression Generation (HMEG) is challenging due to the complex two-dimensional layouts and long-range structural dependencies of mathematical expressions. Existing methods typically rely on explicit spatial supervision, such as symbol-level bounding boxes, which incurs high annotation costs and limits scalability. In this work, we propose DiffMath, a symbol- and graph-aware latent diffusion framework that leverages the hierarchical structure inherent in LaTeX as a structural prior, eliminating the need for positional supervision. First, we design a Relational Abstract Syntax Tree (RelAST), a generation-oriented representation that distills MathML trees into compact triplet sequences [S, R, D], where each token directly encodes a symbol identity, spatial relation, or nesting depth. Second, we introduce MathVAE, which learns structure-preserving latent representations through symbol-aware and relation-aware perceptual regularization, ensuring that the latent space captures both character semantics and spatial topology. Third, MathDiT performs conditional denoising in this structured latent space, further guided by a global symbol-count prior via Adaptive Layer Normalization (AdaLN) to improve structural coherence. Experiments show that DiffMath produces structurally consistent handwritten expressions, achieves superior performance over existing methods, and improves the accuracy of downstream OCR models through synthetic data augmentation.

25.
arXiv (quant-ph) 2026-06-24

A Quantum Non-Gaussianity Criterion Based on Photon Correlations $g^{(2)}$ and $g^{(3)}$

arXiv:2511.08488v2 Announce Type: replace Abstract: Quantum non-Gaussian states, which cannot be written as mixtures of Gaussian states, are necessary to achieve a quantum advantage in continuous variable systems. They represent an important benchmark for the realization of an advanced quantum light source, as they cannot be made by simple means such as displacement and squeezing. We introduce an attenuation-resistant sufficient criterion for quantum non-Gaussian states based on the second- and third-order correlation functions, $g^{(2)}$ and $g^{(3)}$. The general non-linear bound for classical mixtures of Gaussian states is $\sqrt{g^{(3)}} + 3 \sqrt{g^{(2)}} \geq 2$. Any mixture of Gaussian states must fulfill this inequality, thus, the violation of it represents a direct confirmation of quantum non-Gaussianity. We experimentally show the non-Gaussianity of the state produced by a quantum dot single-photon source, where we obtain $\sqrt{g^{(3)}} + 3 \sqrt{g^{(2)}} = 0.174 (13)$, which represents a statistical significance of more than $100$ standard deviations.