Gradient-boosted trees achieve strong performance on tabular data, yet often leave a long tail of poorly predicted instances. We introduce a Trajectory-based Difficulty Score (TDS), an instance-level difficulty estimator for boosted ensembles derived from per-tree cumulative prediction trajectories. For each instance, we compute interpretable trajectory descriptors (e.g., variance, oscillation peaks, sign switches, and tail stability) and train a lightweight regression model to predict held-out loss. An empirical CDF calibrates the resulting signal into a score in $[0,1]$ that supports ranking hard cases. Across diverse tabular benchmarks and ensemble sizes, TDS exhibits strong rank correlation with error and outperforms established instance-hardness and uncertainty baselines on classification, while remaining competitive on regression. We then show how a single difficulty signal improves multiple data mining workflows: difficulty-driven active learning for label-efficient training, difficulty-thresholded selective prediction for improved risk-coverage trade-offs, and TDS-stratified (Mondrian) conformal prediction for more uniform conditional coverage. Finally, clustering high-TDS instances using SHAP attributions reveals coherent failure modes characterized by compact feature-value ranges, supporting error analysis and targeted data acquisition.

Cross-subject brain-to-visual decoding remains a core challenge in brain-computer interfaces due to severe inter-individual variability that induces systematic subject-specific functional misalignment. To address this issue, we propose MindAdapter, a parameter-efficient few-shot calibration framework for pretrained brain-to-visual decoding models. MindAdapter adopts a decoupled linear-residual cascade alignment paradigm by freezing a pretrained explicit brain functional alignment backbone (coarse) and introducing a lightweight nonlinear residual adapter (fine), thereby disentangling global cross-subject correspondence from subject-specific residual corrections for fine-grained spatial and semantic calibration. To further preserve global representational stability, we design a topology-anchored dual-stream manifold constraint, where a small set of shared stimuli serves as topological pins with voxel-level paired supervision, while a semantic stream enforces consistency through a frozen vision-language decoder on unpaired brain data. Together, MindAdapter efficiently injects subject-specific corrections while maintaining the global representational geometry learned during pretraining. Experiments on the Natural Scenes Dataset (NSD) demonstrate that MindAdapter substantially improves cross-subject visual reconstruction and retrieval accuracy using only a few shared stimuli, offering a practical and data-efficient solution for personalized brain-to-visual decoding.

Translating text embedded in Web images is crucial for improving content accessibility and cross-lingual information retrieval, particularly within social media and e-commerce domains. Although Large Vision-Language Models (LVLMs) have advanced multimodal understanding, applying them to Web image translation remains challenging due to the visual representation gap: standard encoders often prioritize high-level semantics over the fine-grained visual details required for recognizing diverse character morphologies. To address this challenge, we propose VaaWIT, an end-to-end framework that adapts Large Language Models for multilingual Web image translation. The framework introduces two key technical contributions: (1) a Dual-Stream Attention Module (DSAM), which facilitates bidirectional interaction between multilingual semantic features and detailed visual representations, thereby synthesizing unified features robust to textual variations; and (2) a Visual-Aware Adapter (VAA), a parameter-efficient fine-tuning strategy that dynamically injects these fused visual cues into the frozen LLM backbone. This design enables the model to align the visual context with linguistic reasoning effectively while minimizing computational costs. Extensive experiments on eight tasks on three public benchmarks demonstrate that VaaWIT significantly outperforms state-of-the-art (SOTA) open-source baselines and achieves competitive performance against proprietary models. These results validate the efficacy of integrating fine-grained visual perception into LLMs for complex Web content analysis.

Instruction-based video editing requires transforming a source video according to a natural-language instruction while preserving irrelevant content and remaining temporally coherent. We argue that existing Diffusion Transformer (DiT) editors struggle with this task for two structural reasons. First, conditioning signals are fed undifferentiated into all transformer blocks, forcing a single token stream to encode both global editing intent and fine-grained visual evidence. Second, the cross-attention patterns that govern the edit are supervised only indirectly through pixel-level reconstruction, leaving the model's internal reasoning process under-constrained. To address both limitations, we propose RVEDiT, an implicit Reasoning Video Editing DiT framework built around two complementary components. The first, Granularity-Routed Token Conditioning, introduces learnable editing tokens distilled from a multimodal LLM and routes them to shallow blocks, while reserving native visual and textual tokens for deeper blocks, thereby inducing a coarse-to-fine editing process inside the backbone. The second, Reference-Anchored Attention Alignment, employs a parameter-sharing reference branch during training and maximizes the mutual information between the attention features of the editing and reference branches, regularizing the model's internal reasoning without incurring any additional inference cost. Experiments on standard instruction-based video editing benchmarks show that RVEDiT consistently outperforms state-of-the-art baselines, with particularly strong gains on localized and compositional edits.

Mean cross-entropy is the standard validation metric for language models, but it can fail to track model quality during training. We examine this in two common scenarios. First, in Qwen2.5-1.5B SFT on synthetic fact-learning, we find that mean CE rises substantially after the initial learning phase while held-out fact-recall accuracy remains near its peak. Second, we find that in top-K distillation on TinyStories, decreasing K improves median CE while worsening mean CE; the Top-5 student attains the highest LLM-judge score and crosses below its teacher on median CE, despite having the worst mean CE. In both cases, median CE correlates much more closely with task performance than does mean CE. Analyzing how bulk and tail percentile CE move during training reveals that training reshapes the empirical per-token CE distribution. In top-K distillation, smaller K yields a distribution with more mass at both extremes, decreasing the median and increasing the mean. In Qwen SFT, the bulk saturates quickly while the tail extends in the latter half of training. In both, the task-evaluation metric appears more sensitive to the bulk than to the tail. Practically, we recommend reporting a small set of percentile CE summaries alongside the mean, and using concordance among them as a tool to keep track of distribution reshaping, as well as a low-cost diagnostic for when mean and median CE disagree on model selection.

LLMs have achieved remarkable success in complex reasoning tasks, yet current evaluation approaches predominantly rely on final-answer correctness, offering limited insight into the underlying reasoning processes that produce those answers. To address this gap, this study proposes a unified multi-dimensional framework for measuring reasoning quality in LLMs from a behavioral perspective, operationalizing six theoretically grounded dimensions: Correctness (CQ), Consistency (CS), Robustness (RS), Logical Coherence (LS), Efficiency (ES), and Stability (SS). Extensive experiments on seven LLMs across 975 items from four benchmarks demonstrate that the framework reveals behaviors invisible to accuracy-only metrics. Notably, logical coherence is orthogonal to correctness (r = -0.172, ns), confirming that correct answers can arise from incoherent reasoning, while Claude-Haiku-4.5 achieves the highest multi-dimensional score (Q_bal = 0.778). Furthermore, the framework exposes critical ranking inversions: DeepSeek-V3 ranks second under accuracy-priority but fifth under legal/compliance weighting, a reversal that single-metric evaluation cannot detect. Discriminant validity confirms 11/15 dimension pairs are independent (|r| < 0.50), providing psychometric support for treating each dimension as a distinct signal. The dimensional profiles produced by the framework directly support three classes of deployment decision: identifying models whose reasoning traces would fail accountability audits despite correct final answers (LS--CQ orthogonality); preventing ranking errors caused by accuracy-only benchmarking; and ensuring that no single metric silently substitutes for the six independent signals the framework captures.

LLM-based agents are increasingly deployed for complex tasks requiring planning, tool use, and interaction with external services. Their reliance on untrusted external content exposes them to indirect prompt injection (IPI), in which adversarial instructions embedded in retrieved data hijack agent behavior. Existing attacks rely on static payloads that cannot adapt to agent-specific defenses; even recent adaptive methods lack structured feedback to guide optimization. We introduce \oursys, a feedback-guided iterative framework that closes the loop between injection, diagnosis, and refinement: a rule-based diagnoser produces structured outcome labels with behavioral descriptions, and an LLM-based optimizer refines payloads conditioned on the full optimization history. A synthesis step generates new disguise seeds from failure patterns, enabling the strategy space to self-evolve. On AgentDojo and InjectAgent, \oursys substantially outperforms static baselines and existing adaptive methods across four victim models. Extension experiments on Claude Code, a production-grade coding agent with layered defenses, show that optimized payloads achieve full success on 5 of 9 targets; even those that resist full exploitation exhibit measurable improvement from iterative refinement. We further present a mechanistic analysis of IPI, identifying an attention-mediated threshold mechanism in mid-to-late layers; three causal interventions validate this finding and point to concrete defense directions.

This work introduces the Wavelet-Laplace Neural Operator (WLNO), a novel neural operator that fuses Haar wavelet multi-scale spatial decomposition with the Laplace-domain pole-residue formulation of the Laplace Neural Operator (LNO). While LNO captures transient and steady-state dynamics through learnable system poles and residues, it lacks an explicit mechanism for extracting spatially localized multi-scale features inherent in complex PDE solutions. WLNO addresses this by augmenting the LNO core with a parallel single-level Haar discrete wavelet transform (DWT) branch that decomposes the lifted feature map into four frequency subbands: approximation (LL), horizontal detail (LH), vertical detail (HL), and diagonal detail (HH) and applies independent learned $1\times1$ convolutions to each subband before reconstruction via the inverse DWT. The two branches are fused through a learnable sigmoid-gated weight $α_\mathrm{wav}$, initialized to give a small initial contribution to the wavelet branch, allowing the model to adaptively balance Laplace-domain dynamics against spatial multi-scale features throughout training. WLNO is evaluated against LNO on five benchmark PDE problems using identical hyperparameters, training data, and evaluation protocols: the diffusion equation, the Burgers equation, the reaction-diffusion system, Darcy flow, and the two-dimensional Navier-Stokes equation. WLNO consistently outperforms LNO on all five problems, with the most pronounced improvement on problems with strong spatial multi-scale structure, such as the Burgers equation with sharp shock fronts and the Navier-Stokes equation with coherent vortical structures, while remaining consistent across smoother and elliptic problems. These results demonstrate that wavelet-based multi-scale spatial decomposition is a principled and effective complement to Laplace-domain operator learning.

Major LLM platforms deploy models in an inference-only configuration: the model serves requests but never updates per-user weights. Users must repeatedly re-teach preferences, corrections, and project context, and context-based workarounds consume context-window space and degrade under cascading compaction. We evaluate an alternative: nightly consolidation of interaction knowledge into model weights via reflection, synthesis, and Low-Rank Adaptation (LoRA) fine-tuning on a single consumer GPU. Across ten realistic software development conversations (n = 10, 1,146 test questions across three memory types), three cycles of cascading compaction retain 36.8 +/- 3.0% of knowledge (between an 11.8% no-context floor and a 90.1% full-context ceiling), while consolidation retains 80.4 +/- 1.3% -- a 43.6 pp gain (paired t(9) = 14.8, p < 0.001) that more than doubles what compaction preserves, with the largest gains on procedural corrections (36.3% -> 74.6%) and episodic project facts (31.5% -> 78.2%). As a methodological aside, mean per-token validation cross-entropy is negatively correlated with LLM-judged accuracy (r = -0.51) while median per-token validation cross-entropy tracks accuracy almost exactly (r = +0.99): under evaluators that tolerate surface-form variation, the mean is misleading and a heavy-tail-robust statistic is the faithful signal. Persistent personalization requires moving beyond inference-only deployment toward architectures that consolidate knowledge into weights.

Rapid advances in audio-video (AV) generation have enabled high-fidelity synthesis with synchronized sound, particularly for human-related scenarios involving speech and interactions. Yet evaluation for AV generation remains at an early stage, with only a few coarse-grained benchmarks for human-related scenarios and relying on limited preset evaluations with generic multimodal LLMs, leading to inaccurate assessments of model capabilities. To address these issues, we introduce AVBench, a fully automated benchmark tailored for human-centric AV generation. AVBench is built on two key designs for comprehensive and accurate evaluation: (i) Human-centric and fine-grained metrics. AVBench integrates ten evaluation dimensions designed for human-centered real-world scenarios, covering visual quality, audio quality, and multi-level consistency across modalities. These practical metrics capture human-related details that existing benchmarks often overlook. (ii) Specialized evaluators via preference learning. To address the lack of specialized training data, we construct large-scale supervision by transforming real-world videos into diverse training pairs with controlled perturbations. After fine-tuning on this high-quality dataset, the evaluators learn to reliably detect subtle cross-modal inconsistencies. Crucially, instead of producing discrete textual judgment, AVBench derives continuous evaluation scores from the model's prediction confidence on binary decisions. This probabilistic scoring mechanism enables a more reliable assessment than traditional VQA-style evaluation and aligns closely with human judgment. Taken together, AVBench offers automated evaluation for AV generation, demonstrates strong potential for data filtering, and serves as a differentiable reward signal for Reinforcement Learning from Human Feedback (RLHF).

Personalized dialogue requires more than recalling explicit user histories: systems also need to infer hidden user states that evolve through interaction and shape appropriate response strategies. Existing memory- and profile-based methods primarily reuse observable user information, offering limited support for modeling user-state dynamics or selecting actions based on how they shape future user states. We propose PUMA (Prospective User-state Modeling for Action selection), a framework grounded in the Free Energy Principle (FEP) that formulates personalization as decision-making under partial observability, centered on an explicit user state model that captures latent user states and their action-conditioned dynamics. At each turn, PUMA maintains a belief over the user's hidden state, refines the user state model for observation generation and action-conditioned state transition, and selects dialogue actions by minimizing expected free energy, balancing epistemic and pragmatic objectives under a unified criterion. This formulation shifts personalization from passive memory retrieval to model-based decision-making over user evolution. We instantiate PUMA on healthcare-oriented counseling and motivational interviewing benchmarks with latent state annotations for rigorous evaluation. Experiments show that PUMA improves long-horizon dialogue outcomes while maintaining strong response quality, and a cross-dataset study demonstrates more reliable user-state estimation and next-state prediction.

This paper presents reinforcement learning (RL) policies for dynamic quadrupedal locomotion in planetary exploration scenarios. Building on a taskoptimized quadruped with a 5-bar leg design, we develop RL policies for walking, vertical jumping, forward jumping, and in-flight attitude control, explicitly tailored to the reduced gravity on Mars. These policies jointly enable such robots to overcome obstacles larger than themselves through coordinated jumping and precise in-flight reorientation for safe landings. We demonstrate Sim2Real transfer of the attitude control policy on the Olympus quadruped through single-axis reorientation tests, while all locomotion policies are validated in simulation. A complete Mars exploration mission scenario demonstrates coordinated policy deployment across challenging terrain. Experimental results show 90° attitude reorientation in 2.6 seconds, with simulations demonstrating 3.1 meter vertical jumps and 3.9 meter forward jumps under Martian gravity conditions. - Supplementary video: https://www.youtube.com/watch?v=qlSJ3P87A4A

Recent work explores new opportunities at the intersection of vision-language-action models (VLAs) and geometric foundation models (GFMs) for 3D reconstruction, such as VGGT. While the resulting geometric VLAs often show improved performance, it remains unclear (i) if modern VLAs already have sufficient geometric understanding to start with, (ii) what is the best architecture to inject geometric understanding into a VLA, and (iii) what is the effect of other design choices that affect geometric VLAs. In this paper we provide a rigorous experimental analysis to shed light on these questions, for a specific choice of VLA (GR00T-N1.5) and GFM (VGGT). Our first contribution is to formalize prior work's intuition that current VLAs lack geometric understanding, by providing a rigorous analysis based on linear probing. The analysis quantifies, for the first time, the "geometric gap" between VLAs and GFMs. Our second contribution is to identify and compare different strategies to bridge GFMs with VLAs. We implement three different architectures, which differ in the way they inject geometry in the VLA, while keeping low-level implementation details as similar as possible, to ensure a fair comparison. Finally, we analyze the impact of non-architectural choices (e.g., training data, number of cameras, reconstruction quality) on the performance of the geometric VLAs.

With the widespread application of drones in recent years, object detection of aerial images has attracted increasing attention, especially open-vocabulary aerial detection which is not restricted to predefined categories. Due to the scarcity of drone's viewpoint images and their significant differences from natural images, it is difficult to achieve satisfying results by directly applying vanilla open-vocabulary detection methods designed for natural scenarios. Some studies propose to transfer knowledge from pre-trained models by using lightweight networks or generating pseudo labels, but they tend to rely on models trained on natural images, neglecting the potential of foundation models specifically tailored for remote sensing and aerial imagery. To address this limitation, we propose DisDop, a unified framework that systematically distills multi-level domain priors from remote sensing foundation models (e.g., RemoteCLIP and DINOv3) into a lightweight detector. Specifically, we first distill visual priors through a teacher fusion strategy that combines RemoteCLIP's cross-modal alignment capability with DINOv3's fine-grained local feature extraction ability, transferring their complementary strengths to the detector's backbone. Second, we distill textual priors embedded in RemoteCLIP's text encoder by explicitly modeling inter-category semantic relationships, while incorporating global contextual priors to enhance local feature representation for small objects. Through this multi-level prior distillation framework, our DisDop achieves new state-of-the-art performance on open-vocabulary aerial detection benchmarks. Extensive ablation analysis also demonstrates the rationality and effectiveness of our proposed modules.

Medical large language models hold promise for reducing healthcare disparities, yet Hindi remains severely underrepresented. While medical LLMs excel in high-resource languages, their performance degrades sharply in Hindi, particularly on Indian systems of medicine. We argue that robust cross-lingual medical transfer requires Hindi reasoning. To this end, we introduce HiMed, a Hindi reasoning medical corpus and benchmark suite covering both Western and Indian medicine. We further propose HiMed-8B, a Hindi-form medical reasoning LLM, through the design of decaying scaffolding reward. Extensive experiments demonstrate improvement in Hindi medical reasoning performance and reduction in the English--Hindi accuracy gap. Ablation studies validate the contribution of each training stage and reward component. All data and code are available on GitHub: https://github.com/FreedomIntelligence/HiMed.

Minority sampling aims to generate low-density instances on a data manifold and is of central importance in applications such as medical diagnosis, anomaly detection, and creative AI. Existing approaches, however, define minority samples relative to generative priors learned from training data, confining rarity to model-specific notions that may poorly reflect real-world semantics. In this work, we propose a world-centric perspective on minority sampling, which defines rarity with respect to real-world priors rather than generator-induced densities. To this end, we introduce JEPA guidance, a diffusion sampling framework guided by a Joint-Embedding Predictive Architecture (JEPA) -- a class of world models that encode broad, semantically rich representations. JEPA guidance steers diffusion trajectories toward low-density regions under the implicit density induced by the JEPA, thereby aligning generated minorities with real-world semantic rarity. To make JEPA guidance computationally practical, we develop principled approximation strategies accompanied by theoretical error bounds, significantly reducing the overhead of guidance computation. Extensive experiments across unconditional, class-conditional, and text-to-image generation demonstrate that JEPA guidance consistently improves the fidelity and semantic validity of minority samples, outperforming generator-centric baselines in capturing real-world notions of rarity. Code is available at https://github.com/soobin-um/jepa-guidance.

Recent progress of video diffusion models have enabled extensive simulation of the physical world. While simulation with hand object interaction has been less explored. We propose DexSIM, a dexterous simulation framework for simulating dexterous manipulation in real-time. While previous works utilizing video diffusion and 3D reconstruction focus on navigation, dexterous manipulation has been limited while it has extensive applications for creating interactive experiences with the simulated world and for generating synthetic data for robotics. Existing methods lack real-time interactivity and long-term spatial consistency and memory. We propose a 2-stage training framework for DexSIM. First we train a bi-directional video diffusion model by jointly embedding the hand action trajectory and video in a unified feature space. We utilize gaussian heatmap hand encoding for more accurate hand representation. Then we conduct a roll-out based autoregressive training with updated spatial cache as attention sink for spatial memory, which improves long-term consistency and 3D aware dexterous manipulation simulation. DexSIM outperforms the baseline on pixel and semantic similarity, motion fidelity, and hand projection accuracy. It also allows new applications such as hand motion transfer and runs at 15.24 FPS real-time interactivity.

Ultra-low-field (ULF) MRI offers portable and accessible neuroimaging but suffers from reduced signal-to-noise ratio and limited spatial resolution compared to high-field (HF) systems. Acquiring paired ULF-HF data for supervised enhancement is often difficult, particularly in resource-limited settings. We introduce ULF-Synth, a framework that combines: (i) acquisition-based synthesis of realistic ULF images from HF volumes to create large-scale paired training data, (ii) a spatial-frequency domain objective that prioritizes recovery of high-frequency anatomical detail. This formulation is architecture-agnostic, consistently improving structural similarity and perceptual fidelity across encoder-decoder, adversarial, and diffusion-based translation models. When trained exclusively on synthetic data, the resulting models generalize effectively to real 64mT ULF acquisitions, improving downstream multiclass brain segmentation and achieving higher radiologist preference and diagnostic acceptability in a blinded reader study. These findings demonstrate that synthetic paired supervision provides a practical and scalable pathway for enhancing ULF MRI without requiring real paired acquisitions. Code, Models and Dataset: https://github.com/toufiqmusah/ULF-Synth

In-context image generation models such as FLUX.2 take a text prompt and an optional reference image as visual conditioning for the output. Internally, all three inputs -- text, reference image, and the noise tokens -- are concatenated and processed through a single attention stream, where all tokens can attend to one another. This leaves open how reference information flows through the model to produce the output image. We show that an implicit cross-modal binding emerges between the text tokens and the reference image: the text tokens absorb visual reference content during the forward pass, and that absorbed content causally influences the generated output. We surface this binding with three causal interventions on FLUX.2: T2I Lens, which decodes intermediate text-token activations through a text-to-image path; Attention Knockout, which severs specific attention edges; and I2I-to-I2I Patching, which copies text token activations between editing runs. Across 2,875 editing tasks on various images, including SUN397 and DreamBench++ datasets and images collected online, we observe a consistent division of labor: properties of the reference image, like color, style, and scene setting, are first written into the text tokens, which carry them to the generated image; pixel-exact properties like a specific face or instance identity bypass the text tokens and flow directly from reference to image through image-to-image attention. We further localize the reference-text binding to the padding tokens of the text sequence. These results show that text tokens in a multimodal DiT are not just prompt holders, but a structured channel for reference image content. More broadly, they suggest that even in unified-attention multimodal generative models, token modality structures how conditioning information is represented and routed across the network.

A robot resolving ``put the cup on that one'' must fuse gesture, language, and scene geometry, yet 3D grounding benchmarks only partially capture this regime: descriptions are written post-hoc, gestures are templated, or pointing is staged for the camera. MM-Conv captures natural co-speech gesture from dyadic VR interaction alongside full-body motion capture and 3D scene graphs. We use it to evaluate pose-language fusion with a decoupled late-fusion architecture in which pose and text pathways share no learned parameters. The two choices together make category, pose, and text contributions easier to isolate through controlled ablations. Fusion with frozen MiniLM category embeddings exceeds pose alone and the best text-only pathway on every reference type, reaching 31.9% top-1. The learned scalar gate flips between opposing policies depending on whether the text pathway has category access. This is a reliability diagnostic: fusion-accuracy claims for semantic grounding systems are indistinguishable from category-representation artifacts unless pathways are architecturally decoupled.

Scattering transforms achieve Lipschitz stability and translation invariance, but dense prediction tasks require preserving spatial structure lost in global averaging. We propose Phase-Aware Scattering Encoder-Decoder, which restores this information by explicitly preserving phase in skip connections. On image denoising (BSD68), breaking translation invariance improves PSNR by $+2.17$~dB; phase preservation adds $+1.03$~dB. A novel spatial shuffling ablation ($-1.26$~dB penalty) demonstrates phase encodes location-dependent structure. We conduct a preliminary extensibility study on a second dense prediction task (ISIC skin lesion segmentation), with full cross-validation as ongoing work. This work advances principled wavelet-deep learning integration, showing how phase information complements scattering's stability-expressiveness trade-off in pixel-level prediction.

Large language model (LLM) unlearning has emerged as a crucial post-hoc mechanism for privacy protection and AI safety, yet auditing whether target knowledge is truly erased remains challenging. Existing output-level metrics fail to detect when this knowledge remains recoverable from internal representations. Recent white-box studies reveal such residual knowledge but often rely on auxiliary training or dataset-specific adaptations, leaving no generalizable metric. To address these limitations, we propose the Unlearning Depth Score (UDS), a metric that quantifies the mechanistic depth of unlearning via activation patching. UDS first identifies layers that encode the target knowledge using a retain model baseline, then measures how much of it is erased in the unlearned model on a 0-1 scale. In a meta-evaluation across 20 metrics on 150 unlearned models spanning 8 methods, UDS achieves the highest faithfulness and robustness, confirming our causal approach as the most reliable for unlearning evaluation. Case studies further reveal that white-box metrics can disagree at the layer level and that erasure depth varies across examples. We provide guidelines for integrating UDS into existing benchmarking frameworks and streamlining the evaluation pipeline. Code and data are available at https://github.com/gnueaj/unlearning-depth-score

Post-hoc repair of LLM mathematical reasoning introduces an asymmetric risk: fixing an incorrect reasoning trace is useful, but replacing a trace that was already correct can be harmful. We study this problem under a selective replacement setting, where a system must decide whether a repaired candidate is safer than preserving the original cached trace. We present GuardedRepair, a guarded best-of-N repair framework that diagnoses cached reasoning traces, selectively triggers repair, and accepts answer-changing candidates only when deterministic verification guards support replacement. The framework combines lightweight symbolic checks, surface semantic-risk diagnostics, bounded candidate generation, and conservative acceptance policies. On the full GSM8K test set, where the initial reasoner already achieves 95.60% accuracy, GuardedRepair improves final accuracy to 96.89%, fixing 17 of 58 remaining errors without measured broken-correct cases in the main run. On a weak-reasoner ASDiv setting, accuracy improves from 78.40% to 87.60%. Direct regeneration baselines show that this gain is not explained by stronger-model re-solving alone: re-solving all GSM8K examples lowers accuracy to 93.03% and breaks 47 initially correct answers. Additional analyses show that guarded repair substantially improves the fixed/broken tradeoff, while also revealing that replacement risk is reduced rather than eliminated. These results support viewing post-hoc repair as harm-aware selective replacement rather than unconstrained re-solving.

Classical Hopfield networks are limited to static patterns due to symmetric weights, whereas asymmetric networks can encode temporal sequences via limit-cycle attractors. Achieving high-capacity storage of long sequences in classical synchronous asymmetric networks, however, has remained a challenge. We present a simple and robust construction within the classical asymmetric Hopfield model with binary neurons and synchronous updates, that allows $n$ neurons to support $\exp\!\big(Ω(n/(\log n)^2)\big)$ distinct limit-cycle attractors, each with period $\exp\!\big(Ω(\sqrt n/\log n)\big)$ and robust to random noise with flip probability up to $\frac12-o(1)$, yielding superpolynomial capacity in both the number and length of stored sequences. This is the first demonstration of such capacity for asymmetric Hopfield networks, which we obtain by combining results from combinatorics, number theory and the analysis of opinion dynamics. Our findings show that synchronous asymmetric Hopfield networks possess a sequence-memory capacity which is larger and more robust than previously recognized, demonstrating that, in both biological and artificial neural systems, robust sequence representation can be achieved through coarse architectural motifs rather than complex nonlinearities.

We develop a rigorous algebraic framework for deep convolutional architectures, CNNs, ResNets, and encoder--decoder networks such as UNet, grounded in lattice theory and mathematical morphology. The central tool is the Matheron--Maragos--Banon--Barrera (MMBB) universal representation theory for translation-invariant operators, which we apply systematically to every layer of a standard deep network. The principal finding is that the standard CNN pipeline (linear convolution~$+$ ReLU~$+$ flat max-pooling) is a cross-lattice operator: the convolution is an erosion in the Fourier inf-semilattice while ReLU is a lattice-join closing and max-pooling is a dilation in the pointwise max-plus lattice, and their composition is a morphological opening in neither. A second finding is that the upper adjoint of ReLU in the pointwise lattice is a global (non-local) operator, the identity on globally non-negative functions and $-\infty$ otherwise, so no local morphological erosion can form an adjunction pair with ReLU. These two results together provide the precise algebraic reason why depth in standard CNNs introduces genuine representational power: the composed layer is not idempotent. Three layer designs that are genuine idempotent openings are identified and fully characterised: the pure max-plus morphological layer (pointwise lattice), the spectral Wiener layer (Fourier lattice), and the self-dual morphological layer. We establish a complete fixed-point and convergence theory. The framework also unifies max-pooling, strided convolution, and the Laplacian pyramid under the Goutsias--Heijmans adjoint pyramid theory, and gives the Activation--Pooling Dilation (APD) factorisation with its correct adjoint.

Event cameras capture brightness changes asynchronously with microsecond resolution, yet existing optical flow methods fail to fully exploit this temporal continuity. Frame-based approaches impose artificial accumulation latency and suffer from domain overfitting, while model-based local methods operate statelessly, discarding temporal history between predictions and yielding inaccurate flows. We propose \textbf{LC-Flow}, the first temporally continuous, learning-based optical flow estimator that operates purely from local events. At its core, a Continuous Local Recurrent Network maintains persistent hidden states per spatial grid, incrementally accumulating temporal context as events arrive. Unlike frame-based methods constrained to fixed accumulation windows, and unlike stateless model-based methods that recompute motion from scratch at each step, LC-Flow produces sparse local flow estimates at arbitrary timestamps with full motion history. To address the inherent ambiguity of local observations, we jointly learn a confidence score that quantifies the reliability of each prediction, explicitly handling event sparsity and the aperture problem. This confidence serves a dual role: filtering unreliable estimates for downstream tasks such as visual odometry, and providing principled weights for a multi-scale confidence-guided aggregation that reconstructs globally consistent flow from the sparse local outputs. LC-Flow achieves state-of-the-art performance among local methods on both MVSEC and DSEC, while the confidence-guided aggregation establishes a new overall state-of-the-art on the MVSEC benchmark, surpassing heavy frame-based networks that rely on global spatial priors.

A sparse 8-layer code transformer develops dedicated neural circuitry for every Python construct tested, and that circuitry is organised by a clean computational principle rather than by semantic category. We extract neural circuits for 106 concepts (43 AST node types, 63 builtin objects) by marginalising across 63,800 controlled prompts, and decompose each circuit into concept-specific and token-driven components using contrastive checker prompts that present a keyword token without its associated syntactic structure. Three findings emerge. First, all 106 concepts produce non-empty universal circuits at every one of nine parameter settings, and the ranking of concept-specificity across constructs is stable across the sweep - survival is not an artifact of a permissive threshold. Second, AST circuits contain a genuine concept component distinct from token activation: concept-only neurons constitute up to 62.5% of the loudest-firing neurons at mid-to-late layers, while builtin circuits are almost entirely token-driven. Third, six computationally atomic constructs - Import, ImportFrom, Break, Continue, Pass, Assert - cluster together despite being semantically unrelated, sharing only the property of being single-statement constructs requiring no nested body; this atomicity super-cluster, together with a four-tier hierarchy organised by token ambiguity and structural distinctiveness, shows that the model's internal organisation tracks computational structure rather than meaning. The methodology, full decomposition data, and analysis code are released.

Large language models (LLMs) are increasingly used for qualitative data analysis (QDA), yet their outputs often miss the depth and nuance of human analysis. We argue this gap reflects a missing credibility practice from human QDA: peer debriefing, in which an analyst seeks feedback from a disinterested peer and uses it to refine their coding. To bring this practice into LLM-assisted QDA, we propose Agent-as-Peer-Debriefer, a multi-agent QDA framework that builds peer debriefing into key coding steps. In our framework, a Hierarchical Coding Agent follows the standard QDA process to generate codes, sub-themes, and themes, along with self-explanations and reflection memos. It then shares these outputs with three Peer-Debriefing Agents, each applying a distinct analytical perspective (Theory-Driven, Data-Driven, or Applied) and refining the codes by keeping, renaming, reassigning, merging, or splitting them. These perspectives are drawn from established human QDA practices that generalize across domains and datasets. To evaluate the framework, we test it on three datasets across two domains with three LLMs, measuring semantic similarity to human-annotated codes. Across all settings, perspective-based, peer-debriefing refinement aligns more closely with human codes than a single-LLM baseline, and an ablation further shows the gain is not merely from additional refinement. The three perspectives also produce distinct trade-offs, showing that the choice of perspective is a meaningful and controllable design decision. More broadly, these findings suggest that simulating peer debriefing with explicit perspectives is a promising route to more credible LLM-assisted QDA.

Large language model (LLM) agents excel at solving complex long-horizon tasks through autonomous interaction with environments. However, their real-world deployment faces a fundamental device--cloud dilemma: on-device models are efficient but often brittle, while cloud models are stronger but costly in computation. State-of-the-art LLM device--cloud routers usually make coarse task-level decisions, which cannot adapt to the changing difficulty of multi-step agent interactions. To address this issue, we present Hera, a step-level device--cloud LLM agent coordinator for long-horizon tasks achieving a strong performance--cost Pareto frontier. Hera adopts a novel two-stage training paradigm: (1) imitation learning for cold-start, followed by (2) reinforcement learning that jointly optimizes task success and cloud usage efficiency. The first stage casts step-level routing as a supervised classification problem: the device agent is replayed on cloud trajectories, with each state labeled by the agreement between device and cloud actions. In the second stage, we perform cost-aware reinforcement learning by grouping identical states across trajectories and updating Hera with labels favoring higher expected return and fewer future cloud calls. We evaluate Hera on ALFWorld, WebShop, and AppWorld, where it consistently outperforms prior methods, achieving 92.5% of the cloud-only success rate with cloud use in only 46.3% of steps.

Many applications of large language models (LLMs) require deductive reasoning, yet models frequently produce incorrect or redundant inference steps. We frame natural language inference as a search problem where the final answer is the valid proof itself, requiring a reasoning procedure in which intermediate inferences are correct. Specifically, we investigate whether LLMs can learn to generate correct and efficient proofs with guidance from A* search -- an algorithm that guarantees an optimally efficient path to a goal. We explore two training techniques: supervised fine-tuning on execution traces from A* and reinforcement learning with A*-informed process reward models. Empirically, we find that Llama-3.2 models in the 1B--3B range benefit substantially from A* post training, going from near-zero accuracy to outperforming DeepSeek-V3.2 -- a much larger model. Our analysis uncovers a trade-off: while simple correctness rewards maximize accuracy, A*-informed signals strike a balance between accuracy and efficiency. Furthermore, we find that on larger search spaces, models trained with imperfect heuristics exhibit superior accuracy. Our results demonstrate a promising direction towards reasoning guided by principles derived from classical search algorithms.