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01.
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.

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

CoVar: Confidence-Variance-Guided Pseudo-Label Selection for Semi-Supervised Learning

arXiv:2601.11670v3 Announce Type: replace-cross Abstract: Pseudo-label selection in semi-supervised learning is commonly driven by maximum-confidence thresholds, yet confidence alone can be unreliable under model overconfidence and class imbalance. We propose CoVar, a confidence–variance framework that assesses pseudo-label reliability by jointly modeling Maximum Confidence (MC) and Residual-Class Variance (RCV). Starting from entropy minimization, we derive a second-order cross-entropy approximation showing that low-loss pseudo-labels are favored when MC is high and RCV is low, with a confidence-dependent penalty that becomes stronger for near-certain predictions. Based on this criterion, CoVar embeds predictions into a two-dimensional confidence–variance space and uses SVD-based spectral relaxation to separate reliable and unreliable predictions without hand-tuned confidence thresholds. Cluster-wise Gaussian weighting then converts this separation into per-sample training weights. The resulting weights can be integrated into existing semi-supervised segmentation and classification pipelines during training and introduce no inference-time overhead. Experiments on PASCAL VOC 2012, Cityscapes, CIFAR-10, CIFAR-100, SVHN, and STL-10 show clear gains on VOC and Cityscapes under matched backbones, as well as competitive or improved error rates on standard classification benchmarks. These results indicate that residual-class dispersion provides a useful signal complementary to confidence for robust pseudo-label selection.

03.
medRxiv (Medicine) 2026-06-16

Daily Healthy Eating Index (HEI-2020) scoring reveals diet quality patterns masked by aggregation

The Healthy Eating Index (HEI-2020) is conventionally computed by aggregating intake across days before scoring. Digital food logging enables an alternative: scoring each day and averaging daily scores. These methods are not equivalent. The HEI's density-based structure and component caps cause aggregation to inflate adequacy scores when intake is irregular. Using Food & You data, we show daily HEI correlates more strongly with microbiome diversity, and recommend co-reporting both metrics.

04.
arXiv (CS.CL) 2026-06-16

Does Traversal Order Matter? A Systematic Study of Tree Traversal Methods in Transformer Grammars

Transformer Grammars (TGs) enhance language modeling by incorporating syntactic tree structures. Despite the potentially significant impact on model performance of how syntactic trees are linearized in TGs, existing studies rely solely on Depth-First Traversal (DFT) for linearization. In this paper, we expand the traversal design space by exploring Breadth-First Traversal (BFT) and a novel hybrid traversal strategy, Production-Rule Traversal (PRT), which combines the structural lookahead of BFT with the early lexical generation of DFT. We integrate these traversal methods with varying tree configurations and masking strategies, and empirically evaluate their performance on language modeling, syntactic generalization and summarization. We reveal the inherent trade-offs between nested composition and global lookahead, providing actionable recommendations for designing task-aware Transformer Grammars.

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

Evaluation Sovereignty in Metadata-Driven Classification: A Multi-Track Framework for Weakly Supervised Information Systems

arXiv:2606.13436v1 Announce Type: new Abstract: Evaluation in machine learning is typically treated as a neutral measurement process. However, in operational information systems, evaluation outcomes are often conditioned by the processes used to generate labels. This paper does not seek to improve classification performance. Instead, it examines the validity of performance measurement under differing label-authority regimes. This issue is particularly relevant in large-scale metadata-driven systems, where labels are often incomplete, inconsistent, or weakly supervised. We introduce evaluation sovereignty, defined as the degree to which performance metrics are independent of label authority and supervision regime, and propose a multi-track evaluation framework that systematically varies training and evaluation label sources. Using hierarchical multi-label classification on large-scale scientific metadata, we demonstrate that models exhibiting strong performance under operational ("silver") evaluation degrade substantially under independent ("gold") evaluation, particularly for fine-grained classification. For example, Micro-F1 decreases from approximately 0.54 to 0.03. Notably, ranking-based metrics remain above baseline, revealing a divergence between latent model signal and classification validity. These findings suggest that commonly reported performance metrics may reflect alignment with labeling processes rather than true predictive capability. We therefore reconceptualize evaluation validity as a system-level property shaped by label governance and provide a practical methodology for auditing intelligent systems operating under weak supervision.

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

Finite-Element Matrix Product States for Continuum Models in One Dimension

arXiv:2606.14873v1 Announce Type: new Abstract: We present a matrix product state framework for simulating one-dimensional quantum many-body systems in the continuum using non-orthogonal single-particle basis sets. By mapping the physical problem to an auxiliary computational space, we show that the resulting many-body overlap operator can be efficiently encoded as a matrix product operator for sufficiently localized orbitals, thereby generalizing a construction that first appeared in [arXiv:2405.10285]. This construction recasts the variational ground-state search into a generalized eigenvalue problem, which can be solved using a generalized density matrix renormalization group algorithm. As a primary application, we employ a first-order finite-element expansion to study the ground state properties of the Lieb-Liniger gas in the presence of inhomogeneities. This approach also provides a natural setting for exactly refining the lattice, thereby enabling multigrid optimization strategies for matrix product states.

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

Optimizing Encoder Circuits of Entanglement-Assisted Quantum LDPC Codes via Beam Search

arXiv:2606.11468v1 Announce Type: new Abstract: Entanglement-assisted (EA) quantum QC-LDPC codes offer strong error-correction capabilities with structured parity-check matrices, but their practical use depends on efficient encoder circuits and the availability of pre-shared Bell pairs (ebits). In all encoder implementations based on the stabilizer formalism, the dominant contribution to this complexity comes from the use of controlled gates. In this paper, we adopt the Sharma-Kumar-Garani (SKG) encoder construction. We formulate the encoder optimization as a search over GF(2) row operations that decompose the binary matrix derived from its CNOT sub-sequence. We solve this problem using a beam search algorithm guided by a Hamming-distance heuristic. For the tested EA quantum QC-LDPC code families, the proposed method achieves CNOT-count reductions of 7.3-34.0% relative to the SKG baseline encoder. The optimized circuits also yield lower CNOT counts than Patel-Markov-Hayes synthesis on all tested instances and are verified by stabilizer-tableau simulation. These results show that substantial encoder simplification is possible for structured EA QC-LDPC codes.

08.
arXiv (quant-ph) 2026-06-19

Operational Tube-Sector Theory of Quantum State Distinguishability Under Generalized Symmetries

Authors:

arXiv:2606.19678v1 Announce Type: cross Abstract: A variational principle for quantum-state distinguishability is established in many-body systems with generalized symmetries, including noninvertible cases described by fusion categories. Standard fidelity and symmetry-resolved diagnostics emerge as coarse-grained limits of a more refined operational structure. When symmetry actions terminate at entanglement cuts, distinguishability is governed by boundary tube algebras within a symmetry-constrained measurement resource theory. The physically admissible instruments are characterized by complete positivity, entanglement-cut locality, boundary-module covariance, and sequential stability. The resulting optimal measurement structure is uniquely fixed by the center of the boundary tube algebra, $\mathcal{A}_{\mathrm{phys}} = Z\!\left(\mathrm{Tube}_{\mathcal{C}}(\mathcal{M}_A)\right)$, whose primitive idempotents define tube-sector probabilities that refine fidelity-based and symmetry-resolved descriptions. The associated tube positive-operator-valued measures (POVM) are extremal and yield optimal one-shot hypothesis-testing distinguishability under symmetry constraints. The construction is universal across fusion categories and independent of microscopic realization.

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

Deep Dense Exploration for LLM Reinforcement Learning via Pivot-Driven Resampling

Effective exploration is a key challenge in reinforcement learning for large language models: discovering high-quality trajectories within a limited sampling budget from the vast natural language sequence space. Existing methods face notable limitations: GRPO samples exclusively from the root, saturating high-probability trajectories while leaving deep, error-prone states under-explored. Tree-based methods blindly disperse budgets across trivial or unrecoverable states, causing sampling dilution that fails to uncover rare correct suffixes and destabilizes local baselines. To address this, we propose Deep Dense Exploration (DDE), a strategy that focuses exploration on $pivots$-deep, recoverable states within unsuccessful trajectories. We instantiate DDE with DEEP-GRPO, which introduces three key innovations: (1) a lightweight data-driven utility function that automatically balances recoverability and depth bias to identify pivot states; (2) local dense resampling at each pivot to increase the probability of discovering correct subsequent trajectories; and (3) a dual-stream optimization objective that decouples global policy learning from local corrective updates. Experiments on mathematical reasoning benchmarks demonstrate that our method consistently outperforms GRPO, tree-based methods, and other strong baselines. Code is available at https://github.com/AgentCombo/DEEP-GRPO

10.
arXiv (CS.AI) 2026-06-17

Optimism Stabilizes Thompson Sampling for Adaptive Inference

arXiv:2602.06014v2 Announce Type: replace-cross Abstract: Thompson sampling (TS) is widely used for stochastic multi-armed bandits, yet its inferential properties under adaptive data collection are subtle. Classical asymptotic theory for sample means can fail because arm-specific sample sizes are random and coupled with the rewards through the action-selection rule. We study adaptive inference for Thompson sampling with Gaussian randomized indices in $K$-armed stochastic bandits with independent sub-Gaussian reward noises, and identify optimism as a key mechanism for restoring stability, meaning that each arm's pull count concentrates around a deterministic scale. This stability yields asymptotically valid Wald inference despite adaptive sampling. First, we prove that variance-inflated TS is stable for any $K \ge 2$, including the challenging regime where multiple arms are optimal, with asymptotically uniform allocation over optimal arms and sharp logarithmic pull-count asymptotics for suboptimal arms. This resolves the $K$-armed extension question raised by \citet{halder2025stable}, using new winner-map and Lyapunov-drift techniques to control allocation among multiple optimal arms. Second, we analyze an alternative optimistic modification that keeps the Gaussian index variance unchanged but adds an explicit mean bonus to the index center, and establish a similar stability conclusion. In summary, suitably implemented optimism stabilizes Thompson sampling and enables asymptotically valid Wald inference in multi-armed bandits, while incurring only a mild additional regret cost.

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

Physics-Aware Auxiliary Losses Improve Out-of-Distribution Generalization of a GNN Synthesizability Filter

arXiv:2606.12651v1 Announce Type: new Abstract: Machine-learning drug-discovery pipelines increasingly rely on generative models that propose molecules far from the data used to train downstream synthesizability filters. Existing filters (SAScore, SCScore, RAscore, DeepSA) are purely statistical and degrade in exactly this out-of-distribution (OOD) regime. We ask whether cheap, closed-form physical priors, used as auxiliary supervision on a graph neural network (GNN), improve OOD generalization. We add two auxiliary losses to a GINE backbone: a topological complexity regression supervised by the Bertz index, and a strain-energy soft penalty supervised by MMFF94 force-field energy. On a 65,177-molecule corpus (HIV, Tox21, COCONUT) labeled by SAScore thresholds we reproduce a strong in-distribution baseline, then evaluate a 4-way ablation (baseline / +complexity / +strain / +both) on a single-source OOD split (train on drug-like HIV+Tox21, test on COCONUT natural products), repeated over 5 seeds with paired bootstrap confidence intervals. All three physics-aware variants give a small but statistically significant OOD improvement over the baseline (mean OOD AUC 0.9774): +complexity Delta = +0.0060 (95% CI [+0.0023, +0.0102]), +strain Delta = +0.0032 ([+0.0008, +0.0052]), +both Delta = +0.0066 ([+0.0038, +0.0093]); every interval excludes zero, and the combination is best. The variants are indistinguishable in-distribution, so the effect is visible only under OOD evaluation. We are explicit that the effects are modest, and we report a cautionary methodological finding: a single-seed version of this experiment produced a qualitatively different (non-monotone) story that did not survive multi-seed evaluation.

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

An Embodied Simulation Platform, Benchmark, and Data-Efficient Augmentation Framework for Wet-Lab Robotics

arXiv:2606.12936v1 Announce Type: cross Abstract: Wet-lab robots can improve the reproducibility, throughput, and safety of biomedical experiments, but scaling their learning requires customizable simulators for safe and reproducible task generation, open editable laboratory assets, and efficient pipelines that turn limited demonstrations into usable training data. We present Pipette, an embodied simulation platform, benchmark, and data-efficient augmentation framework for wet-lab robot learning. Pipette releases over 43 open-source and re-editable wet-lab assets, together with an extensible asset-building pipeline. A key component of Pipette is its simulation-based data augmentation pipeline, replaying human demonstrations in simulation, applies lighting, camera, speed, and action perturbations, and filters generated episodes with automatic task success checks, rapidly expanding usable training data from limited manual demonstrations. We further introduce an 11-task wet-lab embodied benchmark covering sample handling, culture-ware manipulation, device operation, and precision placement. With only 30 demonstrations per task, ACT achieves 65.5% average success rate, while simulation augmentation improves SmolVLA from 44.1% to 74.7% and {\pi}0 from 40.4% to 46.5%, validating the effectiveness of Pipette for data-efficient VLA training and evaluation. Pipette also supports natural-language-driven scene construction and task registration, lowering the barrier for non-expert users to define new wet-lab robotic tasks.

14.
arXiv (CS.CV) 2026-06-19

FrozenDrive: Zero-Shot Text-Guided Driving Scene Generation and Data Augmentation with Parameter-Free Frozen Diffusion Model

Synthetic data for autonomous driving is surging, powered by diffusion models that promise scalable scene generation. Yet key obstacles remain, as enforcing multi-view and temporal consistency often relies on backbone fine-tuning or added layers, which erodes pre-trained knowledge and weakens text alignment. Models also stay close to the training distribution, struggling under adverse weather and unseen configurations, and fidelity favors frequent over rare classes. We address these gaps with FrozenDrive, a controllable generative framework that preserves a pretrained diffusion models knowledge while achieving strong consistency. FrozenDrive conditions on rich driving-stack signals and text prompts, and introduces knowledge-preserving spatio-temporal attention to impose cross-view alignment and temporal coherence in a single pass within a parameter-free frozen diffusion backbone. An additional object-focused constraint improves per-object fidelity for rare categories. Without any weather- or scene-specific fine-tuning, our model synthesizes globally coherent multi-view driving scenes from text, particularly under adverse and rare conditions, and surpasses prior baselines. On nuScenes, FrozenDrive augmented data significantly improves AD models performance, especially at night and in rain, demonstrating stronger robustness when trained with our scenario-targeted data.

15.
arXiv (CS.LG) 2026-06-16

We Need Explanation Cards to Connect Explanation Algorithms to the Real World

arXiv:2606.16786v1 Announce Type: new Abstract: Algorithmic explanations are intended to help stakeholders understand opaque algorithmic decisions, but in practice, they often fall short. First, the meaning of algorithmic explanations is often not what one might intuitively expect, so expert knowledge is required to interpret them correctly. Second, recent work has shown that popular explanation algorithms are uninformative about the behavior of complex decision functions. Together, these issues create a gap between what explanations appear to convey and what they actually provide. In this work, we propose Explanation Cards for Explanation Algorithms, which augment standard explanations with complementary information about robustness and validity, as well as clear instructions for interpretation. The complementary information can render otherwise uninformative explanations practically useful, while also helping to detect cases where they are not. Importantly, the interpretation instructions in explanation cards shift responsibility from users to providers: Rather than expecting users to recognize what can and cannot be concluded from an explanation, providers must make this explicit upfront. Using counterfactual explanations and SHAP as examples, we demonstrate how providers can construct explanation cards and that these cards provide users with the guidance needed for sound interpretation. We further argue that explanation cards offer a practical means of operationalising the explainability provisions of the EU AI Act. Overall, explanation cards are a significant step toward making explanation algorithms fit for real-world use cases.

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

Triangular-Reference Schrödinger Bridges for Time Series Generation

arXiv:2605.27478v3 Announce Type: replace-cross Abstract: Schrödinger bridges for time series (SBTS) generate synthetic paths by projecting, in relative entropy, a Brownian reference onto the path laws that match the joint distribution of the data on the observation grid. The Brownian reference, however, fixes the quadratic variation of the generated paths, which is restrictive when stochastic volatility, correlated noise, or rank-deficient covariance structures must be reproduced. We introduce "Triangular-Reference Schrödinger Bridges for Time Series" (TR-SBTS), which keeps the entropy-projection backbone of SBTS but replaces the Brownian reference by a triangular, volatility-informed, intervalwise frozen reference on a state augmented with latent covariance descriptors. The construction remains a single entropy projection on the augmented state: the minimiser is the \(h\)-transform of the reference, and on each frozen interval the optimal drift has the logarithmic-gradient form \(b^\star(t,x)=A\,\nabla\log H(t,x)\), intrinsic to the active covariance directions when the frozen covariance \(A\) is degenerate. We prove stability of the frozen approximation and consistency of the associated regularised kernel estimators, describe a reference-aware Nadaraya–Watson implementation of the conditional next-increment law, and evaluate the construction on numerical experiments.

17.
PLOS Computational Biology 2026-05-29

Structural and dynamic basis of NOD2 tandem CARD association and NOD1/2–RIP2 signaling complexes

by Jitendra Maharana, Aritra Bej, Debasish Biswal, Debashis Panda, Arjun Sharma NOD1 and NOD2, founding members of the NOD-like receptor (NLR) family, play a crucial role in host defense against bacterial infections. Recognition of peptidoglycan-derived ligands triggers ATP-dependent oligomerization of the NACHT domain, exposing the CARD domains that recruit the adaptor protein RIP2 via CARD–CARD interactions to activate the NF-κB signaling cascade. Although NOD1/2-RIP2 interactions and RIP2CARD filament assembly are established, the precise interfaces that stabilize hetero–CARD filaments remain poorly defined. Here, we integrate in silico structural modeling with molecular dynamics (MD) simulations to elucidate structurally compatible arrangements of NOD1–RIP2 and NOD2–RIP2 hetero–CARD filaments. Our results reveal that NOD1CARD subunits form a structurally compatible homomeric scaffold via canonical (type-I–III) interfaces, accommodating multiple tiers of RIP2CARD rings at both filament termini. Meanwhile, the NOD2 tandem CARDs adopt multiple discrete conformations, reflecting a more intricate structural mechanism. In stable filament conformations, tandem CARDs converge at the type-II interface, with RIP2CARD rings stacking onto CARDa (top-down) and CARDb (bottom-up) interfaces, highlighting the structural role of NOD2CARDb in RIP2-mediated CARD–CARD interaction. In silico mutagenesis, involving charge-reversal and alanine scanning of key interfacial residues, disrupts NOD1–RIP2 and NOD2–RIP2 interactions at both top-down and bottom-up interfaces, leading to rapid interface destabilization within 0.1–0.4 μs of simulation. Together, these results reveal conserved and receptor-specific mechanisms governing NOD1/2–RIP2 CARD–CARD interactions and provide deeper structural and dynamic insights into the complex structural mechanisms for NLR-mediated inflammatory signaling.

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

Prior-Informed Flow Matching for Graph Reconstruction

arXiv:2601.22107v2 Announce Type: replace Abstract: We introduce Prior-Informed Flow Matching (PIFM), a conditional flow model for graph reconstruction. Reconstructing graphs from partial observations remains a key challenge; classical embedding methods often lack global consistency, while modern generative models struggle to incorporate structural priors. PIFM bridges this gap by integrating embedding-based priors with continuous-time flow matching. Grounded in a permutation equivariant version of the distortion-perception theory, our method first uses a prior, such as GraphSAGE or node2vec, to form an informed initial estimate of the adjacency matrix based on local information. It then applies rectified flow matching to refine this estimate, transporting it toward the true distribution of clean graphs and learning a global coupling. Experiments on different datasets demonstrate that PIFM consistently enhances classical embeddings, outperforming them and state-of-the-art generative baselines in reconstruction accuracy.

19.
arXiv (math.PR) 2026-06-12

Non-commutative Law of iterated logarithm

arXiv:2509.22037v2 Announce Type: replace-cross Abstract: We prove optimal non-commutative analogues of the classical Law of Iterated Logarithm (LIL) for both martingales and sequences of independent (non-commutative) random variables. The classical martingale version was established by Stout [Sto70b] and the independent case by Hartman-Wintner [HW41]. Our approach relies on a key exponential inequality essentially due to Randrianantoanina [Ran24] that improves that from Junge and Zeng [JZ15]. It allows to derive an optimal non-commutative Stout-type LIL just as in [Zen15], from that martingale result we then deduce a non-commutative Hartman-Wintner type LIL for independent sequences of random variables.

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

Battery detection of XRay images using transfer learning

The need for detecting and sorting batteries is drastically increasing for many applications. This study proves the potential of transfer learning in predicting whether the image contains a battery or not, the location and identifying three types of batteries, namely: prismatic, pouch, and cylindrical Lithium-Ion Batteries (LIB). Particularly, it focuses on the transfer learning method in two applications: Training a large-scale dataset to detect electronic devices using a pre-trained YOLOv5m, then using these latter trained weights to detect and classify the batteries. The precision of battery detection achieves 94%, which outperforms the pretrained YOLOv5m weights with 5%, in 22 ms inference time.

21.
arXiv (math.PR) 2026-06-16

Higher-order spectral perturbation expansions II: Kernel matrices and manifold learning

arXiv:2606.16373v1 Announce Type: cross Abstract: We study spectral concentration bounds for kernel matrices as approximation of the corresponding kernel integral operator. Results are established under weak assumptions on the data setting and the reproducing kernel relying only on a Mercer condition and a local Weyl law. This allows us to deal with key features of kernel matrices, such as large multiplicities, large effective dimension, and heavy-tailed distributions. Our results apply to infinite dimensional principal component analysis, manifold learning, and Bayesian nonparametric statistics. We illustrate this via two prototypical examples: The heat kernel on the sphere and a wavelet prior from Bayesian nonparametrics.

22.
arXiv (math.PR) 2026-06-11

The Statistical Compass

arXiv:2606.11282v1 Announce Type: cross Abstract: This monograph develops probability and stochastic-process ideas as a translation language for statistics: from designed observations and data objects to targets, stability statements, inference, and use. The chapters move from motivating examples and randomization through probability measures, kernels, likelihoods, data objects, weak convergence, empirical fields, functional data, M- and Z-estimation, testing, local approximations, event-time processes, and prediction. Historical and biomedical examples are used to keep abstract objects tied to records, mechanisms, and decisions. The aim is to give readers a common grammar for classical probability, modern data structures, and statistical practice.

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

RepNet: Tackling spectral bias in deep neural networks via parameter reparameterization

arXiv:2606.16575v1 Announce Type: new Abstract: Deep neural networks (DNNs) have achieved remarkable success in scientific computing, yet they often suffer from spectral bias in capturing oscillatory and multiscale behaviors. In this study, we investigate this limitation by examining the failure of shallow ReLU neural networks in fitting high-frequency functions. This observation identifies two important factors in resolving rapid oscillations: the initial slope scale and the distribution of partition points induced by the networks. Motivated by this analysis, we propose RepNet, a reparameterized DNN model for ReLU and tanh networks designed for high-frequency and multiscale problems. The key idea is to reparameterize the weights and biases in the first hidden layer, which enables effective control of the initial slope scale and provides an appropriate distribution of the initial partition points. Furthermore, treating the reparameterized weights and biases as trainable parameters allows the DNN to achieve adaptive frequency scaling during training. In addition, we derive quantitative estimates for the output and slope magnitudes of the reparameterized DNN to guide the initialization of the proposed method. Numerical experiments, including multiscale one- and four-dimensional function approximation, forward and inverse PDE problems in combination with physics-informed neural networks (PINNs), and operator learning, demonstrate that RepNet improves the predicted accuracy of vanilla DNNs in capturing highly oscillatory features with slightly additional computational cost. These results indicate that RepNet provides an effective and flexible approach for overcoming spectral bias and applying DNNs to multiscale problems.

24.
arXiv (CS.LG) 2026-06-11

Understanding Sample Efficiency in Predictive Coding

arXiv:2605.11911v2 Announce Type: replace Abstract: Predictive Coding (PC) is an influential account of cortical learning. Much of recent work has focused on comparing PC to Backpropagation (BP) to find whether PC offers any advantages. Small scale experiments show that PC enables learning that is more sample efficient and effective in many contexts, though a thorough theoretical understanding of the phenomena remains elusive. To address this, we quantify the efficiency of learning in BP and PC through a metric called ``target alignment'', which measures how closely the change in the output of the network is aligned to the output prediction error. We then derive and empirically validate analytical expressions for target alignment in Deep Linear Networks. We show that learning in PC is more efficient than BP, which is especially pronounced in deep, narrow and pre-trained networks. We also derive exact conditions for guaranteed optimal target alignment in PC and validate our findings through experiments. We study full training trajectories of linear and non-linear models, and find the predicted benefits of PC persist in practice even when some assumptions are violated. Overall, this work provides a mechanistic understanding of the higher learning efficiency observed for PC over BP in previous works, and can guide how PC should be parametrised to learn most effectively.

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

Dynamic Link Prediction with Temporally Enhanced Signed Graph Neural Networks

arXiv:2605.26290v2 Announce Type: replace Abstract: Temporal signed networks (TSNs) model the time evolution of cooperative and adversarial relationships that arise in applications such as social media analysis, trust and reputation systems, and financial transaction networks. While graph neural networks (GNNs) perform well for static or unsigned link prediction, effective learning in temporal signed graphs remains challenging due to the interaction of signed relations, evolving structure, and balance-theoretic constraints. To address this gap, we propose a modular temporal enhancement framework for signed GNNs that integrates historical context into otherwise static architectures. The framework introduces a Historical Context Integration Module (HCIM) that combines learnable recency-aware temporal weighting, LSTM-based embedding trajectory modeling, and multi-head temporal attention to capture both short- and long-term signed interaction dynamics. Historical information is fused with current node representations using either global or node-adaptive weighting, allowing the architecture-agnostic framework to accommodate heterogeneous temporal behaviors. We instantiate the approach on the Self-Explainable Signed Graph Transformer (SE-SGformer), preserving interpretability while extending it with temporal awareness. Experiments on real-world and synthetic TSNs, including Bitcoin OTC, Bitcoin Alpha, Reddit, and small-world network models, demonstrate consistent and statistically significant improvements over the static baseline.