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arXiv:2611.05004v2cs.CV

ScoreDial: Precise Control of Visual Attributes in Image Generation via Regressor Guidance from Limited Human Ratings

Requested-value control is stricter than continuous steering: given $c$ on a human-rating scale, the generated image should attain that value from only limited ratings. We present ScoreDial, which fits a differentiable regressor $R$ to 100-479 human-rated images; once $R$ is fixed, a requested value $c$ is defined on its output scale, and learned target conditioning is paired with error-adaptive guidance that repeatedly reduces $|R(\mathbf{x})-c|$ during sampling. Across tire slip resistance, interior visual complexity, food desire-to-eat, and soap translucency, using one set of sampler settings, ScoreDial reaches requested values and achieves $R$-MAE at most 0.013 over a range of width 0.8 and Spearman $\rho=0.980$, the maximum attainable under our protocol. Because $R$ also drives sampling, we evaluate agreement with $R$ separately from matched sweeps, an independent auditor fitted to the same ratings on a backbone no deployed regressor uses, and blinded human judgments. MPGD-flow also reaches the requested values under $R$, but ScoreDial has larger auditor displacement on every attribute, the largest among all compared methods, and a stronger MPGD-flow setting gives up target agreement without closing this gap. On every attribute, removing target conditioning leaves low $R$-MAE but more than halves auditor displacement, separating precise score correction from attribute movement. Blinded rating studies with 15 raters per attribute show mean human ratings track $c$ on tire and soap, with linear $R^2=0.665$ and $R^2=0.786$, and in forced-choice comparisons of matched sweeps, raters chose ScoreDial's as the clearer progression in at least 84% of judgments against every baseline. Code: https://github.com/Kamijo-Gen/ScoreDial.

arXiv:2611.05003v2cs.LG

Unifying and Beyond the Theory of Pervasive Capability Degradation in LLM Post-training SFT from Feature Interference

Pervasive Capability Degradation (PCD) refers to the phenomenon in which supervised fine-tuning (SFT), while adapting a large language model (LLM) to a target task, often erodes the general capabilities acquired during pre-training. Prevailing explanations attribute PCD to macroscopic distribution shift and therefore lack microscopic manipulability, leaving existing mitigation methods without a complete theoretical foundation. In this paper, we first develop a bottom-up geometric theory of PCD grounded in feature interference under superposition: narrow-domain SFT data disrupt the almost-orthogonal feature structure formed during pre-training, and the resulting interference drives activations across decision hyperplanes in the output Laguerre-Voronoi geometry, flipping predictions on general tasks. This theory unifies existing methods into six paradigms and reveals both the source of their efficacy and their limitations. We then argue that cross-entropy under one-hot supervision is structurally limited in resolving PCD on its own, and accordingly propose the AEGIS loss, which directly constrains the drift of activation margins along all competing token directions, thereby decoupling interference suppression from task adaptation. Across 3 model families and 14 SFT tasks, AEGIS outperforms representative methods of every paradigm on target tasks and pervasive capabilities simultaneously, at only about 1.3 times the computational cost of standard SFT. Its generality, scalability, and mechanistic interpretability offer a new perspective on mitigating PCD.

arXiv:2611.04879v2cs.AI

ScamWorld: An Interactive Environment for Evaluating Web Agents Against Online Fraud

Web agents increasingly browse, shop, and manage accounts on behalf of their users. Prior work has shown that they can be misled by adversarial content, including prompt injections and deceptive interfaces. Beyond such attacks, agents operating on the open web also encounter online fraud designed to deceive humans, including fraudulent online stores, fake investment platforms, and advance-fee schemes. How web agents respond to such fraud during task execution remains underexplored, in part because scam websites are short-lived, making systematic evaluation difficult. To address this gap, we introduce ScamWorld, an interactive environment that reconstructs reported scam websites across diverse scenarios, fraud mechanisms, and languages. Each reconstructed website reproduces documented fraud mechanisms, making relevant signs of fraud observable before the agent's final action and enabling controlled, repeatable evaluation. Through an extensive study of web agents powered by six frontier LLMs, we find that baseline deception rates range from 11% to 35% across models. Agents proceed more readily with payments than with requests for credentials or wallet information. A closer analysis of agent trajectories shows that some agents acknowledge suspicious conditions yet proceed, at times treating the user's instructions as authorisation to accept additional terms imposed by the website. ScamWorld provides a reusable testbed for systematically evaluating and stress-testing web agents against real-world online fraud.

arXiv:2611.04813v2cs.AI

AgenticFinBench: Benchmarking Financial Agents on Diverse Tasks from Real-World Requests

Financial agents are becoming an important class of real-world AI systems. Financial tasks vary widely in type and difficulty, and many are open-ended with no ground-truth answers. However, existing benchmarks neither capture this breadth and open-endedness nor separate grounding from correctness. To bridge this gap, we introduce $\textbf{AgenticFinBench}$, a benchmark of 230 real-world financial tasks spanning 8 categories, 2 languages, and 4 complexity levels. We also propose a reference-free evaluation framework that combines question-specific rubrics with a two-stage claim audit that detects hallucinations, defined as claims absent from the agent's trace and refuted by external evidence. This framework better matches how financial work is assessed in practice. Experiments across 18 agent configurations reveal three key findings: (1) Ignoring hallucinations can overstate agent performance: hallucination auditing lowers the baseline leader's score by 7.58 points and moves it to fourth place. (2) Harness differences explain more variation in evidence grounding than model differences (28.6% vs 8.8%). (3) Quality scores fall from 89.44 on direct retrieval to 79.18 on the most complex tasks. Case studies show that agents struggle to explain how events affect company profits or stock prices, compare financial data on a consistent basis, and justify their conclusions. By releasing AgenticFinBench, we aim to advance financial reasoning, factual verification, and agent design for more reliable responses to diverse real-world financial requests.

arXiv:2611.04507v2cs.AI

Signals: Continuous Diagnostics of AI Agents

AI agents can make incorrect decisions or waste resources even when their tools and infrastructure work normally. Their nondeterministic behavior makes these problems difficult to reproduce and diagnose. We developed Signals to identify such problems from agentic traces and suggest concrete remediations. We built the method around a taxonomy of 45 problem types across eight families, with definitions and evidence requirements for each type. The method distinguishes realized failures, risk exposures, and inefficiencies, groups related findings into engineering issues called Signals, and assesses their severity from the supporting evidence. Each Signal includes actions a developer can take and checks for evaluating the change. Further executions can add evidence to an existing Signal or reveal a new problem. We evaluated the method on public agent executions and achieved 91.43% F1 when matching Signals to reference issues, about 18 percentage points higher than a one-pass LLM control that used the same model and taxonomy.

arXiv:2611.04287v2q-bio.BM

Predicting protein structures at any folding stage from sequence

Protein structure prediction has largely focused on native conformations, leaving the continuum of unfolded states, folding intermediates, and native structures difficult to access. We present FoldScape, a sequence-conditioned deep learning framework for generating protein conformational ensembles at specified folding fractions $Q$. Trained on approximately one million conformations from 10,000 protein sequences, FoldScape combines coarse-grained folding and all-atom mechanical-unfolding trajectories. It reconstructs three-dimensional $C_\alpha$ chains through hierarchical sliding-window regressions of inter-residue distances, chain-level assembly, and a rectified-flow decoder. By conditioning on folding progress, FoldScape generates conformations from unfolded states through intermediates to native-state structures without protein-specific molecular dynamics at inference. In matched-sample comparisons, FoldScape achieves median conformational-space coverage of 0.989, 0.722, and 0.877 along radius of gyration, fraction of native contacts $Q$, and secondary-structure fraction, respectively, versus 0.05, 0.05, and 0.10 for seed-varied AlphaFold 3 ensembles. Coverage advantages are consistent across the evaluated proteins and robust to binning choices. Reconstruction accuracy remains approximately stable across the evaluated stages of a folding trajectory, and stride-one crop-and-superpose inference extends predictions to chains several times longer than the single-pass limit. Analyses of mechanical-unfolding trajectories show residue-resolved pathways, reproducible extension-conditioned observables across pulling velocities, and geometrically coherent segments in partially unfolded chains. FoldScape extends sequence-based structure prediction beyond a single folded endpoint to controllable conformational-ensemble generation across protein folding.

arXiv:2611.04279v2cs.AI

Bidirectional Centered Score Matching for Discrete Diffusion Distillation

Discrete diffusion models with parallel decoding are often distilled using token-wise KL objectives. Although token-wise KL exactly matches the corresponding product-form block distributions, its probability-space optimization geometry and teacher-only candidate truncation may provide insufficient supervision under aggressive few-step distillation. Concrete Score Matching (CSM) provides an alternative within-position objective by aligning relative logit geometry, but its complete pairwise form incurs \mathcal{O}(|\mathcal{V}|^2) complexity. We propose Bidirectional Centered Score Matching (BCSM), an efficient within-position distillation objective that constructs an \mathcal{O}(K) bidirectional active set, reduces pairwise comparisons to \mathcal{O}(K^2), and factorizes them into an \mathcal{O}(K) objective. We further introduce cross-timestep transition alignment. Experiments demonstrate strong quality--efficiency trade-offs, including up to 6\times NFE reduction with a 16.9\% relative HumanEval gain and a 15.1\% relative MMMU gain at single-step inference.

arXiv:2611.04216v2cs.CV

LiSA: Linear Stochastic Attention for Long-Range Visual Modeling

Self-attention has become the standard for modern sequence modeling, enabling Transformers to model long-range dependencies across a wide range of modalities. Despite these advances, its quadratic cost with respect to sequence length remains a significant computational bottleneck. Recent work addresses this limitation by introducing linear variants of self-attention, namely with kernel approximations of the softmax operator. However, their first-order aggregation restricts expressivity and struggles to capture higher-order structure. We propose Linear Stochastic Attention (LiSA), a linear attention plug-in module that enables higher-order token interactions via a stochastic diffusion process based on truncated random walks. LiSA incorporates adaptive locality, favoring semantically similar neighbors to preserve fine-grained structures, while maintaining stable and efficient training. We conduct extensive experiments on classification, semantic segmentation, and object detection tasks and show improved results over state-of-the-art methods.

arXiv:2611.03953v2cs.LG

P$^2$-MOPD: Accelerating Multi-Teacher On-Policy Distillation via Parameter Priors

Multi-teacher on-policy distillation consolidates expert capabilities by supervising student-generated trajectories, whereas task arithmetic offers a training-free alternative through linear parameter combinations. We view the linear combination of student and expert parameters as a single differentiable model and propose P$^2$-MOPD, which jointly optimizes the mixing coefficients and the student weights under the same on-policy distillation objective. Unlike task arithmetic, which stays within the span of the frozen student and expert parameters for any choice of merging coefficients, P$^2$-MOPD keeps the student trainable, so the experts act as parameter priors without confining it to this span. Across four domains at 1.7B and 4B scales, P$^2$-MOPD achieves faster and more balanced recovery than MOPD from the same initialization, surpassing its final average recovery in half the training steps. At the end of training, our 1.7B model reaches 94.7% average recovery, versus 80.9% for MOPD.

arXiv:2611.03625v2cs.LG

FADE: Factored Ability--Difficulty Filtering for Online RLVR Scheduling

Group-based reinforcement learning with verifiable rewards (RLVR) learns only from prompts whose sampled completions disagree: all-pass and all-fail groups produce zero relative advantage and burn generation budget without moving the policy. Adaptive schedulers try to steer rollouts toward informative prompts, yet they rely on per-prompt pass-rate trackers that entangle two quantities evolving at very different speeds---the policy's shifting competence across reasoning skills and each prompt's intrinsic difficulty. When a single exponential average or Beta counter tracks both at once, short memory scrambles the relative ordering of prompts whereas long memory reports stale pass rates. We introduce FADE (Factored Ability--Difficulty Estimation), a bilinear state-space filter that separates the two timescales. FADE represents each prompt's success logit as the inner product of a whitened $K$-dimensional skill loading with a fast-drifting policy ability vector, minus a slow-shrinking scalar item intercept. Using P\'olya--Gamma augmentation, each minibatch of binary rollout outcomes updates the $K$-dimensional ability posterior in closed form via a rank-$K$ Woodbury step, instantly transferring competence shifts to all unobserved prompts that share those skills while leaving item intercepts stable. From the resulting posterior mean and variance we derive a closed-form utility for the probability of drawing a non-degenerate rollout group. Across five reasoning benchmarks, two base models, and four scheduling paradigms under a matched rollout budget, FADE consistently improves downstream accuracy and calibration while adding less than $0.6$\,ms per step.

arXiv:2611.03577v2cs.LG

Sonar-MoE: In-Backward Expert Updates for Memory-Efficient Mixture-of-Experts Training

Most parameters of a Mixture-of-Experts (MoE) model belong to its experts, and standard training keeps every expert gradient in GPU memory until the optimizer step. This memory grows with the number and size of the experts, so it rises as MoE models scale. We introduce Sonar-MoE, which updates each expert tensor during the backward pass and frees its gradient right away. It brings optimizer-in-backward from dense models to batched MoE expert tensors, so the GPU never holds more than one layer of expert gradients. When we fine-tune OLMoE-1B-7B and Granite-3.1-3B-A800M in bf16 with two expert-kernel backends, Sonar-MoE lowers peak memory by 19% to 22%. Its updates are bitwise identical to standard training without expert gradient clipping, and held-out loss stays within 0.003 of all baselines. Each step also takes 17% to 23% less time than standard training with global-norm clipping. Updating whole batched tensors rather than individual experts is what keeps Sonar-MoE fast, as it avoids a 20% to 72% slowdown while using the same memory. Sonar-MoE matches optimizer-in-backward over all parameters in memory and speed while still clipping the dense parameters.

arXiv:2611.02902v2cs.CV

TailorRig: Controllable and Structured Auxiliary Skeleton Generation for Garment-Aware Rigging

Humanoid rigging for modern characters with complex garments remains challenging due to the need for dense auxiliary skeletons and precise skinning control. Existing automatic methods primarily recover rigs from geometry, providing limited artist control over auxiliary articulation and often lacking explicit semantic or kinematic-chain structure for dense garment bones, leading to instability and weight bleeding. We present TailorRig, a framework that reformulates garment-aware humanoid rigging as a structured, controllable full-rig generation problem. This formulation shifts the goal from automatic rig recovery to artist-driven rig authoring, where both body-template compatibility and auxiliary articulation are explicit design choices. TailorRig exposes two explicit axes of artist control within a unified framework: a user-specified body skeleton template that preserves body-rig compatibility, and artist-provided semantic labels that drive an autoregressive generator to synthesize requested category-specific auxiliary bone chains. To robustly assign skinning weights under dense skeletal configurations, we further introduce a hierarchical chain-to-bone formulation: vertices are first associated to a kinematic chain, and bone weights are then refined within that chain, reducing weight bleeding between spatially adjacent but semantically unrelated structures. We evaluate TailorRig on a diverse set of characters and introduce Human-Mix, a large-scale dataset of over 38,000 humanoid models curated for garment-aware rigging. Experiments show that TailorRig improves skeleton accuracy, deformation stability, controllability, and practical usability over existing methods. Project page: https://xxxx0601.github.io/trig/ ; code: https://github.com/Tencent/TailorRig ; dataset: https://huggingface.co/datasets/tencent/TailorRig

arXiv:2611.02775v2cs.CV

Human-Centred, Risk-Constrained Evaluation of Financial Document Recognition: Evidence, Critical Errors, and Selective Automation

Financial document recognition is often assessed using character and word error rates, although these metrics do not express whether a system preserves the financial facts on which people and organisations act. This paper develops a human-centred, risk-constrained framework for evaluating financial document recognition as evidence recovery and decision support. It defines typed financial facts linked to visible source regions and separates verbatim transcription, deterministic normalization, and business interpretation. A layered quality model covers text, localization, layout, tables, fields, fact correctness, evidence grounding, uncertainty, robustness, and operational performance. Non-compensatory acceptance gates use one-sided uncertainty bounds for critical-field errors, preventing strong aggregate scores from masking failures in amounts, identifiers, signs, periods, or entity associations. Selective automation is formulated as a constrained routing problem that accounts for residual risk, human-review capacity, and review cost. The framework further specifies annotation and adjudication procedures, leakage-resistant benchmark partitions, statistical estimands, subgroup analyses, and a reproducibility card. Formal results establish the limitations of compensatory scoring, the non-zero upper risk bound after zero observed errors, and a loss sensitive decision rule for routing uncertain cases to human review. The contribution is theoretical and methodological; no new model, dataset, or empirical performance result is claimed.

arXiv:2611.02216v2q-bio.NC

Do agents need to sleep?

LLM-based agents, which increasingly operate persistently across sessions and accumulate memory through interaction, already exhibit the familiar symptoms of unchecked plasticity: semantic drift, degraded retrieval precision, propagation of stored errors, and saturation of memory capacity. Drawing on the selectionist "ringing, resonance and renormalization" (RRR) account of sleep, we propose that each of its three phases maps onto an operation feasible in digital memory architectures. Engineers building stateful agents, meanwhile, are independently rediscovering the problems sleep evolved to solve: what to forget, and when to do the forgetting. From this we derive the falsifiable prediction that selectionist consolidation will outperform instructionist alternatives as memory stores grow large. The core claim concerns the nature of continuous learning itself: plasticity has a price, and for any system that learns continuously under finite capacity while coupled to its environment, that price is sleep.

arXiv:2611.01993v3quant-ph

Seeing Why: Exact Evidence Maps for Quantum and Optical Image Classifiers

When an image classifier decides, we can usually only estimate why. For quantum and all-optical classifiers that act linearly on amplitude-encoded pictures up to the measurement, with no trained classical network before or after them, each class's Born probability above its no-information share, $P_g - b_g$, splits exactly into contributions of the encoded amplitudes, shown as Born evidence maps (BEM). The split itself follows from known results on quadratic forms: with the transmitted light held fixed, it is what Integrated Gradients from a zero baseline and the Shapley value give. What we add is a way to measure it on the hardware that classifies, from class probabilities on a quantum chip or, in simulation, from camera frames on a lens bench, with no gradient circuit and no light sent backwards; a $g\times g$ map takes $1 + 2g^2$ runs. Deleting the 5% of pixels with the highest evidence drops accuracy from 73% to 9% (one seed), as occlusion and gradient $\times$ input do, while plain gradients remove much less. The classifiers share one architecture, a Fourier-plane mask followed by a brickwall circuit on qubits or by phase plates on a lens bench, read by a fixed Born headroom readout with no trained parameter; centring each picture on its own mean lets dark features count as much as bright ones. In simulation, four phase plates at one wavelength reach 72.3% on Caltech-10 colour photographs. On IBM's ibm_kingston, with the mask computed classically before approximate loading, 300 test pictures were classified at 37.7% against 10% chance (56.3% in exact simulation), and $2\times2$ maps of the filtered input of 30 test pictures drawn at random in advance, measured on the chip, agreed with the exact ones ($r = 0.88$; standard estimator 0.82). The maps also revealed a shortcut in the data; as the trim that removed it was chosen on test pictures, the Caltech-10 results are exploratory.

arXiv:2611.01536v2cs.CV

CUFormer: Modality-Aware CT-Ultrasound Point Cloud Registration for Orthopedic Navigation

Registering intraoperative Ultrasound (US) bone-surface point clouds to preoperative Computed Tomography (CT) models can support radiation-free orthopedic navigation. Differences in imaging physics produce distinct surface sampling patterns, complicating cross-modal feature matching. Bone strongly reflects ultrasound and casts an acoustic shadow, so US captures only the probe-facing bone surface and leaves most CT points unmatched. This partial coverage makes correspondences ambiguous on near-symmetric bones. We propose CUFormer, a modality-aware registration framework. We introduce a Modality-Aware Transformer (MAT) that encodes input modality through identity embeddings and updates features through modality-specific adapters within a shared geometric matcher. We model imaging visibility and use predicted reference-side visibility to weight coarse and fine correspondences. CUFormer achieves the lowest mean registration errors among evaluated methods on two CT-US datasets, UltraBones100k and UltraBonesHip, and the CT-RGB-D dataset SpineDepth. On UltraBones100k, it reaches mean rotation error 4.53$^\circ$, translation error 3.19\,mm, and Root Mean Squared Error (RMSE) 2.54\,mm, reducing RMSE by 65.8\% relative to the best-performing baseline by this metric. These results demonstrate CUFormer's effectiveness in aligning partial bone surfaces with preoperative CT across anatomical sites.

arXiv:2611.01519v3cs.CL

Write Facts the Way Models Read Them: Lifting the Two-Hop Curse

A language model that learns a new fact by fine-tuning can repeat it but cannot reason with it: taught that a person is a citizen of a new country, it still cannot say, without chain-of-thought, who the head of state of that person's country is. This two-hop curse is widely treated as a reasoning deficit, and the strongest knowledge editors answer it with synthesized reasoning data. We show that the reasoning is intact and the writing is wrong. Fine-tuning writes a new fact as an answer to be said, whereas the second hop reads the bridge ("that person's country") as an entity, from the middle layers on: patching the model's own representation of the entity into the bridge at those layers largely restores the second hop, yet after fine-tuning the bridge there is no closer to the new entity than before the edit. We therefore propose read-equivalent writing (Legible): one loss term makes the bridge phrase, at the layer where the second hop finishes reading it, match the model's own reading of the new entity, and keeps the same relation's other subjects unchanged. Phrases and targets come from the edited model itself, and no multi-hop training data is used. Across Qwen2.5, Llama-3 and Qwen3, Legible (I) composes learned facts more often than the model composes its own knowledge, on MQuAKE's two-hop-curse questions; (II) reaches 1.8-2.6x the bridge accuracy of CaKE, whose reasoning data composes no better than plain fine-tuning, and has the best average over composition, accuracy and locality against four families of writers; and (III) lifts the curse on RippleEdits, on the benchmark of Balesni et al., who named the curse, and at 14B.

arXiv:2611.01466v2cs.CV

Resolve, Clear, or Defer: Training-Free Active Prototype Triage for Ecological Detection Pipelines

Ecological monitoring increasingly relies on camera traps and aerial surveys that generate large image collections. High-recall animal detectors can localize candidate animals at scale. However, they also produce many detections that still require expert review, including false positives, ambiguous cases, and animals difficult to identify at the species level. Since exhaustive review requires substantial effort, we propose training-free active prototype triage, where reviewed detections become reusable evidence to (1) Resolve supported foreground classes, (2) Clear likely background false positives, or (3) Defer insufficiently supported cases for expert review. Across camera-trap and aerial datasets, foreground recognition and false-positive rejection benefit from different pretrained representations: BioCLIP2 provides foreground evidence while DINOv3 provides background evidence, reducing erroneous foreground clearing while improving automatic foreground recovery. Deferring unsupported cases avoids the higher error rates caused by forced decisions. Compared with confidence-thresholded multiclass k-NN and uncertainty-sampling logistic regression, prototype triage improves foreground recovery while maintaining competitive or lower review burden. Acquisition goes beyond class discovery: even after classes are represented, prototype choice determines how reliably evidence propagates through the remaining detections. Our results suggest that once animal localization reaches high recall, the challenge shifts from finding animals to deciding which examples to review, how to reuse them, and when evidence does not support an automatic decision.

arXiv:2611.01345v2cs.LG

Unified dynamics of training, learning, inference, and reinforcement in neural networks

Through nine nanoGPT experiments, we established training-learning-inference relations: realized updates elicit state-dependent finite-amplitude responses; learning persistently reorganizes distributed functional support, with target-specific readout-boundary crossings determining capability transitions; inference recruits learned support without changing the learned state. Factors identified in the fifth experiment yielded a direct predictor of post-update capability transitions, achieving 91.43% accuracy and 91.49% four-way macro recall across 5,088 targets. We tested these relations and prediction across five additional neural architectures. In a seventh system, concentrated correct feedback eroded previously mastered skills; rebalanced feedback restored their accuracy from 70.31% to 99.48%. Linking inference consequences to subsequent training closes these relations into unified training-learning-inference-reinforcement dynamics. We subsequently established a unified system of dynamical equations, used it to reconcile positive and negative findings across existing research, and derived mathematical relationships in other neural-network theories using only the assumptions of the original studies.

arXiv:2611.01335v2cs.LG

Profile-aware diagnostics of discarded parameter-Hessian mass

Evaluating block-diagonal curvature models involves two questions: how much curvature they omit, and what a specific correction changes at a finite step. We measure the squared off-block fraction of the parameter Hessian against references for group sizes and the observed within-group curvature profile. In CIFAR-100 ResNet-18 and a skip-free counterpart, similar initial discarded fractions accompany different profiles. At saved trained ResNet-18 weights, changing from stage to layer groups moves estimated off-block mass from below to above the profile envelope; an approximate conditional screen resolves this comparison in all six seed/input cells, while some skip free comparisons remain unresolved. Separately, in saved ResNet-50/Stanford Cars states, we compare candidates formed from off-group Hessian action, the remaining model residual and their combination through the same Hessian-informed map. At unit scale off-group input alone raises native minibatch loss relative to the base preconditioner candidate in 17 of 18 state/geometry comparisons, yet the combined candidate has lower loss than the remainder-only candidate in nine of those cases; preferences vary with scale and correction-norm matching. The profiles help assess block models and alternative groupings, while same-state candidate comparisons test a particular correction without equating structural mass with training gain.