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

Entity Labels Are Not Entity Signals: A Framework for Observable Relevance in Document Re-Ranking

Entity-aware document retrieval uses query-associated entities as ranking signals, assuming that semantically relevant entities are also useful retrieval signals. We show this assumption is insufficient- and explain why. Unlike terms, which are ground-truth observations, entity links are hypotheses produced by an imperfect linker: an entity can be topically central yet provide no discriminative signal if the linker fires indiscriminately across relevant and non-relevant documents. We formalize this as a distinction between Conceptual Entity Relevance (CER)- whether an entity is topically related to a query- and Observable Entity Relevance (OER)- whether its observed presence in a collection discriminates relevant from non-relevant documents. Across four collections and annotation sources including human entity judgments, CER and OER exhibit near-chance agreement ($\kappa \approx 0$), while OER operationalizations agree substantially ($\kappa \approx 0.5$), confirming CER as the systematic outlier. CER-based supervision selects topically plausible but weakly discriminative entities, pruning fewer than 4% of non-relevant documents on some collections. Aligning supervision with OER improves non-relevant pruning by up to 10x and open-world MAP by 0.051 over BM25. Our findings motivate a shift from conceptual to observable notions of entity relevance in entity-aware retrieval.

02.
arXiv (CS.LG) 2026-06-12

Machine Learning-based Two-Stage Graph Sparsification for the Travelling Salesman Problem

arXiv:2604.20236v2 Announce Type: replace Abstract: High-performance TSP solvers such as Lin-Kernighan-Helsgaun (LKH) search within a candidate graph – a small subset of edges pre-selected for the solver – rather than over the complete graph. The two leading sparsification heuristics, $\alpha$-Nearest and POPMUSIC, each fall short of the density-coverage balance: $\alpha$-Nearest is dense with stable recall, while POPMUSIC is sparser but its recall degrades with scale. Their union closes the recall gap while remaining far below the complete graph in density, leaving room for further reduction. Existing learning-based sparsifiers score edges on the complete graph, an approach that is expensive and largely limited to Euclidean instances. We propose a two-stage method that inverts this logic. Stage~1 takes the union of $\alpha$-Nearest and POPMUSIC, achieving near-perfect recall at ${\sim}6N$ edges. Crucially, the union annotates each edge with its source provenance – whether it was endorsed by $\alpha$-Nearest, POPMUSIC, or both. Stage~2 trains a lightweight classifier on these annotated edges and prunes the lowest-scoring ones. Because dual-source edges are almost always optimal, the learning problem reduces to filtering the single-source subset – a substantially easier task than classifying all $O(N^2)$ edges from scratch. Across four distance types, five spatial distributions, and problem sizes from 50 to 500, the pipeline reduces candidate-graph density by $37$-$47\%$ while retaining ${\geq}99.69\%$ of optimal-tour edges, and matches or exceeds the coverage of recent Euclidean-only neural sparsifiers at lower density at TSP500.

03.
arXiv (math.PR) 2026-06-12

Sphere Packings in Higher Dimension (after Boaz Klartag)

arXiv:2606.13313v1 Announce Type: cross Abstract: Let $\delta_n^L$ be the maximal density of a lattice sphere packing in the $n$-dimensional Euclidean space. We explain how Boaz Klartag proved the inequality $\delta_n^L \geq c n^2 2^{-n}$ where $c>0$ is a universal constant. In higher dimension, even for non-lattice sphere packings, this new lower bound is a substantial improvement. Klartag's proof uses the probabilistic method in two different ways. The first, very standard, relies on the statistical properties of a uniformly chosen random lattice. The second, completely new, studies the stochastic evolution of an ellipsoid constrained to contain non nonzero lattice points in the interior.

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

Rendering-Aware Sparse Sampling for BRDF Acquisition

Accurate BRDF acquisition is essential for realistic rendering, but dense gonioreflectometer measurements are slow and expensive. We study how to select a small set of BRDF measurements that is most informative for reconstructing material appearance under a learned BRDF prior. Existing sparse-acquisition methods often optimize samples for BRDF-space reconstruction for all materials, while the perceptual importance of a adaptive measurement ultimately depends on its effect on each rendered appearance. We therefore formulate sparse adaptive acquisition as a rendering-aware optimization problem. Our method combines a set encoder for sparse coordinate–value observations, a pretrained hypernetwork-based/PCA-based BRDF reconstructor, and a differentiable renderer. During sampler training, the reconstructor remains fixed, and gradients from a rendered-image loss optimize the measurement locations. This separates acquisition design from prior fitting and encourages the sampler to choose directions that are informative under the learned material distribution. To make the comparison controlled, we evaluate the uniform baseline, meta-learning method, HyperBRDF method, and our learned sampler under matched sample numbers, train/test split, rendering scene, object mask, image mapping, and metrics. Our central claim: rendering-aware sampling improves extremely sparse BRDF acquisition when final rendered appearance is the target. BRDF-space and combined losses are reported only as ablations, together with joint refinement and image-only latent fitting for unseen materials.

05.
arXiv (CS.AI) 2026-06-12

Once-for-All: Scalable Simultaneous Forecasting via Equilibrium State Estimation

arXiv:2606.13285v1 Announce Type: cross Abstract: We introduce Equilibrium State Estimation (ESE), a novel paradigm for simultaneous prediction, where multiple interacting systems require separate yet coordinated forecasts. Such scenarios often arise in real-world settings such as economics and healthcare modeling. Unlike existing approaches that predict one system at a time, ESE forecasts all systems in a single pass. It first estimates the equilibrium state across systems, then generates holistic forecasts based on the difference between the current state and the estimated equilibrium. Extensive experiments on synthetic and real-world datasets, including currency exchange and COVID-19 spread modeling, demonstrate that ESE is at least as accurate as state-of-the-art (SOTA) methods while being significantly faster. In addition, ESE integrates seamlessly with conventional predictors, combining their accuracy with its exceptional efficiency and delivering a 10-70x speedup. With linear-time complexity, ESE scales far better than SOTA methods as the number of systems increases. Moreover, it remains accurate under diverse perturbations, establishing ESE as a fast, generalizable, robust, and scalable multi-prediction method.

07.
arXiv (quant-ph) 2026-06-11

The Simplified Stabilizer ZX-Calculus is Minimal

arXiv:2606.12383v1 Announce Type: new Abstract: The stabilizer fragment of the ZX calculus is amongst the most important fragments of the theory. The closely related Clifford+T fragment is approximately universal (arXiv:1705.11151). Additionally, the stabilizer calculus can be described by a small collection of rewrites, most of which have been shown to be necessary (arXiv:1709.08903). However, two rules, describing the red/green compact-structure coincidence and the important bialgebra law, had not been shown to be necessary. We present a countermodel-style argument showing that both of these rules are individually necessary relative to the connectivity meta-rule of Backens–Perdrix–Wang (arXiv:1709.08903), and hence establish that the rule set presented in arXiv:1709.08903 has no redundant rewrite rule.

08.
arXiv (CS.CV) 2026-06-15

Context-Guided Semantic Alignment for Feature Fusion Networks

Feature fusion networks are fundamental components in modern object detectors, aggregating multi-scale features to detect objects of varying sizes. However, directly fusing features from different pyramid levels often introduces semantic inconsistency due to their heterogeneous representations. In this paper, we propose Feature Interaction NEtwork (FINE), a lightweight semantic alignment module that refines low-level features via high-level contextual guidance using cross-level attention prior to fusion. To bridge the structural gap and ensure computational efficiency, we introduce an Alignment-Aware Token Sampling that aligns corresponding spatial regions across scales, reducing the attention complexity by an order of magnitude. The resulting attention weights generate a spatial-channel modulation map that is upsampled and applied to the low-level features via residual element-wise modulation. This mechanism ensures that the network selectively enhances semantically relevant pixels while preserving the sub-pixel localization accuracy necessary for dense prediction tasks. FINE is generally applicable to various detectors and consistently improves detection accuracy without compromising efficiency.

10.
medRxiv (Medicine) 2026-06-22

Understanding and Usefulness of Effect Size and Certainty of Evidence: A Cross-sectional Survey of Evidence-Based Practice Competencies Among Registered Dietitians

Introduction: Understanding of absolute and relative estimates (i.e., effect size), and certainty of evidence corresponding to those estimates, is a fundamental evidence-based practice competency to promote informed clinical decision-making. While research has been conducted in the medical profession, there is no published research on these competencies in the nutrition and dietetics profession. Methods: Among registered dietitians, our main objectives were to assess (1) their understanding and perceived usefulness of three absolute and two relative estimate approaches to assess effect size, (2) their perceived usefulness of certainty of evidence, and (3) factors influencing their understanding and perceived usefulness. We conducted a web-based, cross-sectional survey among dietitians recruited from the Academy of Nutrition and Dietetics (United States). Participants received effect estimates based on hypothetical dietary interventions vs. usual diet for reducing myocardial infarction risk. Results: Of the 11,050 dietitians who received the survey link, 210 participated (2.0% response rate), and only completers (n=114) were included in the analysis. Participants demonstrated a similar understanding of the relative (27.6%) and absolute (27.5%) estimates, with Risk Difference (30.7% correct responses) being the best understood approach and Number Needed to Treat (24.6%) being the least. The understanding of five approaches was not different than random guessing (p>0.05). While perceived usefulness scores were similar between five approaches, they were highest when data was presented as Relative Risk [mean (SD): 4.82 (1.50)]. Dietitians rated the usefulness of certainty of evidence favorably [mean (SD): 5.07 (1.83), on a 7-point scale), and no factors were associated with correct understanding. Conclusion: Dietitians may have limited understanding of how to interpret effect sizes, a finding consistent with surveys of other health professionals. To optimize informed decision-making between dietitians and clients, dietetic programs and continuing education platforms should consider additional training on interpreting effect sizes and certainty of evidence for effect sizes.

11.
arXiv (quant-ph) 2026-06-24

Certifying Quantum Optimization and Circuit Cutting by Using Quantum-Classical Moment Duality

Authors:

arXiv:2606.23727v1 Announce Type: new Abstract: We establish a direct quantum-classical duality based on the degree-$2$ Sum-of-Squares (SoS) semidefinite programming cone: the matrix of two-qubit Pauli-$Z$ correlation functions obtained from any quantum state $\rho$ is automatically a feasible point of the classical Goemans-Williamson (GW) relaxation. This observation provides a universal ``safety net'' for quantum optimization algorithms: applying GW random hyperplane rounding to the quantum-driven moment matrix yields a certified expected cut value $\mathbb{E}[\mathrm{Cut}] \ge \alpha_{\mathrm{GW}}\langle\mathcal{H}\rangle_\rho$, valid for every state produced by variational algorithms such as QAOA or the Variational Quantum Power Method (VQPM), regardless of convergence quality. We further show that the same moment matrix reveals the tensor-product structure of the underlying unitary circuit, enabling a polynomial-time, correlation-based circuit cutting procedure with rigorous error bounds. The framework is validated numerically on Max-Cut instances for variational quantum algorithms and on random states for circuit cutting, demonstrating that the cheap two-point correlation data are sufficient to locate near-optimal bipartitions and that the theoretical error bounds hold in practice.

12.
arXiv (CS.CL) 2026-06-11

An Ontology-Guided Multi-Anchor Graph Retrieval Framework for Traffic Legal Liability Determination

Traffic law liability determination is critical for assigning legal penalties, requiring the simultaneous identification of interdependent statutory provisions across multiple legal dimensions. However, existing retrieval-augmented generation methods suffer from a multi-dimensional retrieval bottleneck: single axis architectures compress complex legal queries into a single pathway, causing interdependent statutory dimensions to be overlooked. To address this, we propose OMAGR, an ontology-guided framework that decomposes queries into ontology-aligned anchors and executes parallel graph retrieval across each dimension, ensuring independent retrieval across dimensions before fusion. To evaluate the proposed method, we created the TrafficLaw-QA dataset, an expert-validated benchmark dataset containing 200 questions and 527 legal provisions. Results show that TrafficOmni-RAG outperforms baselines on Context Precision and Faithfulness metrics. The findings demonstrate that parallel multi-anchor retrieval effectively resolves the multi-dimensional retrieval bottleneck, offering a promising direction for traffic law liability determination research.

13.
arXiv (CS.CL) 2026-06-17

Security and Privacy Prompts in the Wild: What Users Ask LLMs and How LLMs Respond

Large language models (LLMs) are widely used to fulfill users' information needs; users ask LLMs about the weather, pose educational questions, and consult them for legal assistance. One particularly understudied area is digital security and privacy (S&P), where users may seek LLMs' help on how to secure their online accounts or protect their computers from cyber attacks. To the best of our knowledge, no prior study has collected or analyzed the S&P questions users ask LLMs; prior research on LLM response quality relied on expert-authored S&P misconceptions or FAQs rather than user queries. Drawing from WildChat, a dataset of 3.2M user-LLM conversations collected in the wild, our study identifies 14,727 S&P prompts and categorizes them into nine categories covering a wide range of S&P topics. From the S&P prompts, we sampled 450 and performed a thematic analysis to characterize the S&P questions users ask LLMs. Separate from the thematic analysis, we curated 270 advice-seeking S&P prompts, where users ask for recommendations, guidance, or specific S&P information. We measured LLM response quality and consistency when posing the prompt to LLMs 10 times. We found that commercial LLMs outperform open-weight models (GPT 5.5 provided "good enough" responses on 98% of prompts; Llama 4 on 47%). However, among prompts that received high-quality responses on average, commercial models sometimes produce contradictory responses across runs, risking confusing or misleading users.

14.
arXiv (CS.AI) 2026-06-24

MedPCFM: Improving Medical Point Cloud Completion by Integrating Point Transformers and Flow Matching

arXiv:2606.24433v1 Announce Type: cross Abstract: Medical point cloud completion is important for anatomical reconstruction and downstream clinical workflows, yet generative modeling in this setting remains insufficiently studied. We investigate completion through continuous-time generative modeling and introduce PCFM, a PTv3-backed flow matching approach for medical point cloud completion. We evaluate on SkullFix and SkullBreak, and additionally on the more recent Mandibular Defect dataset. We build strong baselines by adapting PTv3 to a deterministic encoder-decoder completion model and by instantiating diffusion completion (PCDiff) with both PVCNN and PTv3 denoisers. PCFM with PTv3 is competitive with the deterministic PTv3 baseline and achieves state-of-the-art generative performance across datasets, while requiring substantially fewer sampling steps than diffusion. At the best operating points, PTv3 also yields clear throughput gains, providing up to a 7$\times$ speed-up for PCFM compared to a PVCNN backbone. Finally, we study empirical scaling trends by varying model size and point cardinality, showing consistent gains with higher point resolution and informative trade-offs across model scales.

15.
arXiv (CS.AI) 2026-06-12

A Zero-shot Generalized Graph Anomaly Detection Framework via Node Reconstruction

arXiv:2606.12673v1 Announce Type: cross Abstract: Cross-domain graph anomaly detection (GAD) aims to identify abnormal nodes in unseen target graphs, showing strong potential in real-world applications with heterogeneous graph data. However, existing methods often depend on dataset-specific feature semantics and structural patterns, which limits their ability to generalize across different domains. To address this challenge, we propose AlignGAD, a zero-shot generalized graph anomaly detection framework. Our framework is built upon three key components: a Global Unification Module that aligns heterogeneous node features and normalizes graph signals in the spectral domain; a Clustering Module that constructs cluster-aware graph views to capture group-level abnormal patterns; and a Node Discrepancy Scoring Module that measures reconstruction discrepancy and aggregates anomaly evidence from different graph views. Experiments on multiple real-world datasets demonstrate the effectiveness of AlignGAD under the zero-shot GAD setting.

16.
medRxiv (Medicine) 2026-06-22

The Protective Role of Belonging and Socioeconomic Status in Dropout Intent Among Minority Ethnic Students: A Mixed Methods Study

Improving minority ethnic student retention is a global higher education priority. This mixed-methods study investigated how institutional belonging and socioeconomic status interact to shape dropout intentions among minority university students in the UK (N = 182). Quantitative results revealed that perceived course difficulty and lower subjective socioeconomic status were the strongest predictors of dropout intent. While the interaction between socioeconomic status and difficulty was non-significant, qualitative accounts showed distinct structural vulnerabilities. Financial strain restricted social integration, turning socioeconomic disparities into campus isolation. Conversely, representative curricula, diverse peer networks, and stable cultural in-groups (e.g., religious affiliations, living in the parental home) functioned as essential psychological buffers against academic exhaustion and alienation. Universities must shift from transactional models to sustained structural equity to protect vulnerable student groups.

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

MeshLoom: Feed-Forward Non-Rigid Registration of Mesh Sequences

We present MeshLoom, a feed-forward registration network that directly reconstructs vertex deformations across mesh sequences. Our approach advances non-rigid registration beyond existing models, which are typically constrained by costly per-instance optimization, narrow object categories, pairwise-only inputs, or merely intermediate outputs. The network is simple and efficient, registering multiple meshes within seconds. At its core lies a topology-aware encoder–decoder design. Specifically, we first introduce a topology-aware point representation that encodes the anchor (reference) mesh's topology into its per-vertex features. This representation strengthens the network's understanding of the anchor-mesh geometry and disambiguates points that are Euclidean-close yet geodesically distant. We then propose a multi-modal encoder that fuses this anchor-mesh representation with complementary cues from each frame, such as shape latents and image features. These multi-source signals are compressed into a compact global motion embedding that captures dense inter-frame correspondence. A lightweight decoder then queries this global embedding with the anchor-mesh point representation, retrieving per-vertex deformations at target timestamps. Through extensive experiments across diverse motions and object categories, we show that MeshLoom achieves state-of-the-art results on non-rigid registration. In addition, we find that our global embedding-then-query paradigm naturally enables the network to generate deformations at intermediate timestamps, which extends MeshLoom to motion interpolation and mesh morphing. Project page: https://meshloom.github.io/ .

18.
bioRxiv (Bioinfo) 2026-06-21

Antibody-Antigen Affinity Prediction with Chain-Aware Protein Language Modeling

Motivation: Antibody-antigen affinity determines which antibodies advance in therapeutic discovery, repertoire analysis and affinity maturation, but experimental measurements are sparse relative to the scale of sequence libraries. Structure-based predictors can exploit interface geometry when reliable complexes are available, yet early discovery often requires ranking many heavy-light chain pairs against antigens for which no complex structure exists. Existing sequence-based models are scalable, but frequently compress heavy and light chains into a single antibody representation or concatenate antibody and antigen features obscuring the chain-specific and epitope-specific signals that drive binding. Results: We present AbAffinity, a sequence-only chain-aware three-stream architecture that maintains heavy chain, light chain and antigen as distinct streams. It integrates frozen ESM-2 embeddings with heavy-chain CDR-focused pooling, heavy-light self-attention, adaptive fusion gating and gated cross-attention, training only a compact interaction module. On the SAAINT-DB benchmark, AbAffinity achieves strong predictive performance under ten-fold cross-validation and maintains robust accuracy on novel antigens. It consistently outperforms recent sequence-based models across external benchmarks including SAbDab, AB-Bind and SKEMPI 2.0. Ablation studies highlight the contributions of chain-specific representations, CDR-focused pooling and the gated interaction pathway. Integrated Gradients attributions recover known paratope and epitope residues at structurally validated interfaces. AbAffinity provides a lightweight, explainable sequence-first framework for antibody triage and prioritisation when structural information is limited or unavailable.

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

The Value Axis: Language Models Encode Whether They're on the Right Track

We investigate whether language models internally track the value of their current trajectory, defined as the likelihood that their ongoing strategy will achieve their goals. Using synthetic, in-context reinforcement learning data, we construct a "value" axis for Qwen3-8B. We find that activations along this axis distinguish between high vs. low verbalized confidence, rollouts without and with backtracking, and correct vs. corrupted code. Steering towards high value causally suppresses self-correction and reduces explanatory verbosity, while steering towards low value induces backtracking and exploration. We demonstrate that direct preference optimization (DPO) can increase the internal value of rewarded behaviors (e.g. use a certain word), causing the model to act more confidently after exhibiting them. Finally, we apply the value axis to study in-the-wild settings. For example, we find that Qwen assigns low value to politically sensitive chat queries after post-training and that supervised fine-tuning increases internal confidence within the training domain. Our results suggest that language models linearly encode an estimate of expected goal success that modulates their confidence in pursuing a direction.

20.
arXiv (CS.CL) 2026-06-24

CORE-BREW: LLR-Based Soft Decoding for Robust Multi-Bit LLM Watermarking

Reliable provenance for LLM outputs requires multi-bit watermarks that remain robust under editing while maintaining strict false-positive control. Existing ECC-based LLM watermarks rely largely on hard-decision decoding, discarding token-level reliability information. We propose CORE-BREW, a Constant-hit-Rate Embedding extension of block-wise BREW for robust multi-bit watermarking. CORE-BREW calibrates the watermark channel by targeting a fixed hit rate p-star, yielding closed-form per-token log-likelihood ratios (LLRs) for principled soft-decision decoding. It supports two detection modes: Strict-Safe, which preserves the bounded-distance designated-codeword acceptance region, and FPR-Calibrated, which uses likelihood-based scoring and lightweight list decoding to characterize the FPR-TPR trade-off. Experiments on open-source LLMs under token-level edits and paraphrasing demonstrate improved low-FPR discrimination and robustness over prior multi-bit watermarking baselines while maintaining comparable semantic quality.

21.
arXiv (CS.CL) 2026-06-16

Deep Temporal Modeling and Ensemble Fusion for Multimodal Emotion Recognition from Physiological Signals

Physiological stress and emotion recognition are important for health monitoring and affective computing. In this work, we present a comprehensive evaluation of deep learning models such as Long Short-Term Memory (LSTM), Temporal Convolutional Networks (TCN), and Transformer on the WESAD dataset for multimodal affect recognition using wrist and chest sensor signals. We perform ablation studies to assess the individual contributions of each modality by training models on wrist-only and chest-only inputs. In addition, we implement a late-fusion ensemble strategy that combines predictions from all three architectures trained on multimodal input. We also employ early fusion at the sensor level by concatenating wrist and chest signals before feeding them into each model. Our results show that Transformer models consistently achieve the highest accuracy in multimodal settings, while TCN models perform best in the wrist-only configuration. The ensemble method yields the highest overall accuracy (98.91 +/- 0.13%) and macro-F1 score (98.56 +/- 0.17%). These findings demonstrate the effectiveness of sensor fusion and ensemble-based fusion in developing robust systems for physiological emotion recognition.

22.
medRxiv (Medicine) 2026-06-22

Discovering Novel intracranial EEG Biomarkers of Seizure Generating Tissue through Time-Frequency Analysis

Objective: EEG biomarkers for seizure-generating tissue have historically been identified visually, which lacks objectivity and limits utility of automated approaches. For example, high frequency oscillations and interictal epileptiform discharges were promising markers to improve surgical outcomes for refractory epilepsy, but low specificity has hindered clinical implementation, and automated algorithms have not improved this. Methods: We developed Intracranial EEG Pattern Identification and Categorization, an automated, data-driven time-frequency framework for EEG biomarker discovery. It detects transient high-power intracranial EEG waveforms (1-500 Hz) and characterizes them using eight features. In seizure-free patients, waveforms occurring predominantly in resected intracranial EEG channels are candidate biomarkers. Results: In retrospective data from 14 seizure-free post-surgical patients from University of California, Los Angeles, we identified 9 waveform categories strongly associated with resected intracranial EEG channels. These included beta, gamma, and ripple band bursts, sometimes co-occurring with interictal epileptiform discharges; however, many were visually imperceptible in the broadband EEG. Using a support vector machine, we generated a unified classification metric based on these waveforms and tested it on 87 seizure-free subjects from Detroit Medical Center. This metric achieved higher area under the precision-recall curve than six state-of-the-art benchmark algorithms (p

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

Knowledge Manifold: A Riemannian Geometric Framework for Semantic Mapping and Geodesic Analysis of Scientific Literature

arXiv:2606.05907v2 Announce Type: replace-cross Abstract: We present the knowledge manifold: a Riemannian geometric space in which a corpus of documents is arranged according to semantic positional relationships derived from character n-gram TF-IDF representations. The framework proceeds in five tightly coupled stages. First, each document is converted to a character-level n-gram TF-IDF vector (4-7 grams, up to 250,000 features, L2-normalized) and embedded in a two-dimensional knowledge map via constrained stress minimization with repulsion, variance, and centering regularizers. Second, knowledge at an arbitrary query point is estimated through Smoothed Particle Hydrodynamics (SPH) interpolation using a cubic-spline kernel, yielding an interpolated TF-IDF feature vector that can be linguistically characterized. Third, directional knowledge gradients at 0, 45, and 90 degrees are computed from the SPH interpolation map, and pairwise directional similarity is quantified via inner product and cosine similarity. Fourth, a Gaussian Process Regression (GPR) model, with a Constant x RBF + White kernel fitted on a 10-dimensional SVD projection, provides a Bayesian posterior mean, uncertainty estimate, and per-document contribution rate at the query point. Fifth, geodesics in the knowledge space are obtained by minimizing a discrete Riemannian path energy derived from the SPH-induced metric tensor, using L-BFGS-B with seven deterministic initial-path candidates. We apply the formulation to a corpus of 20 papers in fiber-reinforced composite materials and aerospace structural mechanics, showing that the semantic map recovers meaningful research clusters, geodesic paths reveal natural conceptual bridges between distant topics, and SPH/GPR interpolation enables the generation of virtual knowledge: hypothetical paper abstracts describing unstudied but geometrically predicted research directions.

24.
arXiv (quant-ph) 2026-06-15

Who can compete with quantum computers? Lecture notes on quantum inspired tensor networks computational techniques

arXiv:2601.03035v2 Announce Type: replace Abstract: This is a set of lectures on tensor networks with a strong emphasis on the core algorithms involving Matrix Product States (MPS) and Matrix Product Operators (MPO). Compared to other presentations, particular care has been given to disentangle aspects of tensor networks from the quantum many-body problem: MPO/MPS algorithms are presented as a way to deal with linear algebra on extremely (exponentially) large matrices and vectors, regardless of any particular application. The lectures include well-known algorithms to find eigenvectors of MPOs (the celebrated DMRG), solve linear problems, and recent learning algorithms that allow one to map a known function into an MPS (the Tensor Cross Interpolation, or TCI, algorithm). The lectures end with a discussion of how to represent functions and perform calculus with tensor networks using the "quantics" representation. They include the detailed analytical construction of important MPOs such as those for differentiation, indefinite integration, convolution, and the quantum Fourier transform. Three concrete applications are discussed in detail: the simulation of a quantum computer (either exactly or with compression), the simulation of a quantum annealer, and techniques to solve partial differential equations (e.g. Poisson, diffusion, or Gross-Pitaevskii) within the "quantics" representation. The lectures have been designed to be accessible to a first-year PhD student and include detailed proofs of all statements.

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

The Structural Attention Tax: How Retrieval Format Hijacks In-Context Learning Independent of Content

Retrieval-augmented generation (RAG) systems inject external knowledge to improve LLM outputs, yet the format of injected content – distinct from its semantic relevance – can independently distort the model's attention distribution. We identify and formalise a phenomenon we term the structural attention tax: knowledge graph (KG) triples, due to their relational delimiters and repeated slot patterns, capture 2-3x more attention per token than semantically equivalent natural-language text ($\hat{o}$(KG) $\approx$ 0.70 vs. $\hat{o}$(neutral) $\approx$ 0.25), compressing demonstration attention by up to 42% – regardless of whether the triples are relevant or noise. We develop a formal framework decomposing attention scores into semantic and structural components (Eq. 2), derive a compression bound (Proposition 1) connecting token-level format bias to demonstration attention loss, and show that the structural term governs how much attention is diverted while the semantic term governs whether this helps or hurts. This decoupling reveals two orthogonal axes for improving retrieval-augmented ICL: optimising retrieval quality (semantic axis) and reducing format-driven attention capture (structural axis). Empirically, across two model families (Mistral-7B, LLaMA-3-8B) and three QA benchmarks, we observe that source-task alignment dominates: task-matched BM25 retrieval achieves 58-62% on HotpotQA vs. ConceptNet's 25-27%, a >30 pp gap that dwarfs all gating strategies ($\leq$2 pp). We derive five structure-aware mitigation strategies from the framework, ranging from zero-cost prompt modifications to training-time regularisation; format flattening (S3) is validated by both accuracy and attention-level evidence from a verbalized-triple control, while structural dispersal (S1) yields mixed results that illuminate the challenges of format-level intervention.