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

A comparative and critical study of EEGNet for fNIRS-driven cognitive load classification

arXiv:2606.16160v1 Announce Type: cross Abstract: Accurately classifying cognitive load from functional near-infrared spectroscopy (fNIRS) signals remains a significant challenge due to temporal variability, inter-subject differences, and sensitivity to preprocessing choices. This study provides a comprehensive evaluation of EEGNet for fNIRS-based cognitive load classification by systematically examining the effects of temporal segmentation strategies (overlapping vs. non-overlapping), window lengths (10s, 20s, 30s), feature extraction methods (Analysis of Variance (ANOVA), Principal Component Analysis (PCA), Fast Independent Component Analysis (FastICA)), learning rate configurations (fixed and adaptive), and evaluation protocols (random split vs. subject-independent (SI)). Results from random-split experiments show that overlapping segmentation, combined with smaller fixed learning rates (0.01-0.001), yields the highest accuracies, due to temporal redundancy and dense sampling of hemodynamic transitions. However, SI evaluation reveals a substantial drop in accuracy, demonstrating limited generalization to unseen participants. Under SI evaluation, non-overlapping segmentation outperformed overlapping windows, with the best accuracy of 56.11% achieved using PCA features with a 20-second window and a 0.1 learning rate. These findings indicate that eliminating temporal redundancy helps the model learn more robust and generalizable representations of cognitive load across individuals. Although adaptive learning rate strategy improved training stability, it did not surpass the performance of optimally selected fixed learning rates. The study highlights the critical role of segmentation strategy and learning rate selection in improving model generalization and identifies methodological considerations essential for developing reliable, real-time, and SI cognitive load classification systems using fNIRS.

02.
arXiv (quant-ph) 2026-06-19

Steady-state entanglement of spin qubits mediated by nonreciprocal and chiral magnons

arXiv:2509.13094v3 Announce Type: replace Abstract: We propose a hybrid quantum system in which a magnet supporting non-reciprocal magnons, chiral magnons, or both mediates the dissipative and unidirectional coupling of spin qubits. By driving the qubits, the steady state of this qubit-qubit coupling scheme becomes the maximally entangled Bell state. We devise a protocol where the system converges to this entangled state and benchmark it including qubit decay and dephasing. The protocol is numerically tested on a hybrid system consisting of nitrogen-vacancy (NV) centers coupled to magnon surface modes of an yttrium iron garnet (YIG) film. We show that the dephasing time of the NV centers forms the bottleneck for achieving the entanglement of NV centers separated by a distance within the magnon coherence length. Our findings identify the key technological requirements and demonstrate a viable route toward steady-state entanglement of solid-state spins over distances of several microns using magnonic quantum networks, expanding the toolbox of magnonics for quantum information purposes.

03.
arXiv (math.PR) 2026-06-16

A Tail-Respecting Splitting Numerical Scheme for Lévy-Driven SDEs With Superlinear Drifts

arXiv:2504.07255v3 Announce Type: replace Abstract: We present an explicit numerical approximation scheme, denoted by $\{X^n\}$, for the effective simulation of solutions $X$ to a multivariate stochastic differential equation (SDE) with a superlinearly growing $\kappa$-dissipative drift, where $\kappa>1$, driven by a multiplicative heavy-tailed Lévy process that has a finite $p$-th moment, with $p>0$. We show that the strong $L^{p_X}$-convergence $\sup_{t\in[0,T]}\mathbf E \|X^n_t-X_t\|^{p_X}=\mathcal O (h_n^{\gamma})$ holds for any $p_X\in (0,p+\kappa-1)$, which is exactly the range where the $p_X$-moment of the solution is known to be finite. Additionally, for any $p_X\in (0,p)$ we establish strong uniform convergence: $\mathbf E\sup_{t\in[0,T]} \|X^n_t-X_t\|^{p_X}=\mathcal{O} ( h_n^{\delta} )$. In both cases we determine the convergence rates $\gamma$ and $\delta$. In the special case of SDEs driven solely by a Brownian motion, our numerical scheme preserves super-exponential moments of the solution. The scheme $\{X^n\}$ is realized as a combination of a well-known Euler method with a Lie-Trotter type splitting technique.

04.
arXiv (CS.LG) 2026-06-12

Scale Buys Interpolation, Structure Buys a Horizon: Certified Predictability for Equivariant World Models

作者:

arXiv:2606.13092v1 Announce Type: new Abstract: Scale buys interpolation; structure buys a certified horizon. A world model's average error says nothing about whether a particular prediction can be trusted, or for how long. For equivariant latent world models we give a computable, multi-step certificate of the predictable horizon: $T$-step rollout error is provably constant over each symmetry orbit (Theorem A) and stratified channel-by-channel by the predictor's Lyapunov spectrum, $T_j(\epsilon)\sim\log(1/\epsilon)/\lambda_j$. The horizon is two-sided – a matching lower bound makes approximate equivariance provably horizon-limited – and the certificate is exclusive to structure: orbit-constant error characterizes equivariance, so no non-equivariant model has it at any scale. Empirically, on 40-D Lorenz-96 only a $\mathbb{Z}_N$-equivariant network recovers the full Lyapunov spectrum ($R^2{=}0.98$); dense and recurrent baselines fail. Because the spectrum is faithful, the certificate acts, a priori: under a fixed sensing budget a $c\times$-inflated certificate provably needs $c\times$ the budget, and the equivariant certificate meets a budget its inflated dense counterpart cannot – with zero calibration data. The same read-out, unchanged, audits public pretrained world models training-free: TD-MPC2 checkpoints land on the certificate's own scope taxonomy – calibrated where strongly expansive (ratio 0.94-1.02), optimistic where weakly expansive, correctly abstaining where contracting – a map a deployed monitor replicates cell-by-cell, out-of-sample. Across the official 1M-317M multitask ladder, calibration does not improve with parameters. On V-JEPA 2-AC (1B, real robot data) the measured cross-check correctly overrides an over-promising tangent spectrum – the cross-validated audit, not the raw number, is the deployable object. Scale buys interpolation, not a calibrated horizon.

05.
bioRxiv (Bioinfo) 2026-06-18

Population-associated molecular variation in histologically normal breast tissue is context-dependent and associated with distinct transcriptional states

Population-associated molecular variation in breast tissue may contribute to differences in tissue biology and disease susceptibility, yet the extent to which such variation is shaped by underlying tissue states remains unclear. Here, we performed RNA-seq and lipidomic profiling of histologically normal breast tissue samples from African American (AA) and Caucasian White (CW) individuals, followed by conceptual integration of the resulting transcriptomic and lipidomic patterns. Unsupervised analysis revealed two distinct baseline transcriptional states (G1 and G2) that defined the primary axis of molecular variation across the cohort and corresponded to epithelial-enriched (G1) and vascular-enriched (G2) tissue contexts as determined by cell-type deconvolution. Global comparisons between AA and CW samples showed minimal transcriptomic differences, with only a single gene reaching significance after multiple testing correction. However, when stratified by baseline tissue state, 191 genes were differentially expressed within G1, with coordinated upregulation of extracellular matrix organization and proliferative/cytoskeletal processes in AA samples. These patterns were consistently supported across multiple enrichment approaches. No comparable population-associated differences were observed within G2. Lipidomic analyses showed partial but non-significant trends consistent with transcriptomic structure, suggesting that lipid variation provides complementary but limited support for baseline molecular differences, likely reflecting constraints of bulk tissue composition. Together, these findings suggest that population-associated molecular differences in normal breast tissue are context-dependent and emerge within specific baseline transcriptional states, where distinct biological programs can coexist and be differentially modulated. These findings highlight the importance of tissue heterogeneity in shaping molecular variation and its potential relevance to disease-associated tissue states.

06.
arXiv (CS.CL) 2026-06-11

Verifiable Environments Are LEGO Bricks: Recursive Composition for Reasoning Generalization

Reinforcement Learning (RL) with verifiable environments has emerged as a powerful approach for enhancing the reasoning capabilities of Large Language Models (LLMs). While prior research demonstrates that scaling environment quantity improves RL performance, existing manual or individual construction methods suffer from linear scaling limits, thereby hindering scalable reasoning generalization. This paper introduces RACES (Recursive Automated Composition for Environment Scaling), a framework that conceptualizes verifiable environments as composable building blocks that can be recursively assembled. The key insight is that when the codomain (output type) of one environment matches the domain (input type) of another, they can be automatically fused into a new verifiable environment, enabling recursive composition. RACES is implemented with 300 individual environments and defines a set of composition operators (\textsc{SEQUENTIAL}, \textsc{PARALLEL}, \textsc{SORT}, and \textsc{SELECT}) that induce diverse reasoning patterns. Extensive experiments show that RL training on these composite environments consistently enhances reasoning generalization. Specifically, RACES improves DeepSeek-R1-Distill-Qwen-14B by an average of 3.1 points (from 48.2 to 51.3) and boosts Qwen3-14B performance from 58.8 to 61.1 on six benchmarks, which are unseen during the construction of training environments. Moreover, RACES achieves performance comparable to training on 300 individual environments using only 50 base environments, demonstrating significant efficiency in environment utilization.

07.
arXiv (CS.AI) 2026-06-16

Recurrent Reasoning on Symbolic Puzzles with Sequence Models

arXiv:2606.15686v1 Announce Type: new Abstract: Large language models often appear strong on symbolic and algorithmic tasks, yet this apparent strength can hide brittle behaviour when problems become longer, harder, or slightly out of distribution. A major limitation of current reasoning benchmarks is that many primarily test whether a model can produce a valid answer, while paying less attention to whether the solution is minimal, robust, and stable under controlled difficulty scaling. We introduce RecurrReason, a difficulty-controlled benchmark of four recurrent logic puzzles (Tower of Hanoi, River Crossing, Block World, and Checkers Jumping) with BFS-optimal trajectories and a single interpretable difficulty parameter $N \in \{1,\dots,10\}$, totalling 10{,}817 unique puzzles and 285{,}933 moves. We benchmark two Transformer families, an encoder-decoder model (T5-style) and a decoder-only model (GPT-2-style), under consistent data splits and evaluation criteria, training on $N{=}1$ to $7$ and evaluating on both held-out in-distribution instances and harder out-of-distribution instances at $N{=}8$ to $10$. Fine-tuned pre-trained T5 achieves 97.27\% validation and 81.00\% OOD accuracy on Block World; all models score 0.00\% on River Crossing under all conditions. Failure mode analysis reveals that architecture is a stronger determinant of success than scale. Pre-training transfers only to puzzles with locally structured transition functions. Our code and dataset will be open-sourced upon acceptance.

08.
arXiv (quant-ph) 2026-06-16

Classical Explanations in (and of) General Probabilistic Theories

arXiv:2603.05627v2 Announce Type: replace Abstract: We introduce a notion of the ``explanation" of one (generalized) probabilistic model by another as particular kind of span in the category $\Prob$ of probabilistic models and morphisms. We show that explanations compose under a standard pullback construction (notwithstanding that $\Prob$ does not support arbitrary pullbacks). We then show that every locally-finite probabilistic model has a canonical, sharp classical explanation. The construction is functorial, so every locally-finite probabilistic theory has a canonical, sharp classical (though of course, usually non-local) representation.

09.
arXiv (CS.LG) 2026-06-15

Neural Slack Variables for Shape Constraints

arXiv:2606.13803v1 Announce Type: new Abstract: Enforcing functional inequality constraints such as monotonicity and convexity in neural networks is a fundamental challenge in many industrial and scientific applications. Classical one-sided penalty methods, along with primal-dual methods gated by complementary slackness, provide constraint gradients only at violated locations, resulting in fragile satisfaction. Architectures that guarantee feasibility by construction, on the other hand, remain largely limited to elementary cases and impose additional inductive biases. We introduce neural slack variables, a deep learning native primal-side approach that converts constraint enforcement into a regression problem by coupling the primary network with a jointly learned auxiliary network. The auxiliary network serves as a valid target for the primary network's constraint quantities, inducing feasibility and regularity. Neural slack variables achieve zero measured violations on dense-grid monotonicity and convexity test cases, where penalty and primal-dual baselines leave residual violations, and enable arbitrage-free learning of volatility surfaces, an open industrial challenge in quantitative finance.

10.
arXiv (CS.CL) 2026-06-18

RCEM: Robust Conversational Search EMbedder in Distributional Shift

We propose RCEM, a Robust Conversational search EMbedder that is additionally equipped with LLM's query reformulation capability without losing base model's generalization. Unlike prior conversational dense retrieval approaches that learn direct conversation-to-passage matching, RCEM aligns conversations, prepended by special token, to LLM-rewritten queries, while preserving the original embedding space. The unchanged embedding space automatically maps the rewritten-query to the relevant passages. As a result, RCEM (1) reduces overfitting by simplifying the alignment task from long passages to shorter rewritten queries, (2) eliminates the need for conversation-to-passage relevance labels for training, and (3) maintains its original embedding space that allows conversational queries against indexes built by original embedder without rebuilding them. Extensive experiments show that RCEM consistently outperforms prior approaches, achieving up to 30% improvement under distributional shift.

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

Metacognitive Myopia in Large Language Models

Large Language Models (LLMs) exhibit potentially harmful biases that reinforce culturally embedded stereotypes, influence moral judgments, or amplify positive evaluations of majority groups. We propose metacognitive myopia as a cognitive-ecological framework accounting for a conglomerate of established and emerging LLM biases. Our theoretical framework posits that biased samples in the information environment cause five symptoms of metacognitive myopia in LLMs: integration of invalid embeddings, susceptibility to redundant information, neglect of base rates in conditional computation, decision rules based on frequency, and inappropriate higher-order statistical inference for nested data structures. Moreover, it posits that the two main components of metacognition, monitoring and control, could account for these five symptoms. Accordingly, we further outline how monitoring and control could be approximated technically, for instance, through hidden parallel reasoning histories that allow interactive LLMs to evaluate risks of myopic inference before generating overt responses. Our theoretical framework provides a novel perspective on flawed human-machine interactions and agentic AI and raises significant ethical concerns regarding the implementation of LLMs in organizational structures and high-stakes decisions.

12.
arXiv (CS.AI) 2026-06-18

NeSyCat Torch: A Differentiable Tensor Implementation of Categorical Semantics for Neurosymbolic Learning

arXiv:2606.19279v1 Announce Type: new Abstract: Neurosymbolic semantics is fragmented: classical, fuzzy, probabilistic and neural systems each define truth by their own inductive rules. NeSyCat, extending ULLER, subsumes them under a single inductive definition of truth, parametric in a strong monad and an aggregation structure on truth-values. NeSyCat has so far lacked an account of predicates and functions learned by neural networks. We provide NeSyCat Torch as the missing link and interpret computational symbols via neural networks, implementing the framework in probabilistic programming and tensor-based backends. We use the distribution monad for reference semantics and metric evaluation, and complement it by a monad for numerically stable, differentiable training: the lazy log-tensor monad over the log-semiring. For efficient training in batches, we furthermore employ a batch monad. The axioms are the source code: written once in monad-based do-notation, monadic bind performs marginalisation, lazily pruning unneeded branches. On MNIST addition, our HaskTorch, JAX, and PyTorch implementations outperform LTN and DeepProbLog in speed and accuracy, while achieving nearly the accuracy of DeepStochLog. However, unlike DeepStochLog, we stay in a uniform framework that applies to many first-order NeSy approaches. Namely, the construction is parametric in the monad; instantiating it with, e.g., the Giry monad extends the approach to continuous probability (working out a neural representation here is left for future work).

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

TimeROME-DLM: Temporal Causal Tracing and Low-Rank Inference-Time Knowledge Editing for Masked Diffusion Language Models

arXiv:2606.12841v1 Announce Type: cross Abstract: Masked diffusion language models (MDLMs) such as LLaDA now rival autoregressive (AR) LLMs, but every existing knowledge-editing and unlearning method (ROME, MEMIT, etc.) targets AR transformers and either makes assumptions that fail under iterative denoising, or requires gradient updates whose backward-pass activations cost tens of GB of extra VRAM and which collapse MDLMs at standard learning rates. We introduce TimeROME-DLM, the first training-free, gradient-free, inference-time knowledge-editing framework for MDLMs. It couples two components: a Temporal Indirect Effect (TIE) causal-tracing protocol that identifies, for each fact, the coordinate whose intervention most strongly drives the object prediction at later denoising steps; and a closed-form, low-rank residual edit memory that aggregates subject keys and target deltas across all forget facts and applies a single ridge-regularised update at that coordinate at every diffusion forward, with sparsification to limit utility spillover. Backbone weights stay frozen; only three hyperparameters (alpha, lambda, q) are tuned on a small validation split. On TOFU forget01 with TOFU-finetuned LLaDA-8B-Base, TimeROME-DLM cuts forget-set log-probability by roughly 83 nats. The same configuration transfers to LLaDA-8B-Instruct, Dream-7B, MMaDA-8B, DiffuLLaMA-7B, and LLaDA-MoE-1.4B. It keeps retain-set log-probability nearly flat (within ~1 nat at the utility-safe operating point) across 50 sequentially inserted facts, delivers a four- to fourteen-fold wall-clock speedup with zero additional VRAM over the strongest converged training-time baseline, and scales sub-linearly to 400 facts. TimeROME-DLM closes the locate-then-edit gap between AR LLMs and MDLMs at a fraction of the computational cost.

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

Creative Collision: Directorial Persona Steering and Competition in Large Language Models

Activation steering has emerged as a powerful tool for shaping the behaviour of large language models at inference time, yet most prior work injects a single semantic direction into the residual stream. We study the richer setting in which two semantically opposing steering vectors are superimposed – a regime we call Creative Collision. Concretely, we construct directorial persona vectors for Steven Spielberg (optimistic, redemptive moral valence) and Martin Scorsese (dark, morally ambiguous) via mean-difference activation contrast on curated screenplay-derived corpora, then interpolate between them with a scalar mixing parameter $\alpha \in [0,1]$ and a steering coefficient $\lambda$. Across five evaluation axes – moral valence, generation coherence, surface style, directional dominance, and vector geometry – three principal findings emerge: (i)~Spielberg's representational signature exhibits robust directional dominance, suppressing Scorsese's moral influence across almost the entire interpolation range; (ii)~intermediate collision points paradoxically improve generation coherence relative to pure single-director steering at high $\lambda$; and (iii)~both personas localise maximally to layer~28 of a 40-layer decoder-only transformer, revealing a shared moral-tone substrate. These results illuminate the geometry of competing semantic directions in transformer residual streams and have direct implications for controllable creative generation and value-aligned narrative synthesis.

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

LLMs Struggle to Measure What Distinguishes Students of Different Proficiency Levels: A Study of Item Discrimination in Reading Comprehension Assessment

Item discrimination is a fundamental psychometric property of educational assessment, which measures whether an item meaningfully distinguishes students with higher proficiency from students with lower proficiency. While various existing works have explored whether large language models (LLMs) can estimate item difficulty, it remains unclear whether they can capture item discrimination. In this work, we evaluate 42 proprietary and open-weight LLMs in zero-shot settings using two complementary approaches: direct discrimination prediction, where models explicitly estimate an item's discrimination value from its content, and response-based Classical Test Theory (CTT) calibration, where LLM answers are treated as synthetic student responses to compute discrimination scores. Our results show that direct prediction yields weak alignment with human-calibrated discrimination: the best-performing model reaches only a Spearman correlation of 0.152. Response-based CTT calibration provides a stronger but still limited signal, with the all-persona synthetic respondent pool reaching a Spearman correlation of 0.241. These findings highlight item discrimination as an open challenge for LLM-based psychometric evaluation: current LLMs contain non-random discrimination-relevant signal, but they do not yet reliably capture how assessment items distinguish human students.

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

MIVE: A Minimalist Integer Vector Engine for Softmax LayerNorm and RMSNorm Acceleration

arXiv:2606.17781v1 Announce Type: cross Abstract: The rapid growth of Large Language Models (LLMs) has intensified the need for specialized hardware accelerators that can satisfy stringent inference latency and power constraints. Although matrix multiplications dominate the overall computational workload, non-linear vector normalization operations, such as LayerNorm, RMSNorm and Softmax can become critical hardware bottlenecks. Existing accelerators typically implement these functions using dedicated hardware blocks, leading to duplicated resources and inefficient silicon utilization. To address this limitation, we propose a Minimalist Integer Vector Engine (MIVE), a programmable architecture capable of executing all three operations within a unified datapath. By exploiting common computational patterns across LayerNorm, RMSNorm and Softmax the proposed vector engine maximizes hardware sharing while reducing implementation overhead. Physical ASIC implementation results show that MIVE provides comprehensive multi-function support while achieving higher area and hardware efficiency than most state-of-the-art standalone accelerators.

17.
arXiv (CS.LG) 2026-06-18

Multi-Agent Systems are Mixtures of Experts: Who Becomes an Influencer?

arXiv:2605.25929v2 Announce Type: replace-cross Abstract: The effectiveness of multi-agent LLM deliberation depends not only on the agents' individual predictions, but also on how they communicate and collaborate. We study this mechanism through the lens of Friedkin-Johnsen (FJ) opinion dynamics, a tractable model for analyzing stubbornness, influence, and opinion change in multi-agent systems that captures empirically observed deliberation patterns. We show that the FJ parameters are input-dependent, turning multi-agent deliberation into a mixture of experts. This perspective implies that multi-agent systems can outperform single agents and static ensembles when routing reflects agent competence. Since competence is latent in practice, we analyze how influence is established through observable proxies: agents' self-assessed confidence, their perceived confidence, and initial alignment with other agents' views.

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

Learning to Distort: Weakly-Supervised Image Quality Transfer for Prostate DWI Correction

Single-shot echo-planar prostate diffusion-weighted imaging (DWI) is frequently complicated by geometric distortions, which impact the ability to derive reliable diagnoses from such images. Developing automated correction methods is challenged by the absence of paired distorted and undistorted clinical scans. In this paper, we first propose a novel weakly-supervised image quality transfer (IQT) framework from undistorted to distorted images that utilizes image quality assessment (IQA) signals to supervise the transfer process. Unlike traditional methods that require expensive, voxel-wise paired data or resort to developing unpaired algorithms, our approach utilizes image-level quality labels (here, distorted vs. undistorted) to establish latent quality prototypes within a pre-trained feature space. Recognizing that simulating realistic distortions is more reliable than direct unpaired correction, we describe a weakly-supervised prototype flow matching algorithm to explicitly regularize generative trajectories towards distorted prototypes, producing realistic susceptibility artifacts that mimic clinical degradations. By synthesizing these realistic pairs, we enable a second IQT model to be trained in the forward direction for distortion correction. Experimental results demonstrate that our generated images successfully mimic the diagnostic interference of real-world artifacts, which leads to more capable distortion correction IQT models. In addition to qualitative comparisons, we also conduct exhaustive quantitative evaluations that compare our approach with existing unpaired approaches (e.g., CycleGAN, UNIT-DDPM, and OT-FM) - as either forward or reverse alternatives - by assessing clinical downstream task performance in PI-RADS and Gleason score classification, using both in-distribution and external data sets.

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

EARS: Explanatory Abstention for Reliable Sub-Agent Modeling in Large-scale Multi-Agent Systems

In large-scale enterprise settings, centralized multi-agent systems (MAS) are increasingly adopted, in which a coordinator delegates user requests to lightweight, domain-specialized sub-agents. While this architecture improves modularity, scalability, and cost efficiency, its reliability depends not only on accurate routing but also on sub-agents' ability to calibrate their responses to capability constraints. In particular, sub-agents built on smaller fine-tuned models often struggle with such calibration, leading them to over-answer ambiguous, underspecified, misrouted, or unsupported requests and produce hallucinated outputs instead of actionable feedback. To address this challenge, we present EARS (Explanatory Abstention for Reliable Sub-Agent Modeling), a production-oriented framework that reframes sub-agent abstention as an inter-agent communication protocol: a sub-agent does not merely abstain, but exposes an actionable failure state to the coordinator. EARS curates human-agent interaction data using an ensemble of calibrated LLM-as-a-Judge models, producing structured abstention labels and rationales under a taxonomy of sub-agent failure modes. These data are used to fine-tune sub-agents to detect failure conditions and return rationales for coordinator-level clarification, rerouting, or fallback. We evaluate EARS in a large-scale production e-commerce assistant supporting enterprise business intelligence workflows. EARS improves the overall response pass rate from 68.5% to 78.9%, demonstrating that sub-agent-side explanatory abstention improves MAS reliability.

20.
arXiv (quant-ph) 2026-06-19

Quantum Algebraic Diversity: Single-Copy Density Matrix Estimation via Group-Structured Measurements

arXiv:2604.03725v3 Announce Type: replace Abstract: We extend the algebraic diversity (AD) framework from classical signal processing to quantum measurement theory. The Quantum Algebraic Diversity (QAD) Theorem establishes that a group-structured positive operator-valued measure (POVM) applied to a single copy of a quantum state produces a full-rank, group-averaged density matrix estimator whose eigenbasis and eigenvalue ordering track those of the true density matrix, with a bias toward the symmetrized state, analogous to the classical recovery of covariance eigenstructure from a single observation. We establish a Classical-Quantum Duality Map connecting classical covariance estimation to quantum state tomography, and an Optimality Inheritance Theorem showing that classical group optimality transfers to quantum settings via the Born map within the group-averaged family. SIC-POVMs are identified as AD with the Heisenberg-Weyl group and mutually unbiased bases as AD with the Clifford group, revealing the hierarchy $\mathrm{HW}(d) \subseteq \mathcal{C}(d) \subseteq S_d$ that mirrors the classical $\mathbb{Z}_M \subseteq G_{\min} \subseteq S_M$. The double-commutator eigenvalue theorem gives polynomial-time adaptive POVM selection. A worked qubit example shows the group-averaged estimator from a single computational-basis measurement, averaged over a matched $\mathbb{Z}_2$ group, reaching fidelity 0.99 where standard single-basis tomography gives a rank-1 estimate of fidelity 0.80. Monte Carlo simulations for $d = 2$ to $13$ confirm fidelity above 0.90 from a single outcome while standard fidelity degrades as $\sim 1/d$. The growing ratio reflects collapse of the rank-1 standard estimator, not fewer copies per parameter: the biased single-copy estimator reduces the number of distinct measurement settings, not the per-parameter sampling cost, and a genuine copy reduction holds only under exact symmetry.

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

How Low Can You Go? Active Learning for Sparse Model Discovery in the Ultra-Low-Data Limit

arXiv:2606.12182v1 Announce Type: new Abstract: Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering. While early approaches relied on empirical data and heuristics, modern data-driven methods offer greater flexibility and fewer assumptions. However, data acquisition in real-world settings is often expensive. This work addresses this challenge by introducing an active learning strategy for dynamics discovery in the ultra-low data limit. Rather than sampling randomly, our method iteratively prioritizes regions that are most informative for model identification. This approach builds on Sparse Identification of Nonlinear Dynamics (SINDy), and utilizes an ensemble extension, E-SINDy, to estimate epistemic uncertainty and guide the sampling for both ordinary and partial differential equations (ODEs/PDEs). For ODEs, an exhaustive analysis is conducted on the Lorenz system across varying data budgets and noise levels. For PDEs, two systems with contrasting dynamical characteristics are examined: the Burgers' equation, where a sharp shock front creates a distinction between informative and uninformative regions, and the Kuramoto-Sivashinsky equation, which presents a more spatially complex sampling landscape. Across all scenarios, the proposed method accurately identifies the governing dynamics with significantly fewer data samples than random sampling.

22.
arXiv (CS.CV) 2026-06-18

VGGHeads: 3D Multi Head Alignment with a Large-Scale Synthetic Dataset

Human head detection, keypoint estimation, and 3D head model fitting are essential tasks with many applications. However, traditional real-world datasets often suffer from bias, privacy, and ethical concerns, and they have been recorded in laboratory environments, which makes it difficult for trained models to generalize. Here, we introduce \method – a large-scale synthetic dataset generated with diffusion models for human head detection and 3D mesh estimation. Our dataset comprises over 1 million high-resolution images, each annotated with detailed 3D head meshes, facial landmarks, and bounding boxes. Using this dataset, we introduce a new model architecture capable of simultaneous head detection and head mesh reconstruction from a single image in a single step. Through extensive experimental evaluations, we demonstrate that models trained on our synthetic data achieve strong performance on real images. Furthermore, the versatility of our dataset makes it applicable across a broad spectrum of tasks, offering a general and comprehensive representation of human heads.

23.
arXiv (CS.CV) 2026-06-16

The Circumplex Degeneracy Behind the Rare-Class Limit in Affect Recognition

In-the-wild expression recognition persistently fails on a few rare emotions, and the standard explanation is class imbalance. Through a controlled multi-task study on two benchmarks, we show the failure is instead a property of affect geometry: the rare classes are degenerate on Russell's circumplex, and that degeneracy bounds what any loss or cost can achieve. Our instrument is a circumplex-cost optimal-transport term that prices expression confusions by their valence-arousal distance. The term improves the official score and expression macro-F1, but a control most studies omit shows the gain is not geometric: a uniform cost, equivalent to a generic confidence penalty, matches it on Aff-Wild2 (p=0.625) and significantly exceeds it on AffectNet (+0.057 over base, larger than the circumplex). What the geometry reshapes is the structure of the errors, making them affectively nearer the truth on Aff-Wild2 (p=0.031 against the uniform control), an effect that does not survive on AffectNet, where a visual confound at the far corner of the circumplex overwhelms it. The rare-class failure, by contrast, is stable across both datasets we examine: the degenerate pairs (anger-fear on Aff-Wild2, anger-contempt on AffectNet) resist frequency-based interventions, the transport term, and an action-unit-augmented cost built specifically to separate them. We conclude that progress on rare expressions requires representations that distinguish the classes, not supervision that reprices their confusions, and we provide the controls and metrics needed to tell the two apart.

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

False Sense of Safety in Selective Signal Classification: Auditing Bound Tightness and Exchangeability for Risk Control

arXiv:2606.15153v1 Announce Type: new Abstract: Selective prediction with distribution-free risk control promises that, with confidence 1-delta over the calibration draw, the error rate of accepted inputs stays below a user budget alpha. We audit this promise on signal-domain detectors – machine anomalous-sound detection (ASD) and AI-generated-image forensics – for four calibration rules: uncertified empirical thresholding (NAIVE) and certified Hoeffding, Clopper-Pearson (CP), and betting (WSR) upper confidence bounds. We report three findings. (i) NAIVE thresholding, common in practice, exceeds its declared budget in 49-73% of synthetic trials (n=200 calibration points) and in up to 68% of real-data splits: a false sense of safety rather than a broken theorem, since the rule never had a certificate. (ii) Tightness matters: CP and WSR certify substantial coverage where Hoeffding certifies none, with zero observed budget overruns under exchangeable splits. (iii) Under grouped deployment (unseen machine types or generators), certified rules overrun in 9-30% of trials – far above delta – showing the failure lies in the broken exchangeability premise, not in the bounds; a conservative per-group threshold restores validity at a severe coverage cost.

25.
arXiv (CS.CL) 2026-06-11

GraphInfer-Bench: Benchmarking LLM's Inference Capability on Graphs

Graph analysis underlies many applications whose answers cannot be looked up in a single record or retrieved along a path: laundering rings, drug repurposing, user preference, and scientific theme are all inferred from a node together with its neighbourhood. We introduce GraphInfer-Bench, a benchmark for whether LLMs can perform this graph inference: producing an open-ended answer that no single node supports and no path retrieves. Existing graph-QA protocols cannot test this capability: algorithm simulation, node classification, single-node description, KG-QA, and GraphRAG all admit answers retrievable from one node or along a path. GraphInfer-Bench defines five tasks along Description (what a region is) and Comparison (how regions differ), each constructed so the ground truth lives in no single node. The release contains 42,000 samples across six real-world graphs, produced automatically and screened by a four-layer quality-control protocol. We evaluate four method families against the same tasks: graph-token alignment models, zero-shot frontier closed-source LLMs, Graph2Text supervised fine-tuning, and plain GNNs as a structural reference. No method family closes the gap. Graph-token alignment partially handles description tasks (relational, theme) but collapses on comparison tasks. Frontier LLMs lead on outlier detection and community partition among LLM-based methods but lag on masked-node prediction. Graph2Text SFT is the strongest LLM-based method on the description side yet falls behind frontier LLMs on comparison. Across every task, plain GNNs match or beat the strongest LLM-based row, with the largest margin on community detection. GraphInfer-Bench surfaces graph inference as an open capability gap rather than a property of any one architecture.