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

FineREX: Fine-Tuned NER-RE for Human Smuggling Knowledge Graphs

Court proceedings contain valuable evidence about human smuggling networks, but this information is often buried within unstructured, jargon-heavy legal documents. While large language models (LLMs) can support knowledge graph construction through automated information extraction, existing approaches rely on general-purpose models that are not tailored to the entity and relationship definitions required in this domain. We introduce FineREX, a streamlined knowledge graph construction pipeline built around a fine-tuned LLM for named entity recognition and relationship extraction (NER-RE). Using a manually annotated dataset of $512$ text chunks, FineREX achieves absolute improvements of 15.50% and 31.46% in entity and relationship F1-score, respectively, compared to a larger general-purpose baseline. These gains translate into higher-quality knowledge graphs, reducing legal noise by nearly half and lowering node duplication on long documents from 17.78% to 11.17%. By eliminating document rewriting and redundant extraction stages, FineREX also reduces end-to-end processing time by 50.0%. Our results demonstrate that domain-specific fine-tuning can substantially outperform larger general-purpose models while improving both the quality and efficiency of knowledge graph construction for illicit network analysis.

02.
arXiv (quant-ph) 2026-06-25

Quantum magic of strongly correlated fermions $-$ the Hubbard dimer

arXiv:2605.18494v2 Announce Type: replace Abstract: We study the non-stabilizerness (quantum magic) content of the Hubbard dimer, an analytically solvable, yet completely non-trivial, model of strongly correlated fermions. We consider zero- and finite-temperature properties as well as the time evolution after a quantum quench drives the system out of equilibrium. We evaluate local and nonlocal non-stabilizerness using both the robustness of magic and the stabilizer Renyi entropy, demonstrating how the latter often fails in detecting the mixed stabilizer states that are typically found in this kind of systems. Finally, we compare the non-stabilizerness with other genuine resources of quantum-state complexity, i.e., the fermionic non-Gaussianity and the superselected two-site entanglement. Our findings corroborate the role of non-stabilizerness as a fundamental quantum resource, capturing aspects of quantum complexity that elude traditional information-theoretic measures and providing a novel perspective on fermionic systems with tunable interactions.

03.
arXiv (CS.LG) 2026-06-18

Complementary Attention Head Pruning for Efficient Transformers

arXiv:2606.19150v1 Announce Type: new Abstract: The remarkable success of Transformer-based models in natural language processing stems from architectural scaling, which leads to a large number of parameters and hinders deployment in resource-constrained environments. While structured pruning offers a pathway to compression, existing state-of-the-art methods often rely on gradient-based importance ranking or stochastic gating, which suffer from instability, structural degeneration, and the need for extensive manual hyperparameter tuning. In this paper, we introduce CAHP (Complementary Attention Head Pruning), a novel post-hoc framework that redefines head selection as a global graph-theoretical problem. Rather than evaluating heads in isolation, CAHP utilizes graph-based clustering combined with information-theoretic distance measures to identify and preserve a topologically diverse subset of complementary attention heads. Without requiring a predefined sparsity level or pruning ratio, the framework automatically determines the number of selected attention heads across layers by identifying a diminishing marginal performance curve, where pruning additional heads leads to a sharp degradation in performance, as determined by the chosen polynomial degree. Extensive evaluations on the SST-5 and MNLI benchmarks, across different Transformer model scales, demonstrate that CAHP consistently outperforms competitive baselines, particularly in high-compression regimes. Furthermore, our structural analysis shows that CAHP avoids the "proximity bias" of gradient-based pruning methods, which tend to preserve heads mainly in layers close to the output, and instead retains a functionally critical set of attention heads in the model's intermediate layers.

04.
arXiv (CS.CV) 2026-06-17

Predicting Immune Biomarkers with MultiModal Mixture-of-Expert Pathology Foundation Models Empowers Precision Oncology

Predicting immune biomarkers associated with the tumor immune microenvironment (TIME) is critical for advancing precision oncology, yet existing approaches are largely limited to single image modalities and suffer from insufficient resolution and incomplete utilization of complementary clinical and biological information. Here we introduce MixTIME, a multimodal foundation model that leverages a mixture-of-experts (MoE) architecture to integrate pathology foundation models trained across distinct modalities: image only (UNIv2), image text (CONCHv1.5), and image transcriptomic (STPath) representations for pixel-level and slide-level prediction of multiplex immunofluorescence (mIF) protein expression from hematoxylin and eosin (HE) whole-slide images. MixTIME employs a learnable router to dynamically weight expert contributions and is trained with a distribution- and tendency-aware loss function. Benchmarked on two datasets of different scales, MixTIME achieves state-of-the-art performance across 17 protein markers as measured by correlation metrics. The predicted mIF profiles substantially enhance downstream tasks, including spatial domain identification, survival prediction, and AI-assisted pathology report generation validated by expert pathologists from multiple institutes across the world. Furthermore, MixTIME enables longitudinal tracking of protein expression dynamics across clinical time points and reveals protein gene interaction patterns linked to drug resistance and immune suppression in tumor microenvironments. Collectively, MixTIME provides a scalable framework for multimodal biomarker discovery and clinical translation in computational pathology.

05.
arXiv (CS.AI) 2026-06-16

Heteroskedastic Signals in Budgeted LLM Verification: Structural Heterogeneity Limits Optimization Gains

作者:

arXiv:2606.15841v1 Announce Type: new Abstract: Large language model (LLM) systems increasingly use uncertainty signals to allocate limited computation across verification, test-time scaling, tool execution, and other selective-compute decisions. Such policies rely on a global signal comparability assumption: equal scores should carry comparable decision value across inputs. Using budgeted verification as a controlled diagnostic setting, we identify a failure mode of this assumption: uncertainty quality is heteroskedastic across cost strata, with some regions exhibiting near-random discriminability despite concentrating many errors. Under an explicit local model, we characterize the resulting distortion of global allocation and show that its upper bound scales with cross-stratum signal-quality dispersion. We separate weak signals, optimization instability, and structural heterogeneity through a controlled intervention hierarchy: Threshold, MP-Adapt, MP-Strat, and a deliberately simple cost-stratified thresholding intervention (CST). Across MBPP and MATH using Qwen3-8B, LLaMA3-8B, and GPT-4o-mini, global online adaptation yields inconsistent gains over static thresholding; MP-Strat partially recovers performance, while CST improves hit rate by up to 17 percentage points in strongly heterogeneous settings without gradient updates. These results identify structural heterogeneity, rather than optimizer weakness alone, as the primary bottleneck in the observed settings. More broadly, misaligned feedback structure cannot always be repaired by stronger optimization.

06.
Nature (Science) 2026-06-10

SIRT7 regulates dosage compensation and safeguards the female X chromosome

Sirtuins are deacetylases implicated in stress responses and longevity in mammals1,2. Although their differential impact on disease for the two sexes has been noted3–7, the underlying reasons are unclear. Here, using Sirt7 as a model in mice, we examine the mechanisms leading to sex differences and find that Sirt7−/− female mice have decreased fitness throughout their lifespan. Notably, SIRT7 preferentially localizes to the sex chromosomes. In female individuals, SIRT7 loss affects X-chromosome inactivation, the first arm of dosage compensation that equalizes X-linked gene expression between males and females8–10. Xist is overexpressed and gene silencing becomes more efficient. However, SIRT7 loss has greatest impact on the active X (Xa) chromosome. The Xa chromosome becomes hyperacetylated at Lys36 of histone H3, structurally disorganized, prone to DNA damage and overexpressed. Increased Xa-chromosome expression leads to genome imbalance and augmented X-chromosome upregulation—the second arm of dosage compensation that balances X-chromosome versus autosomal gene expression. These data reveal an essential crosstalk between sirtuins and the sex chromosomes, with SIRT7 safeguarding X-chromosome integrity and dosage balance with autosomes. We propose that the sex bias in SIRT7 biology can be explained in part by unequal effects on the sex chromosomes. SIRT7 safeguards X-chromosome integrity and dosage balance with autosomes.

07.
arXiv (quant-ph) 2026-06-24

Wavelet Matrix Product States for Quantum Fields

arXiv:2606.23823v1 Announce Type: new Abstract: We introduce a variational method to solve continuum quantum models with discrete tensor network techniques. The method leverages wavelet matrix product states (wMPS): matrix product states built on top of sufficiently regular ($N\geq 6$) Daubechies scaling functions. These states live in the continuum field theory Fock space, have finite energy density, and can be optimized with standard algorithms, without restriction to free theories. Further, exploiting the multi-resolution analysis built into wavelets, and its quantum circuit description, we can iteratively refine wMPS to obtain accurate approximations at arbitrarily fine length-scales. We showcase the efficiency of the method on the Lieb-Liniger model, computing energy density and correlation functions.

08.
arXiv (CS.CV) 2026-06-16

Task-Instructed Causal Routing of Vision Foundation Models for Multi-Task Learning

Vision foundation models (VFMs) have demonstrated strong robustness and transferability across a wide range of visual tasks. However, each model typically encodes strong inductive biases shaped by its pre-training objective and data domain, resulting in fragmented yet complementary visual knowledge. As a result, a single model often struggles to capture the diverse visual representations required across multiple dense prediction tasks. To address this limitation, we propose TIGER (Task-Instruction-Guided Expert Routing), a framework that coordinates multiple heterogeneous VFMs for multi-task dense prediction. Instead of naively aggregating expert features, TIGER leverages natural-language task instructions to guide a routing network that assigns token-level expert weights conditioned on task semantics, enabling adaptive integration of complementary expert features. TIGER further introduces a counterfactual loss that aligns routing decisions with each expert's causal contribution by measuring prediction changes when experts are excluded, encouraging more reliable and interpretable routing. We evaluate TIGER on two multi-task dense prediction benchmarks, NYUD-v2 and Pascal Context, where it consistently outperforms recent multi-task learning baselines while keeping all VFMs frozen. These results demonstrate that combining instruction-guided expert routing with counterfactual causal alignment enables effective coordination of heterogeneous vision foundation models.

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

Trimodal Glioma Representation Alignment via Volumetric Contrastive Learning

Glioma grading and survival prediction require the integration of heterogeneous information collected at different spatial and biological scales. Histopathology describes tissue morphology, mRNA expression captures molecular activity, and magnetic resonance imaging provides a non-invasive view of tumor extent and radiological heterogeneity. Existing glioma prognosis models often combine only two of these sources, while their alignment objectives remain mostly pairwise. This paper introduces GLORIA, a novel trimodal framework for GLioma Omics - Radiology - hIstopathology Alignment. GLORIA processes whole-slide image regions, gene-expression profiles, and 3D MRI volumes through modality-specific encoders, projects them into a shared latent space, and aligns them with a Gramian contrastive loss that measures the volume spanned by the three modality embeddings. The aligned representations are fused through a cross-modal gating module and optimized jointly for three-class glioma grading and overall survival prediction. We evaluate GLORIA on a matched TCGA-GBM/LGG and BraTS21 cohort, comprising 132 patients with all three modalities. On the shared trimodal test set, GLORIA improves over the bimodal WSI-mRNA baseline in all the metrics considered.

10.
arXiv (quant-ph) 2026-06-19

Quantifying Entanglement via Quantum Wasserstein Distances

arXiv:2606.04969v2 Announce Type: replace Abstract: We propose a bipartite entanglement measure defined as the minimal order-1 quantum Wasserstein distance from a state to the set of separable states. Owing to the universal data-processing inequality of the Wasserstein metric, the measure satisfies all fundamental axioms within a single geometric framework. A Lipschitz dual formulation yields explicit lower bounds for pure and mixed states, a sharp constant for two-qubit systems, and an expected value for Haar-random pure states. We further establish a quantitative connection to entanglement witnesses: any negative witness expectation value certifies a lower bound, and the dual variational bound is exactly the maximal violation achievable by a Lipschitz-1 witness. The approach naturally provides subadditivity, trace-distance estimates, and bounds on local observables, while pointing toward large-deviation conjectures. This work introduces a framework at the interface of entanglement theory, optimal transport, and experimental entanglement detection.

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

Anatomically Conditioned Recurrent Refinement for Topology-Aware Circle of Willis Segmentation

Segmenting the Circle of Willis (CoW) from Magnetic Resonance Angiography (MRA) is challenging due to complex topology and thin vascular structures that are prone to fragmentation. Standard Convolutional Neural Networks (CNNs) often fail to capture these topological constraints, resulting in "broken vessel" artifacts. To address this, we propose the Anatomically Conditioned Recurrent Refinement U-Net (AC2RUNet). Our architecture decouples segmentation into two streams: a Static Stream that extracts invariant anatomical features and a lightweight Dynamic Stream that iteratively refines topological errors over time. We further introduce a dynamic curriculum learning strategy that transitions from high-recall geometric supervision to topology-aware constraints. Validated on the TopCoW dataset, AC2RUNet substantially reduces Hausdorff Distance (4.72 mm vs 9.17 mm) and Betti number errors (0.19 vs 0.40), improving topological connectivity over the nnU-Net baseline while maintaining comparable volumetric Dice.

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

A Comparative Study of Deep Learning Architectures for Multi-Horizon Behavioural Forecasting for Mobile Health

arXiv:2606.14604v1 Announce Type: cross Abstract: Wearable devices and smartphones generate rich behavioural time series that can support proactive health interventions, yet systematic comparisons of modern forecasting architectures for these data are lacking. In particular, it remains unclear how models generalise across populations, how different architectures respond to participant-level fine-tuning and how forecasting accuracy degrades across multi-day horizons. We benchmark six deep learning architectures, two zero-shot Foundation Models (FM) and statistical baselines on three public datasets encompassing over 800 participants, reporting per-feature metrics for step counts, screen time and sleep duration across 1-8 day horizons. We further conduct a per-feature personalisation study across all six architectures and assess FM transferability across dataset sizes and temporal granularities. Our key findings are: (i) no single architecture dominates, PatchTST leads among trained models while the three runners-up (TCN, MLP, Transformer) show no meaningful performance difference; (ii) the FM TimesFM matches or exceeds trained models zero-shot, especially in low-data regimes and (iii) participant-level fine-tuning reduces per-feature RMSE by 16-60\%, with sleep benefiting most and step counts least. These results provide practical guidance on architecture selection, FM applicability and personalisation strategies for mobile health forecasting. To the best of our knowledge, this is the first study to jointly evaluate modern deep learning, FMs and personalisation for multi-horizon behavioural forecasting from wearables.

13.
arXiv (CS.AI) 2026-06-15

Mood-Aware Music Recommendation: Integrating User Affective Signals into Ranking Systems

arXiv:2606.13858v1 Announce Type: cross Abstract: Recommendation systems are essential in modern music streaming platforms due to the vast amount of available content. While collaborative filtering is widely used to suggest items based on the preferences of others with similar patterns, it performs poorly in domains where user-item interactions are sparse, such as music. Content-based filtering is an alternative approach that examines the qualities of the items themselves. Genre, instrumentation, and lyrics have been explored; however, relatively little attention has been given to emotion recognition. Since a user's emotional state strongly influences their music choice, incorporating mood signals offers a promising direction for personalization. In this work, we propose a mood-conditioned ranking framework that integrates user affective signals into the recommendation process via softmax-based sampling in the energy-valence space. We evaluate the approach via single-blind experiments in which participants compare recommendations from the proposed system against a baseline. The results indicate improved perceived recommendation quality, providing preliminary evidence for the effectiveness of incorporating mood-based inputs into music recommendations.

14.
arXiv (CS.AI) 2026-06-18

InstructTime++: Time Series Classification with Multimodal Language Modeling via Implicit Feature Enhancement

arXiv:2601.14968v2 Announce Type: replace-cross Abstract: Most existing time series classification methods adopt a discriminative paradigm that maps input sequences directly to one-hot encoded class labels. While effective, this paradigm struggles to incorporate contextual features and fails to capture semantic relationships among classes. To address these limitations, we propose InstructTime, a novel framework that reformulates time series classification as a multimodal generative task. Specifically, continuous numerical sequences, contextual textual features, and task instructions are treated as multimodal inputs, while class labels are generated as textual outputs by tuned language models. To bridge the modality gap, InstructTime introduces a time series discretization module that converts continuous sequences into discrete temporal tokens, together with an alignment projection layer and a generative self-supervised pre-training strategy to enhance cross-modal representation alignment. Building upon this framework, we further propose InstructTime++, which extends InstructTime by incorporating implicit feature modeling to compensate for the limited inductive bias of language models. InstructTime++ leverages specialized toolkits to mine informative implicit patterns from raw time series and contextual inputs, including statistical feature extraction and vision-language-based image captioning, and translates them into textual descriptions for seamless integration. Extensive experiments on multiple benchmark datasets demonstrate the superior performance of InstructTime++.

15.
arXiv (math.PR) 2026-06-18

First to reach $n$ game

arXiv:2506.08782v4 Announce Type: replace Abstract: We consider a game with two players, consisting of a number of rounds, where the first player to win $n$ rounds becomes the overall winner. Who wins each individual round is governed by a certain urn having two types of balls (type 1 and type 2). At each round, we randomly pick a ball from the urn, and its type determines which of the two players wins. We study the game under three regimes. In the first and the third regimes, a ball is taken without replacement, whilst in the second regime, it is returned to the urn with one more ball of the same colour. We study the properties of the random variables equal to the properly defined overall net profits of the players, and the results are drastically different in all three regimes.

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

HairPort: In-context 3D-aware Hair Import and Transfer for Images

Transferring hairstyles between images is an important but challenging task in computer graphics, computer vision, and visual effects. It enables users to explore new looks without physically altering their hair, with applications in virtual try-on systems, augmented reality, and entertainment. Most prior works operate best under small pose gaps, and they fall short under large viewpoint and scale differences, where missing hair content must be synthesized rather than transferred. We propose HairPort, a 3D-aware hairstyle transfer framework that attempts to solve these issues by explicitly separating hair removal from transfer and enforcing geometric consistency before synthesis. We introduce a Bald Converter, which produces realistic bald versions of faces through LoRA-based in-context adaptation of FLUX.1 Kontext. To train our Bald Converter, we introduce a new dataset, Baldy, containing 6,000 paired bald and original images across diverse identities and conditions. We also use a 3D-Aware Transfer Pipeline that reconstructs and re-renders the reference hairstyle from the target viewpoint before compositing it onto the source image. Being 3D aware, our method supports large pose and scale discrepancies between the source and target. Finally, a conditional flow-matching generator synthesizes the transferred result from the bald source and geometry-aligned reference guidance. Together, our method enables accurate, pose-consistent, and identity-preserving hairstyle transfer, outperforming existing methods both qualitatively and quantitatively.

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

G-IdiomAlign: A Gloss-Pivoted Benchmark for Cross-Lingual Idiom Alignment

Idioms are difficult to transfer across languages due to their non-compositionality and weak surface-form grounding, making literal mappings unreliable. We present G-IdiomAlign, a gloss-pivoted benchmark where each idiom is anchored by an English gloss from Wiktionary. We further construct a high-confidence reference alignment set for reproducible evaluation. G-IdiomAlign supports two protocols: (1) a controlled Multiple-Choice Idiom Equivalence with typed distractors for error attribution; and (2) a Gloss-Contrastive Generation contrasting No-gloss and With-gloss inputs to isolate the effect of an explicit semantic pivot. Across diverse LLMs, a bias to literal translation is a dominant failure mode, especially when the target is a low-resource language. Glosses consistently improve Gloss-Contrastive Generation under an embedding-based semantic proxy, but performance remains modest, indicating substantial headroom in the open output space. Subsequent analysis on Qwen3-8B further suggests that cross-condition differences are concentrated more in attention heads than in layers, while better With-gloss generations coincide with stronger gloss anchoring.

18.
arXiv (CS.CV) 2026-06-24

SignNet-1M: Large-Scale Multilingual Sign Language Video Dataset with Downstream Benchmarks

Sign language models are typically trained on datasets captured under constrained conditions, with limited viewpoint, background, and signer-identity diversity, leading to poor robustness under real-world distribution shifts. We introduce SignNet-1M, a large-scale augmented dataset spanning ASL, CSL, and German Sign Language (DGS). SignNet-1M synthesizes realistic variations along three axes: (i) novel-view rendering (rotation and zoom) via 3D Gaussian Splatting (3DGS), (ii) scene/identity editing via diffusion models for background replacement and signer substitution while preserving sign motion and linguistic content, and (iii) post-rendering augmentations that emulate capture and compression artifacts (e.g., pose/temporal perturbations and video-level corruptions) to better match in-the-wild recordings. Beyond data release, we provide a unified benchmark suite across downstream tasks (e.g., translation and recognition) and ablations that isolate each augmentation component. Experiments across backbones show that training with SignNet-1M consistently improves generalization under cross-view, cross-background, cross-identity, and post-rendering shifts, while maintaining strong in-distribution performance. The dataset, full augmentation pipeline, and benchmark are available at https://signnet.chatsign.ai/.

19.
arXiv (CS.CV) 2026-06-12

Plug-and-Play image restoration with Stochastic deNOising REgularization

Plug-and-Play (PnP) algorithms are a class of iterative algorithms that address image inverse problems by combining a physical model and a deep neural network for regularization. Even if they produce impressive image restoration results, these algorithms rely on a non-standard use of a denoiser on images that are less and less noisy along the iterations, which contrasts with recent algorithms based on Diffusion Models (DM), where the denoiser is applied only on re-noised images. We propose a new PnP framework, called Stochastic deNOising REgularization (SNORE), which applies the denoiser only on images with noise of the adequate level. It is based on an explicit stochastic regularization, which leads to a stochastic gradient descent algorithm to solve ill-posed inverse problems. A convergence analysis of this algorithm and its annealing extension is provided. Experimentally, we prove that SNORE is competitive with respect to state-of-the-art methods on deblurring and inpainting tasks, both quantitatively and qualitatively.

20.
arXiv (CS.AI) 2026-06-15

The Weight Norm Sets the Grokking Timescale: A Causal Delay Law

arXiv:2606.13753v1 Announce Type: cross Abstract: Grokking is the delayed onset of generalization in neural networks, arising long after they fit the training data. Whether the weight norm causes this delay is disputed: some studies report a critical norm at the transition, others observe grokking with no fixed norm at all. We settle this by intervening on the norm during training rather than only observing it. Under free training with weight decay, networks grok when the weight norm reaches a value Wc that varies little across seeds and learning rates (CV 1 to 2 percent) and grows with the modular base as a power law. When we instead clamp the norm to a fixed multiple rho of Wc and hold it there, the network still groks, but the delay follows T_grok proportional to exp(alpha rho). One exponent, alpha near 7.5, fits this delay across four moduli (R^2 = 0.996). Over the swept ranges the held norm moves the delay by about 19x and the learning rate by only about 2x, and holding the norm above Wc slows grokking rather than preventing it. A final LayerNorm removes the dependence by decoupling weight scale from the network function; without it the exponential law returns. This pinned-norm delay is the exponential counterpart to the logarithmic delay predicted for a freely contracting norm.

21.
Nature (Science) 2026-06-24

The mutational landscape of STING-induced immunity

作者:

Stimulator of interferon genes (STING) is an evolutionary conserved immune signalling protein with key roles in host defence, cancer, senescence and inflammation1–3. Downstream of STING, type I interferon, inflammatory cytokine signalling and non-canonical autophagy are governed by a multilayered mechanism integrating ligand-induced structural transitions, protein–protein interactions and coordinated intracellular trafficking4–13. Despite its central role in immunity and relevance as therapeutic target14, the sequence elements that govern STING (in)activation in cells remain incompletely understood. Here we developed a massively parallel assay to systematically chart the sequence-function landscape of STING. Profiling thousands of single amino-acid variants, we identified structural and functional determinants that shape the immunostimulatory capacity of STING and its ability to translate ligand recognition into distinct signalling outputs. Cryogenic-electron microscopy structures of select STING hyperactive variants revealed new regulatory principles dictating conformational transition from inactive to signalling-competent states of STING. Mutational effects are widespread across the functional landscape and can sensitize STING towards the natural ligand 2′3′-cGAMP15–18 or decouple interferon induction from non-canonical autophagy, demonstrating a diversity of possible responses that can be accessed through single point substitutions. Finally, our data showed the clinical and evolutionary relevance of naturally occurring STING protein variants. Collectively, these findings define molecular principles that tune STING activity and chart the landscape of its functional potential across immune contexts. A massively parallel assay systematically charts the sequence-function landscape of the STING signalling protein, and the findings define molecular principles that tune STING activity and show its functional potential across immune contexts.

22.
arXiv (CS.LG) 2026-06-17

Recursive Learning Without Collapse: A Weighting-Based Stabilization Framework

arXiv:2502.18049v5 Announce Type: replace-cross Abstract: Recent studies identified an intriguing phenomenon in recursive generative model training known as model collapse, where models trained on data generated by previous models exhibit severe performance degradation. Addressing this issue and developing more effective training strategies have become central challenges in generative model research. In this paper, we investigate this phenomenon within a novel framework, where generative models are iteratively trained on a combination of newly collected real data and synthetic data from the previous training step. To develop an optimal training strategy for integrating real and synthetic data, we evaluate the performance of a weighted training scheme in various scenarios, including Gaussian distribution estimation, generalized linear models, and nonparametric estimation. We theoretically characterize the impact of the mixing proportion and weighting scheme of synthetic data on the final model's performance. Our key finding is that, across different settings, the optimal weighting scheme under different proportions of synthetic data asymptotically follows a unified expression, revealing a fundamental trade-off between leveraging synthetic data and model performance. In some cases, the optimal weight assigned to real data corresponds to the reciprocal of the golden ratio. Finally, we validate our theoretical results on extensive simulated datasets and a real tabular dataset.

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

APEX: Automated Prompt Engineering eXpert with Dynamic Data Selection

Large Language Models are highly sensitive to prompt formulation, necessitating automatic prompt optimization to unlock their full potential. While evolutionary algorithms have emerged as the dominant paradigm, they suffer from a critical bottleneck: data efficiency. Current methods treat the development dataset as a static benchmark, wasting significant compute budget on uninformative data. In this work, we introduce APEX (Automatic Prompt Engineering eXpert), a novel framework that optimizes the data usage alongside the prompt search. APEX dynamically stratifies the dataset into Easy, Hard, and Mixed tiers based on the optimization lineage. By prioritizing the Mixed tier, which identifies the data where the LLM has mixed performance, we identify two high-leverage subsets: the addressable frontier for generating informative mutations and the rank-sensitive frontier for distinguishing candidate quality. We evaluate APEX across three diverse benchmarks: IFBench, SimpleQA Verified, and FACTS Grounding. Under a fixed budget of 5,000 evaluation calls, due to its data efficiency, APEX outperforms the initial prompt by an average of 11.2% on Gemini 2.5 Flash and 6.8% on Gemma 3 27B, demonstrating that a data-centric approach is key to efficient and effective prompt optimization.

24.
arXiv (CS.AI) 2026-06-17

The Discrete-Log Clock: How a Transformer Learns Modular Multiplication

arXiv:2606.17399v1 Announce Type: cross Abstract: When small transformers grok modular multiplication, prior work reports that the learned embedding has a "dense" Fourier spectrum requiring all frequencies. This contrasts with modular addition, where only a sparse set of key frequencies suffices. We show this density is an artifact of analyzing in the wrong basis. The natural Fourier transform for multiplication is not the standard additive DFT but the multiplicative character transform, which decomposes functions on the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ into its irreducible representations. Applying this transform to a grokked transformer trained on $a \cdot b \bmod 113$, we find the embedding spectrum becomes highly sparse (Gini coefficient 0.58 vs. 0.07 in the additive basis) with only 4 key frequencies carrying significant energy. Furthermore, 96.9% of MLP neurons are cleanly tuned to a single multiplicative frequency, and neuron activation heatmaps reveal 2D-periodic structure when reordered by the discrete logarithm. These results demonstrate the transformer reduces multiplication to addition in discrete-log space, implementing a "Discrete-Log Clock" algorithm analogous to Nanda et al.'s Clock algorithm for addition. The methodology generalizes: matching the analysis basis to the algebraic structure of the task reveals interpretable structure where standard tools see noise.

25.
arXiv (CS.AI) 2026-06-19

AURA: Adaptive Uncertainty-aware Refinement for LLM-as-a-Judge Auditing

arXiv:2606.19714v1 Announce Type: cross Abstract: Large language models (LLMs) are increasingly used as judges for open-ended generation, as large-scale human evaluation is often expensive and difficult to scale, yet their preferences remain imperfect proxies for human judgment. Existing auditing pipelines often assume that a reliable subset of examples or clean supervision signals are available beforehand, for example from human annotation, heuristic filtering, or the outputs of strong judges. In LLM evaluation, this assumption is fragile: the initial split may inherit judge bias, while human verification is typically too scarce to define stable groups at scale. We propose AURA, an adaptive uncertainty–aware refinement framework for auditing pairwise LLM–as–a–judge decisions under selected human verification. AURA iteratively learns a human-consistency signal, propagates reliable evidence, and prioritizes uncertain comparisons for human review. The key idea is to treat trust in a judge as a latent quantity that is progressively refined as evidence accumulates. We provide a compact formulation, a stable refinement procedure, and a comprehensive evaluation on both synthetic and real pairwise LLM-answer data.