Residual Learning

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17 papers in the last four weeks, up 143% on the four weeks before. 0.2% of all new papers.

Jul 13Week of Sep 28

Latest papers 103

Jun 16, 2026cs.LG

Reducing Learner Redundancy in Boosting via Residual Orthogonalization

While sequential residual fitting is the bedrock of standard boosting frameworks, it inherently breeds learner redundancy by repeatedly revisiting correlated error components. To address this bottleneck, we propose a shift from residual fitting to \textit{residual orthogonalization} and introduce SCBoost. Our framework tackles redundancy through two complementary mechanisms: Spectral Residual Projection (SRP) and Covariance-Regularized Weighting (CRW). During training, SRP projects each residual target onto the orthogonal complement of the historical prediction subspace, forcing successive learners to capture only novel empirical innovations. During aggregation, CRW optimizes ensemble weights on a validation set with an explicit covariance penalty to mitigate remaining correlations. Theoretically, we provide a finite-sample geometric characterization proving that SRP yields an exact additive residual-energy decomposition. Furthermore, under an isotropic-noise assumption, we rigorously establish the conditions under which this projection improves the effective Signal-to-Noise Ratio. Extensive experiments across ten benchmark datasets demonstrate that SCBoost delivers strong out-of-the-box performance, particularly in accuracy and F1 score. This work reinterprets boosting through a geometric lens, suggesting that explicit redundancy control is a principled and necessary step toward more efficient ensemble architectures.

Ye Su, Jipeng Guo, Yong Liu +5

Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China · College of Information Science and Technology, Beijing University of Chemical Technology,2026 Beijing 100029, China · Gaoling School of Artificial Intelligence, Renmin University of China, Beijing 100872, China +2

Ensemble Learning Residual Learning Ensemble Diversity

Jun 16, 2026cs.CV

MeiBRD: Meta-Learning Intraoperative Biomechanical Residual Deformation

Accurate intraoperative liver registration is challenging due to substantial soft-tissue deformation yet sparse intraoperative measurements. Biomechanical models regularize this ill-posedness with prior knowledge but exhibit persistent prediction bias due to simplifying assumptions, while data-driven learning solutions struggle with data efficiency, generalization, and physical plausibility. We propose a hybrid registration framework that adapts a biomechanical prior using sparse intraoperative correspondences. Rather than learning a full deformation field, we learn a residual deformation function that corrects linear biomechanical predictions, modeled as a graph neural diffusion function with geometry-aware attention over the 3D liver mesh. To enable long-range information transfer of sparse observations, we take a novel perspective of sparse intraoperative measurements as \textit{context} samples where input-output pairs of the residual deformation function are fully observed, casting the problem into learning-to-learn this residual function from intraoperative context samples with feedforward meta-learners. Experiments on a deformable liver phantom dataset demonstrate improved registration accuracy and generalization compared to rigid, biomechanical, and data-driven baselines, particularly for out-of-distribution geometries and deformations.

Casey Meisenzahl, Jon Heiselman, Michael Holtz +3

Rochester Institute of Technology, NY, USA · Vanderbilt University, Nashville TN, USA

Residual Learning Medical Image Registration Deformable Image Registration

Jun 15, 2026math.OC

Exploding and vanishing gradients in deep neural networks: the effect of residual connections

The well known phenomenon of exploding and vanishing gradients in deep neural networks is analyzed using multiplicative ergodic theory. The effect of adding a residual connection is explained in this context. Specifically, a characterization of Liapunov exponents due to Furstenberg and Kifer is exploited in order to make a precise statement about the Liapunov spectrum and the effect of residual connections on it.

Vivek S Borkar

Residual Learning Neural Network Training Dynamics

Jun 15, 2026cs.LG

Scaling Adaptive Depth with Norm-Agnostic Residual Networks

Residual architectures are ubiquitous in deep learning, but they suffer from a subtle structural limitation: the norm of the residual stream can grow rapidly with depth. As a result, updates from later layers become small relative to the accumulated residual state. This reduces their impact on the representation and limits the benefits of scaling models in depth. To address this, we introduce NAG, a norm-agnostic residual architecture that separates magnitude from directional information in the residual stream, preserving meaningful layer contributions throughout depth and preventing later updates from being systematically suppressed by residual-norm growth. Importantly, NAG introduces only a negligible number of additional parameters and relies on simple operations that are easily kernel-fusible, preserving training efficiency in practice. We show that this architecture outperforms baseline Transformers, with gains that increase substantially as depth grows, enabling effective training of much deeper models. The norm-agnostic formulation also leads to an interpretable Mixture-of-Depths (MoD) mechanism that adaptively skips both attention and MLP layers. Beyond serving as a post-training accuracy-compute tradeoff, this mechanism can be used as a pretraining-time scaling strategy: under iso-FLOP training, compute saved by reducing per-token forward-pass cost can be reinvested into training on more tokens while keeping the total parameter count and KV-cache budget fixed. In our experiments, moderate Mixture-of-Depths rates of approximately 20%-25% match full-depth baseline performance under equal training compute while substantially reducing the number of executed layer parameters and forward-pass FLOPs. These results identify sparsity in depth as a new scaling axis for fixed-compute training, enabling very deep yet FLOP-efficient models.

Tomás Figliolia, Beren Millidge

Zyphra San Francisco, CA

Efficient Neural Network Inference Dynamic Neural Networks Transformer Residual Learning

Jun 13, 2026cs.LG

Hybrid NARX-LLM for Greenland Iceberg Discharge: Prompt-Driven Residual Correction

Greenland iceberg discharge exhibits complex nonlinear dynamics with limited observability, challenging traditional predictive models. We present a Hybrid NARX-LLM framework that combines a nonlinear autoregressive model with exogenous inputs (NARX) and a large language model (LLM) for residual correction. We further propose a Physics-Informed Prompt (PIP) method that transforms unstructured physical knowledge into structured prompts for zero-shot in-context reasoning. The primary objective is to explore the corrective potential of this framework for modeling Greenland iceberg discharge, rather than merely optimizing predictive accuracy. The NARX component captures intrinsic temporal dependencies, while the LLM, guided by PIP, encodes glacier dynamics and environmental drivers and perceives key trend patterns to correct systematic prediction errors. This integration allows the model to reason about unmodeled factors and produce interpretable residuals, enhancing overall predictive accuracy. Applied to Greenland iceberg discharge time series, our approach addresses extreme events that are difficult to predict due to rare variations and nonstationary trends, a limitation often overlooked by traditional methods. By fusing structured time-series modeling with knowledge-driven foundation AI, the framework offers a scalable and interpretable pathway to bridge data-limited climate forecasting with physics-informed LLM reasoning. The code is available.

Yiquan Gao, Duohui Xu

1Heriot-Watt University. · 2StudioYG. · This work was completed before the first author’s affiliation with Heriot-Watt University and was conducted entirely independently of the institution.

Zero-Shot Time Series Forecasting Residual Learning Time Series Forecasting LLM-Based Time Series Forecasting

Jun 12, 2026cs.LG

Learning the Context of Errors: Black-Box Online Adaptation of Time Series Foundation Models

The rapid evolution of Time Series Foundation Models (TSFMs) has advanced zero-shot forecasting across diverse domains. Inspired by the current form of Large Language Models, future TSFMs may be offered as commercialized, closed-source API services. However, many existing online adaptation methods still rely on white-box access for parameter fine-tuning or gradient backpropagation. This paradigm mismatch raises a question: In black-box online adaptation for TSFMs, what should we learn? We answer this with an insight: the predictive errors of the base model are conditioned on both the input and output of the base model (i.e., the context of errors). To validate this insight, we propose ORCA (Online Residual Contextual Adaptation). We conduct extensive experiments across 5 state-of-the-art TSFMs and 8 datasets to demonstrate the effectiveness of our approach. Furthermore, through ablation studies, we quantitatively analyze the impact of different adapter learning hypotheses on the final adaptation performance in black-box online adaptation. Code available at https://github.com/Fifthky/ORCA.

Xilin Dai, Yiding Liu, Hongjie Xia +4

Ant International · The Chinese University of Hong Kong

Test-Time Adaptation Residual Learning Time Series Forecasting Time-Series Foundation Models

Jun 9, 2026cs.LG

One Step Closer to Ground Truth: A Multi-Scale Residual-Aware Representation Learning Pipeline for Predicting Time Series Data

Transformer-based models have emerged as leading paradigms in time-series forecasting in recent years, employing self-attention mechanisms to capture long-range dependencies. Despite their success, these single-stage forecasting architectures exhibit persistent systematic residual biases arising from structural discrepancies, unmodeled stochastic components, or inadequate multi-scale temporal representations. This limitation persists when residuals are treated as irreducible noise, precluding adaptive correction of structured error patterns. To address this limitation, we introduce a two-stage, model-agnostic framework that explicitly decouples forecasting and residual learning into distinct stages of representation learning. A base transformer first generates the initial predictions. Subsequently, a dedicated meta-corrector dynamically models structured error patterns across multivariate channels, preserves cross-variable dependencies, and iteratively refines the residual bias of the base transformer. By formalizing this pipeline as a hypothesis space expansion, our framework addresses approximation limitations inherent in single-stage architectures, removes reliance on restrictive assumptions, and enables end-to-end learning of complex error dynamics. Evaluated on eight popular benchmark datasets using established protocols, our approach achieves state-of-the-art performance, with significant improvements in standard metrics (MSE, MAE). The results demonstrate the framework's ability to mitigate systematic biases and enhance robustness to complex temporal dynamics, advancing the practical applicability of transformer-based forecasting models.

Amrijit Biswas, Mustafa Kamal, Robin Krambroeckers +4

Artificial Intelligence Department, RobotBulls Labs Geneva, Switzerland · Department of Electrical and Computer Engineering, North South University Dhaka, Bangladesh

Multivariate Time Series Forecasting Residual Learning Time Series Forecasting Time Series Representation Learning Time Series Transformers Multiscale Time-Series Modeling

Jun 8, 2026cs.RO

Physics-Aware Sparse Learning and Selective Online Adaptation for Euler-Lagrange Robot Dynamics

Accurate dynamics models are essential for model-based robotic control, yet nominal Euler--Lagrange models often become inaccurate in the presence of payload variation, unmodeled coupling, friction, aerodynamic effects, and changing operating conditions. Most learning-based correction methods improve prediction accuracy by introducing a single additive residual, but do not preserve the internal mechanical structure of Euler--Lagrange systems. This leads to models that do not preserve symmetry, positive-definiteness, or the coupling between inertia and velocity-dependent terms, which can result in physically inconsistent predictions and reduced reliability when embedded in model-based controllers. We propose a structure-preserving residual learning framework that decomposes model mismatch into an inertia correction, the corresponding induced Coriolis term, and a generalized-force residual. The mechanical component is learned under physical constraints, while the disturbance-sensitive component is represented through a sparse history-dependent latent interaction model and adapted online using Bayesian linear regression. This separation preserves key mechanical structure while restricting adaptation to the part of the dynamics most affected by changing conditions. Experiments across multiple robotic platforms, including mobile, aerial, and manipulator systems, show that the proposed method improves dynamics prediction and trajectory tracking under coupled and time-varying dynamics. These results highlight the value of combining structured residual modeling, compact latent interaction selection, and selective online adaptation for real-world model-based control.

Rishabh Dev Yadav, Samaksh Ujjawal, Sihao Sun +2

Department of Computer Science, The University of Manchaster, U.K. · Department of Cognitive Robotics, Delft University of Technology, Netherlands · International Institute of Information Technology Hyderabad. +1

Robotic Control Robot Dynamics Identification Online System Identification Residual Learning Residual Dynamics Learning Robot Dynamics Learning+2

Jun 4, 2026cs.LG

HAARES Half-Split Residual Basis Routing for Deep Transformers

Block-level residual routing makes learned residual aggregation practical by routing over block summaries, but each summary compresses an ordered sequence of attention and MLP updates into one cumulative vector. We propose \method{}, a lightweight residual basis router that keeps the cumulative block source and adds one half-split detail basis, computed as the difference between first-half and second-half residual updates. The detail basis is RMS-matched and updated online, exposing coarse intra-block trajectory information without dense sublayer-level routing. Across OpenWebText, cross-domain character-level benchmarks, and BPE-tokenized OpenWebText, the empirical pattern is depth-dependent: gains are small or mixed at shallow depth and most reliable in 48-layer models. In the 201M 48-layer setting, \method{} improves over Block AttnRes across all three seeds, while a 453M two-seed probe shows the same direction. Ablations rule out source duplication, random signed details, fixed detail-source biases, or block-count changes alone. Cost analysis shows that the method is FLOP-light but not wall-clock-free: it adds memory and routing overhead, yet its relative arithmetic cost is amortized as width grows and earlier convergence can reduce time-to-target.

Kehan Wang

Paper under double-blind review

Transformer Residual Learning Language Modeling

Jun 4, 2026cs.AI

Multi-ResNets for Subspace Preconditioning in Constrained Optimization

We propose MResOpt, a staged residual neural network architecture for constrained optimization problems. Our architecture fits within predict-complete-correct pipelines and decomposes constraint satisfaction by priority through intermediate re-completion and stage-aware losses. The framework enables domain-informed ordered constraint satisfaction which allows the network to utilize ordinal structure when present. Under an idealized infinite-width regime, we show that our design behaves as sequential Gaussian Process regression. On synthetic QP, QCQP, and SOCP benchmarks, the staged architecture improves high-priority constraint satisfaction across convex and non-convex settings. On line-flow-constrained AC optimal power flow, we introduce a physics-motivated constraint ordering and show that MResOpt supports a learned division of labor that keeps iterates on the equality manifold, achieving substantially lower high-priority violation than reprojected baselines while remaining computationally efficient.

Merve Karakas, Christopher J. Williams, Emmanuel O. Balogun +3

UCLA · University of Oxford · Sunrun† +1

Residual Learning Learning to Optimize Optimal Power Flow Constrained Optimization Constraint Satisfaction

May 23, 2026cs.CV

Physics-Guided Self-Supervised Statistical Residual Learning for Sonar Despeckling with Improved Generalization

This letter introduces a physics-informed self-supervised framework for sonar image despeckling that reformulates despeckling as residual consistency in the homomorphic log domain. By constraining the log-ratio residual to obey multiplicative speckle statistics, the proposed method eliminates the need for clean supervision while preventing degenerate identity solutions. A variance-targeted statistical loss combined with edge-aware structural regularization and median-guided curriculum stabilization enables effective speckle suppression with preserved structural fidelity. This formulation along with a lightweight neural network achieves state-of-the-art performance across multiple real sonar datasets and demonstrates excellent cross-dataset robustness, while remaining suitable for real-time deployment.

Swapna Pillai, Siddharth Singh Savner, Sujit Kumar Sahoo

School of Electrical Sciences, Indian Institute of Technology Goa, Goa 403401, India · Inria, Sophia Antipolis, France

Self-Supervised Image Denoising Self-Supervised Learning Underwater Imaging Residual Learning Physics-Guided Image Restoration Physics-Informed ML+1

May 23, 2026cs.CV

NudgeVAD: Language-Nudged End-to-End Driving via FiLM Residuals

Natural-language instructions promise controllable end-to-end driving, but their benefit can be hidden when planners already receive reliable high-level commands. We propose NudgeVAD, a frozen-planner residual framework that uses language as a calibrated nudge to a VAD trajectory. With identity-initialized FiLM and a zero-initialized residual head, NudgeVAD is equivalent to the frozen planner at initialization, so learned deviations arise only from language-conditioned residuals. We evaluate NudgeVAD along a command-reliability axis. With reliable commands, language improves the initial planner but becomes nearly redundant once compared against VAD-FT (UNCOND), a compute-matched VAD model fine-tuned without language. With random commands, however, language becomes essential: detaching text degrades ADE6s to 3.166 m, while NudgeVAD with text recovers 2.806 m and outperforms VAD-FT (UNCOND) by 0.312 m. These results show that language is not universally additive; it is most valuable when the categorical command channel is unreliable.

Chieh-Chi Yang, Yu-Hsiang Chen, Yi-Ting Chen

National Yang Ming Chiao Tung University

End-to-End Autonomous Driving Residual Learning Autonomous Driving Autonomous Driving Planning

May 22, 2026cs.LG

Multi-Gate Residuals

While Attention Residuals has shown some effectiveness in addressing the widespread issue of unbounded activation growth across deep residual layers, it inevitably incurs significant communication overhead. To circumvent this bottleneck, we propose Multi-Gate Residuals (MGR), which stabilizes activation scales without additional communication burden. It utilizes a straightforward scoring and gating mechanism to maintain multi-stream context, coupled with Attention Pooling to extract hidden states from the stream states. Empirical experiments demonstrate that MGR is practical for large-scale training and deployment, offering tangible performance improvements over existing architectures.

Zhizhan Zheng, Feiyun Zhang, Shuchun Liu +4

Shanghai Yichuang Information Technology Co.,Ltd. · Independent Researcher · Fudan University

Residual Learning

May 21, 2026cs.LG

From Residuals to Reasons: LLM-Guided Mechanism Inference from Tabular Data

A persistent challenge in machine learning for scientific applications is jointly achieving prediction and understanding. Statistical models excel on structured data but operate as black boxes, while existing interpretability methods are largely inspective: they answer "which features matter?" but do not articulate how features interact or refine explanations iteratively alongside human understanding. Asking an LLM to predict the target directly forces it to search the entire output space; we instead anchor predictions with a base model and ask the LLM the narrower question of what that model is missing. We introduce Multi-Agent Residual In-Context Learning (MARICL), an agentic framework in which LLM agents analyze where a base-model fails, hypothesize missing structure from high-residual examples provided in context, and produce explicit correction terms refined through multi-turn textual gradient optimization. Across nine benchmarks spanning scientific, biomedical, socioeconomic, and synthetic settings, MARICL improves consistently over its base model on all datasets. To test whether these corrections reflect real structure or batch-specific noise, we freeze formulas learned on one experimental batch of the Cell-Free Protein dataset and apply them (with no retraining and no further LLM calls) to held-out batches. Within the same reagent protocol, the frozen formulas improve predictions in over 92% of cases; across a different protocol, they fail systematically. The success boundary aligns with the biochemistry, not the batch count; direct evidence of mechanistic generalization.

Mohammad R. Rezaei, Rahul G. Krishnan

Department of Computer Science University of Toronto Vector Institute Toronto, ON, Canada

Residual Learning In-Context Learning Large Language Model-Guided Scientific Discovery Multi-Agent LLMs

May 21, 2026cs.LG

MoSA: Motion-constrained Stress Adaptation for Mitigating Real-to-Sim Gap in Continuum Dynamics via Learning Residual Anisotropy

Learning real-world dynamics from visual observations is crucial for various domains. A common strategy is to calibrate simulators by estimating physical parameters, yet accuracy is ultimately bounded by the underlying physical models, which often assume materials are homogeneous and isotropic. Even if reasonable, real-world objects typically exhibit mild anisotropy and heterogeneity. After the near-isotropic backbone is well calibrated, these residual effects become the key bottleneck for further closing the real-to-sim gap. Although neural networks can fit dynamics end-to-end, such black-box modeling discards strong physical priors, leading to poor data efficiency and overfitting. Therefore, we propose MoSA, a motion-constrained stress adaptation framework that targets these residual effects to further improve real-to-sim dynamics learning. MoSA uses an isotropic model as a physics prior and learns residual stress operators to capture mild anisotropy and heterogeneity. It progressively adapts stresses via microplane-constrained redistribution in a physics-informed cascaded network. We further impose motion constraints by supervising temporal and spatial derivatives of the deformation field. Experimentally, our learned dynamics achieves superior accuracy, generalization, and robustness, while learning physically meaningful residual anisotropy. Finally, we validate MoSA in a robot manipulation setting, showing that better real-to-sim dynamics modeling translates into more reliable sim-to-real transfer. Project Page is available at https://mercerai.github.io/MoSA/.

Jiaxu Wang, Junhao He, Jingkai Sun +5

Hong Kong University of Science and Technology, Guangzhou, China · MMLab, Chinese University of Hong Kong, Hong Kong SAR · The University of Hong Kong, Hong Kong SAR

Residual Learning Sim-to-Real Transfer Physics-Based Simulation Deformable Object Simulation

May 20, 2026cs.CV

Rethinking Cross-Layer Information Routing in Diffusion Transformers

Diffusion Transformers (DiTs) have become a de facto backbone of modern visual generation, and nearly every major axis of their design -- tokenization, attention, conditioning, objectives, and latent autoencoders -- has been extensively revisited. The residual stream that governs how information accumulates across layers, however, has been directly inherited from the original Transformer. In this paper, we present a systematic empirical analysis of cross-layer information flow in DiTs, jointly along depth and denoising timestep, and identify three concrete symptoms of traditional residual addition, namely monotonic forward magnitude inflation, sharp backward gradient decay, and pronounced block-wise redundancy. Motivated by this diagnosis, we propose Diffusion-Adaptive Routing (DAR), a drop-in residual replacement that performs learnable, timestep-adaptive, and non-incremental aggregation over the history of sublayer outputs. Moreover, the proposed DAR is compatible with many modern Transformer enhancement methods, such as REPA. On ImageNet

256\times256

, DAR improves SiT-XL/2 by

2.11

FID (

7.56

vs.

9.67

) and matches the baseline's converged quality with

8.75\times

fewer training iterations. Stacked on top of REPA, it yields a

2\times

training acceleration in the early stage, suggesting cross-layer information routing as an underexplored design axis in diffusion modeling, one that operates orthogonally to existing representation-alignment objectives. Beyond pretraining, DAR can also be applied during the fine-tuning stage of large-scale T2I models and preserves high-frequency details during Distribution Matching Distillation.

Chao Xu, Maohua Li, Qirui Li +9

Alibaba Group · Nanjing University · Zhejiang University

Diffusion Transformer Residual Learning Diffusion Model Acceleration

May 18, 2026cs.LG

Residual Paving: Diagnosing the Routing Bottleneck in Selective Refusal Editing

We study selective refusal editing as a three-way control problem: induce non-refusal on designated edit prompts while preserving benign behavior and harmful refusals outside the edit set. We introduce Residual Paving, a routed residual editing method for frozen instruction-tuned transformers that separates route selectivity, whether to intervene, from residual-edit capacity, what edit to apply. An early-layer router predicts a scalar gate and expert mixture; when active, prompt-conditioned bottleneck residual experts apply later-layer residual updates while leaving the backbone unchanged. This decomposition supports an oracle-routing diagnostic where only the learned scalar gate is replaced with the held-out edit/keep label, leaving the residual editor and frozen backbone fixed. On the primary Gemma-3-4B-IT held-out split, learned Residual Paving reduces edit refusal from 88.6% to 4.0%, with 95.5% benign distribution preservation and 87.3% harmful distribution preservation. Same-protocol one-direction steering controls are much weaker on edit success, leaving edit refusal at 86.8% for Edit-target ActAdd and 78.9% for DIM-style refusal steering. The remaining failure is off-target harmful-keep degradation: harmful refusal remains below the frozen-base rate, 65.3% vs. 81.6%. Across six backbones, oracle routing improves the keep-side diagnostic score on every reported row, with median gain +12.9 pp, supporting the interpretation that learned route selectivity is the main observed bottleneck. Trajectory diagnostics on two backbones further suggest directed movement toward edit-target continuations rather than generic refusal suppression.

Bryce Hinkley, Peyman Najafirad

University of Texas at San Antonio

Residual Learning LLM Refusal Behavior Model Editing

May 15, 2026cs.CV

Res $^2$ CLIP: Few-Shot Generalist Anomaly Detection with Residual-to-Residual Alignment

Few-shot Generalist Anomaly Detection requires models to generalize to novel categories without retraining, posing significant challenges in real-world scenarios with scarce samples and rapidly changing categories. Existing CLIP-based methods face two major challenges: coarse-grained unified text prompts struggle to adapt to fine-grained foreground-background differences, causing cross-granularity mismatch; and fine-tuning on auxiliary datasets disrupts CLIP's inherent open-world generalization due to domain shift, leading to cross-category generalization degradation. To address these, we propose to shift multimodal alignment entirely into a unified residual space, where residual representations naturally eliminate fine-grained normal feature differences across regions and class-specific biases, simultaneously resolving both problems. Based on this insight, Res

^2

CLIP, the first residual-to-residual alignment framework that symmetrically bridges visual and text modalities within CLIP's residual space, is designed. The framework is developed from a residual perspective into three branches: a text prompt-based branch, a visual prompt-based branch, and a novel residual-to-residual alignment branch. All learnable optimizations are constrained within the residual domain, and the residual alignment optimization objectives are designed to force the model to focus on relative anomaly deviations rather than optimizing class-specific features. Experiments on multiple datasets demonstrate the effectiveness of our architecture. The code is available at https://github.com/hito2448/Res2CLIP.

Xinyue Liu, Jianyuan Wang, Biao Leng +1

Beihang University · University of Science and Technology Beijing · Beijing Jiaotong University

Few-Shot Anomaly Detection VLM Adaptation Residual Learning Multimodal Anomaly Detection Vision-Language Alignment Anomaly Detection

May 15, 2026cs.NE

XOResNet: Exclusive-OR Meta-Residuals Facilitate Deep Spiking Neural Networks Learning

Spiking neural networks (SNNs) hold promise for demonstrating superior learning and representation capabilities in deep models. Given the tremendous success of ResNet in deep learning, it would naturally follow to train deep SNNs with residual learning. However, existing residual structures for constructing deep SNNs still present challenges of spike redundancy or information loss, as well as redundant learning. In the present study, we first aim to address issues of relative spike redundancy in identity mapping and information loss in non-identity mapping. To this end, we propose an OR-ADD (OA) shortcut connection to merge output spikes/currents from two branches in the residual structure. Furthermore, to mitigate redundant learning in the backbone branch of the residual structure, we introduce the concept of XOR meta-residuals, i.e., selecting pre-learning residuals using the Exclusive-OR (XOR) operation for the backbone branch. Finally, by integrating the OA shortcut and XOR meta-residuals, we devise the XOR residual block and further construct XOResNet with varying depths based on this block. Extensive experiments on four datasets, Fashion-MNIST, CIFAR-10, CIFAR-100, and miniImageNet, show that the proposed XOResNet outperforms existing state-of-the-art deep SNNs optimized via gradient descent. These results validate the effectiveness of our OA shortcut and XOR meta-residual components in overcoming fundamental limitations of residual learning in SNNs, providing new architectural insights for building high-performance neuromorphic systems.

Jianfang Wu, Junsong Wang

School of Artificial Intelligence, Shenzhen Technology University, Shenzhen 518118, China · Faculty of Data Science, City University of Macau, Macau 999078, China

Residual Learning Spiking Neural Networks

May 13, 2026cs.LG

Delta Attention Residuals

Attention Residuals replace standard additive residual connections with learned softmax attention over previous layer outputs, enabling selective cross-layer routing. However, standard Attention Residuals still attend over cumulative hidden states in previous layers, which are highly redundant. We show that this redundancy leads to routing collapse in deeper layers: attention weights become low-contrast and closer to uniform (max weight

{\approx}

0.2), limiting the model's ability to select informative states in previous layers. This raises a key but underexplored design question: what layer-wise representations should be routed in Attention Residuals? To answer this question, we propose Delta Attention Residuals, which attend over deltas -- the change introduced by each sublayer (

\mathbf{v}_i = \mathbf{h}_{i+1} - \mathbf{h}_i

) -- instead of cumulative states. Delta representations are structurally diverse and yield higher-contrast attention distributions (max weight

{\approx}

0.6), enabling more selective and effective routing across layers. This principle applies at both per-sublayer and block granularity. Across all tested scales (220M--7.6B), Delta Attention Residuals consistently outperform both standard residuals and Attention Residuals, with 1.7--8.2% validation perplexity gains. Delta Attention Residuals also enables converting pretrained checkpoints into Delta Attention Residuals via standard fine-tuning. Code is available at https://github.com/wdlctc/delta-attention-residuals-code.

Cheng Luo, Zefan Cai, Junjie Hu

Independent Researcher · University of Wisconsin–Madison

Attention Residual Connections Residual Learning Transformer Attention Attention Mechanisms

May 12, 2026stat.ML

Spatial Adapter: Structured Spatial Decomposition and Closed-Form Covariance for Frozen Predictors

We present the Spatial Adapter, a parameter-efficient post-hoc layer that equips any frozen first-stage predictor with a structured spatial representation of its residual field and an induced closed-form spatial covariance. The adapter operates as a cascade second stage on residuals, jointly learning a spatially regularized orthonormal basis and per-sample scores via a tractable mini-batch ADMM procedure, without modifying any first-stage parameter. Because the first-stage parameters are frozen, the adapter does not retrain the backbone; its role is to supply a compressed distributional summary of the residual field. Smoothness, sparsity, and orthogonality together turn a generic low-rank factorization into an identifiable spatial representation whose induced residual covariance admits a closed-form low-rank-plus-noise estimator; the effective rank is determined data-adaptively by spectral thresholding, while the nominal rank K is an optimization-side upper bound only. This covariance enables kriging-style spatial prediction at unobserved locations, with plug-in uncertainty quantification as a secondary downstream use. Across synthetic data, Weather2K for spatial-holdout prediction, and GWHD patch grids as a basis-transferability diagnostic, the adapter recovers residual spatial structure when paired with frozen first stages from linear models to deep spatiotemporal and vision backbones; the added representation uses fewer than K(N+T) parameters alongside a compact residual-trend network.

Wen-Ting Wang, Wei-Ying Wu, Hao-Yun Huang +1

Institute of Statistics, National Chung Hsing University · Department of Applied Mathematics, National Dong Hwa University · Department of Applied Mathematics National Dong Hwa University

Representation Learning Residual Learning

May 10, 2026cs.CV

DegBins: Degradation-Driven Binning for Depth Super-Resolution

Depth super-resolution (DSR) aims to recover a high-resolution (HR) depth map from its low-resolution (LR) counterpart. With color image guidance, this task is typically formulated as learning the residual between HR and LR in a low-dimensional feature space. However, this additive formulation is insufficient to accurately capture the complex relationship between HR and LR, especially under spatially varying degradations. In this paper, we introduce DegBins, a novel DSR framework that leverages degradation-driven binning to adaptively enhance residual modeling. Specifically, DegBins reformulates the regression-based DSR as a hybrid classification-regression problem, where the residual depth is represented as a linear combination of discrete depth bins weighted by their learned probability distribution, yielding more flexible and expressive representations. Furthermore, DegBins models the degradation relationship between HR and LR in a high-dimensional feature space, enabling adaptive bin range adjustment and probability optimization conditioned on local degradation characteristics. To progressively improve reconstruction quality, DegBins adopts a multi-stage refinement scheme, where each stage performs finer-grained bin partitioning and probability updating based on the former estimation. This coarse-to-fine design facilitates more accurate depth recovery, particularly in regions with severe degradations or complex structural variations. Extensive experiments across five benchmarks demonstrate that DegBins consistently outperforms existing state-of-the-art methods in terms of accuracy, robustness, and generalization.

Zhiqiang Yan, Zhengxue Wang, Jian Yang +1

Department of Computer Science, National University of Singapore · Nanjing University of Science and Technology

Depth Estimation Residual Learning Image Super-Resolution

May 8, 2026cs.LG

A Qualitative Test-Risk Mechanism for Scaling Behavior in Normalized Residual Networks

The scaling behavior, in which test performance often improves as model size and data increase, is a central empirical phenomenon in modern deep learning, yet its theoretical basis remains incomplete. In this paper, we study depth expansion in normalized residual networks: starting from a trained model in an old hypothesis class, we insert a new residual block at an intermediate layer and ask when such an expansion can yield a provable improvement in test risk. We develop a unified framework that decomposes this question into representational gain, optimization gain, and generalization transfer. First, under a first-order descent condition near zero initialization, we prove that the expanded hypothesis class contains an auxiliary jumpboard model with strictly smaller population risk than the original model. Second, under norm control tailored to post-normalized residual architectures, we establish a norm-based Rademacher complexity bound for the expanded model class. These ingredients lead to two complementary test-risk guarantees: one route passes through population risk and is tighter when a positive population margin is available, while the other works directly at the train/test level, avoids Hoeffding transfer, and is more robust in degenerate regimes. Together, these results provide a theorem-driven mechanism under which residual depth expansion can improve test performance in normalized residual networks. More broadly, they suggest that scaling is inherently joint: depth creates new improving directions, width enhances the finite-sample observability of weak signals, and data determines whether the statistical cost of expansion can be controlled.

Daning Cheng, Zeyu Liu, Jun Sun +4

ICT · Zhejiang Lab · JD corporation +1

Neural Network Generalization Residual Learning Neural Scaling Laws Statistical Learning Theory

May 7, 2026cs.LG

Mean Mode Screaming: Mean--Variance Split Residuals for 1000-Layer Diffusion Transformers

Scaling Diffusion Transformers (DiTs) to hundreds of layers introduces a structural vulnerability: networks can enter a silent, mean-dominated collapse state that homogenizes token representations and suppresses centered variation. Through mechanistic auditing, we isolate the trigger event of this collapse as Mean Mode Screaming (MMS). MMS can occur even when training appears stable, with a mean-coherent backward shock on residual writers that opens deep residual branches and drives the network into a mean-dominated state. We show this behavior is driven by an exact decomposition of these gradients into mean-coherent and centered components, compounded by the structural suppression of attention-logit gradients through the null space of the Softmax Jacobian once values homogenize. To address this, we propose Mean-Variance Split (MV-Split) Residuals, which combine a separately gained centered residual update with a leaky trunk-mean replacement. On a 400-layer single-stream DiT, MV-Split prevents the divergent collapse that crashes the un-stabilized baseline; it tracks close to the baseline's pre-crash trajectory while remaining substantially better than token-isotropic gating methods such as LayerScale across the full schedule. Finally, we present a 1000-layer DiT as a scale-validation run at boundary scales, establishing that the architecture remains stably trainable at extreme depth.

Pengqi Lu

Beijing, China

Deep Learning Optimization Representation Collapse Diffusion Transformer Residual Learning

May 7, 2026cs.LG

The E $Δ$ -MHC-Geo Transformer: Adaptive Geodesic Operations with Guaranteed Orthogonality

We present the E

Δ

-MHC-Geo Transformer, a novel architecture that unifies Manifold-Constrained Hyper-Connections (mHC), Deep Delta Learning (DDL), and the Cayley transform to obtain input-adaptive, unconditionally orthogonal residual connections. Unlike DDL, whose Householder operator is orthogonal only at

β\in \{0,2\}

, our Data-Dependent Cayley rotation

Q(x)=(I+(β/2)A(x))^{-1}(I-(β/2)A(x))

preserves orthogonality for all

β

and all inputs. To handle negation, an eigenvalue

-1

case that Cayley provably excludes, we introduce the E

Δ

-MHC-Geo Hybrid, which combines Cayley rotation with Householder reflection via a learned operator-selection gate

X'=γ(X)Q(X)X+(1-γ(X))H_2(X)X

. A midpoint-collapse regularizer,

4γ(1-γ)

, encourages boundary gate decisions, where each selected component is orthogonal. In matched-parameter comparisons, with approximately 1.79M parameters per model and mean +/- standard deviation over 3 seeds, against four baselines including the concurrent JPmHC, E

Δ

-MHC-Geo achieves the best long-horizon stability, 1.9x over JPmHC and 3.8x over GPT; the best near-

π

rotation loss, 4.5x over JPmHC on single-plane; strong norm preservation, with 0.001 mean deviation; and 0.96 negation cosine alignment in a diagnostic reflection probe, all with 33% fewer layers. While JPmHC's wider representation excels on pure rotation, its finite Cayley residual mixer excludes an exact

λ=-1

operator and has no reflection branch, motivating our hybrid approach for accessing both connected components of

O(n)

.

Arash Shahmansoori

Independent Researcher

Transformer Residual Learning Hyper-Connections Orthogonal Representation Learning

May 5, 2026cs.LG

Transformers with Selective Access to Early Representations

Several recent Transformer architectures expose later layers to representations computed in the earliest layers, motivated by the observation that low-level features can become harder to recover as the residual stream is repeatedly transformed through depth. The cheapest among these methods add static value residuals: learned mixing coefficients that expose the first-layer value projection V_1 uniformly across tokens and heads. More expressive dense or dynamic alternatives recover finer-grained access, but at higher memory cost and lower throughput. The usefulness of V_1 is unlikely to be constant across tokens, heads, and contexts; different positions plausibly require different amounts of access to early lexical or semantic information. We therefore treat early-representation reuse as a retrieval problem rather than a connectivity problem, and introduce Selective Access Transformer (SATFormer), which preserves the first-layer value pathway while controlling access with a context-dependent gate. Across models from 130M to 1.3B parameters, SATFormer consistently improves validation loss and zero-shot accuracy over the static value-residual and Transformer baselines. Its strongest gains appear on retrieval-intensive benchmarks, where it improves over static value residuals by approximately 1.5 average points, while maintaining throughput and memory usage close to the baseline Transformer. Gate analyses suggest sparse, depth-dependent, head-specific, and category-sensitive access patterns, supporting the interpretation that SATFormer learns selective reuse of early representations rather than uniform residual copying. Our code is available at https://github.com/SkyeGunasekaran/SATFormer.

Skye Gunasekaran, Téa Wright, Rui-Jie Zhu +1

UC Santa Cruz · UC Berkeley

Transformer Residual Learning Transformer Attention

May 5, 2026cs.CV

RPBA-Net: An Interpretable Residual Pyramid Bilateral Affine Network for RAW-Domain ISP Enhancement

To address module fragmentation, uninterpretable mappings, and deployment constraints in RAW-domain demosaicing, color correction, and detail enhancement, this paper proposes RPBA-Net, an interpretable residual pyramid bilateral affine network for RAW-domain ISP enhancement. Given packed RAW as input, the method performs residual affine base reconstruction by estimating a base RGB representation and learning identity-guided residual affine corrections, thereby unifying demosaicing and enhancement. It further builds pyramid bilateral affine grids and combines guide-driven autoregressive adaptive slicing with adaptive cross-layer fusion to hierarchically model global tone restoration and local texture enhancement. In addition, smoothness, cross-scale consistency, and magnitude regularization terms are introduced to improve model stability, controllability, and structural interpretability. Extensive experiments demonstrate that RPBA-Net surpasses representative RAW-to-sRGB methods and achieves state-of-the-art performance in reconstruction fidelity and perceptual quality, while maintaining low model complexity and strong deployment potential for mobile and embedded platforms.

Yucheng Xin, Wu Chen, Xiang Chen +7

School of Information Science and Engineering, Shandong Normal University, Jinan, China · National University of Defense Technology, Changsha, China · Nanjing University of Science and Technology, Nanjing, China +2

Image Enhancement Residual Learning

May 5, 2026cs.RO

Robust Path Tracking for Vehicles via Continuous-Time Residual Learning: An ICODE-MPPI Approach

Model Predictive Path Integral (MPPI) control is a powerful sampling-based strategy for nonlinear autonomous systems. However, its performance is often bottlenecked by the fidelity of nominal dynamics. We propose ICODE-MPPI, a robust framework that leverages Input Concomitant Neural Ordinary Differential Equations (ICODEs) to learn and compensate for unmodeled residual dynamics. Unlike discrete-time learners, ICODEs maintain physical consistency and temporal continuity during the MPPI prediction horizon. High-fidelity simulations on complex trajectories demonstrate that ICODE-MPPI achieves up to a 69% reduction in cross-tracking error under persistent disturbances compared to standard MPPI control. Furthermore, our analysis confirms that ICODE-MPPI significantly suppresses control chattering, yielding smoother steering commands and superior robust performance.

Shugen Song, Wenjie Mei, Chengyan Zhao

School of Automation, Southeast University, Nanjing 210096, China · School of Automation and the Key Laboratory of MCCSE of the Ministry of Education, Southeast University, Nanjing 210096, China · Graduate School of Computer Science and Systems Engineering, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka-shi, Fukuoka, Japan

Nonlinear MPC Residual Learning Autonomous Driving Robust Control MPPI Control Neural ODEs

May 4, 2026cs.LG

Forecasting Medium-Horizon Alzheimer's Disease Progression: Residual Gap-Aware Transformers for 24-Month CDR-SB Change from ADNI Clinical and Biomarker Histories

Medium-horizon Alzheimer's disease progression prediction is difficult because future clinical scores can remain tied to baseline severity, while biomarker histories are irregular and incompletely observed. We develop an anchor-based analysis of 24-month Clinical Dementia Rating Sum of Boxes (CDR-SB) change using harmonized Alzheimer's Disease Neuroimaging Initiative (ADNI) tables. Each labeled sample is anchored at a mild cognitive impairment visit, uses only clinical and biomarker history observed at or before that anchor, and defines the response as CDR-SB at the future visit closest to 24 months within an 18--30 month window minus anchor CDR-SB. The analytic cohort contains 2,600 labeled anchors from 858 participants and 7,276 longitudinal rows. We propose a residual gap-aware transformer that combines a mixed-effects statistical reference with transformer-based residual learning from pre-anchor clinical and biomarker histories. The model uses participant-level random intercepts in the mixed-effects reference, observation-level triplet tokenization for irregular histories, and a learned nonnegative time-gap penalty inside self-attention. We compare the proposed model with a Bayesian-information-criterion-selected linear mixed-effects baseline, GRU-D, and STraTS under repeated participant-level train--test splits. Across five participant-level random seeds, the proposed model achieves the best mean test performance across all reported metrics, reducing MSE by 13.1% and increasing prediction--observation correlation by 26.4% relative to the mixed-effects baseline. It also improves over both GRU-D and STraTS in mean error and correlation. These results show that statistical anchoring and gap-aware residual learning provide a useful structure for medium-horizon Alzheimer's disease progression prediction.

Ran Tong, Tong Wang, Lanruo Wang +1

Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75080, United States · Department of Plant Science and Landscape Architecture, University of Connecticut, Storrs, CT, United States · Naveen Jindal School of Management, University of Texas at Dallas, Richardson, TX 75080, United States +1

Irregular Time-Series Modeling Alzheimer's Disease Residual Learning Clinical Outcome Prediction Alzheimer's Disease Progression Prediction Time Series Transformers

May 4, 2026cs.LG

Geometric and Spectral Alignment for Deep Neural Network I

Deep residual architectures are modeled as products of near-identity Jacobians. This paper proves deterministic quotient-geometric estimates for singular spectra of Frobenius-normalized layer factors, emphasizing a normalized top-radial Cartan coordinate and fitted power-law chart. Full-rank factors are mapped from

\mathrm{GL}(d)

to the positive cone by

A\mapsto A^\top A

, then to ordered eigenvalue data. Under Frobenius normalization, exact power-law spectra form a trace-normalized Cartan orbit. This orbit is a Gibbs family on ranks, a Fisher information line, and a Bures--Wasserstein curve with line element

d/4

times Fisher information. The main rigidity theorem is a slack-aware margin inequality: interface radial amplitude, non-backtracking slack, and signed residual variation control displacement of the fitted Cartan coordinate. In the exact-chart zero-slack case, a depth-

L

budget gives exponent drift of order

(\log M)/L

; generally, slack and residual increments augment the bound. We separate scalar top-radial from full-Cartan spectral control, which also needs Bures/Hellinger residual variation. We prove approximate-power-law and metric-chart versions, converse lower bounds, Fisher--KL/Bures action estimates, and near-identity expansions for normalized residual chains. Near-identity results verify transport budgets; chart quality remains measurable. Effective rank is a spectral-energy quantile, giving finite-width power-law tail bounds and robust rank-window transition estimates. Empirical static-weight exponent profiles serve as diagnostics; full verification also requires interface budgets, slacks, and residuals for the same operator chain.

Ziran Liu, Wei Wang, Jinhao Wang +5

Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS), Shanghai 200433, China · Futurewei Technologies, Inc., San Jose, CA 95131 · Dept. of Computer Science and Engineering, Santa Clara University, Santa Clara, CA 95050 +2

Residual Learning Spectral Methods