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

Oct 8, 2026stat.ML

LAIR-Net: Leaky Alignment-Impulse Residual Networks for Tabular Regression

Deep randomized models fix hidden-layer parameters through random initialization and learn only closed-form readouts, typically adding depth by stacking random trans formations without target-aware control of hidden-state evolution. We propose LAIR Net, the Leaky Alignment-Impulse Residual Network, which mixes a shallow learned anchor into each hidden state through a leaky residual transition. We derive a depth uniform bound on input-perturbation sensitivity and use controlled simulations to attribute gains over a randomized baseline to the anchor rather than recursion or added capacity. Benefits emerge when a nonlinear target structure is learnable at the available noise level and diminish for nearly linear targets or dominant noise. Across 23 benchmark datasets, LAIR-Net achieves the best average rank among eight randomized networks and twelve conventional models, with relative performance associated with the same nonlinear-structure and noise quantities identified in simulation.

Rahul Goswami, Aryan Bhambu, Bittu Karmakar

Indian Institute of Technology Guwahati · SAFIR, Sorbonne University Abu Dhabi · Indian Institute of Technology Bombay

Tabular Regression Residual Learning Neural Network Robustness

Oct 8, 2026cs.CV

Conditional Residual Prediction: Improving Autoregressive Video Diffusion without a Bidirectional Teacher

Causal video diffusion models generate video autoregressively, which suits streaming, interactive, and long-video generation. Under standard training, however, they often yield lower generation quality than bidirectional models of the same size. Many existing approaches address this gap by initializing from or distilling a pretrained bidirectional teacher. We instead train a causal model from an image-model initialization, with no bidirectional video model at any stage. Because this path requires neither a large bidirectional teacher nor a complex distillation pipeline, it is simpler and more scalable. On this path, we find that a causal model trained on ground-truth history becomes strongly dependent on it, so that at inference errors in its own generated history propagate forward. We hypothesize that much of this dependence is unnecessary, because the current input already determines much of what the history provides. We propose Conditional Residual Prediction (CRP), a simple recipe for reducing a model's reliance on a condition: the model first predicts the target without the condition, and the condition may only add a residual on top of this prediction. Applied to history, CRP makes the model predict each chunk from the present as far as it can and use the past only for what the present cannot supply. In controlled experiments, CRP nearly closes the 6.14-point gap to a bidirectional model trained under the same setup. Scaling this recipe, we train Optica, a 2B-parameter causal video model that autoregressively generates 5-second 480p videos and reaches 82.78 on VBench with only about 15M training videos.

Bowen Zheng, Zhiguang Liu, Jiarong Ou +2

The Chinese University of Hong Kong, Shenzhen · Tencent Hunyuan

Video Diffusion Models Video Generation Autoregressive Video Generation Residual Learning

Oct 8, 2026cs.SC

RISR: Residual-Informed Scientific Equation Discovery with Large Language Models

Symbolic regression combines structural search with numerical fitting, but aggregate fit scores do not describe how the remaining error varies across inputs. We introduce RISR, a residual-informed method that uses these error patterns to guide formula discovery and learn which corrections are worth fitting. A residual encoder compresses aligned inputs, targets, current predictions, and residuals into continuous tokens that condition a language model to propose formulas. For subsequent refinement, a dual-view relational encoder uses additive and regularized multiplicative residuals to predict the post-fit utility of candidate corrections. We evaluate RISR on scientific tasks from the LLM-SRBench. RISR achieves 63.57% and 38.50% ID accuracy at the 1% and 0.1% pointwise relative-error tolerances, respectively. The corresponding OOD accuracies are 56.07% and 38.24%. RISR outperforms the reported baselines using the same backbone. The results show that our residual-informed approach can improve numerical equation recovery.

Haobo Li, Wenshuo Zhang, Wenxiao Zhao +6

Shanghai AI Laboratory · The Hong Kong University of Science and Technology · University of California, Los Angeles

Symbolic Regression Large Language Model-Guided Scientific Discovery Residual Learning

Oct 8, 2026cs.LG

CARE: A Lightweight Plug-in Gated Correction and Uncertainty-aware Module for Long-term Time Series Forecasting

Multivariate long-horizon forecasting is critical to electricity load scheduling and traffic flow management, and to financial risk control. Existing deterministic backbones output a single trajectory, masking heterogeneous prediction difficulty across horizons and channels and providing no localized reliability signal. We present CARE (Corrective branch with Aligned context and Relative-error Estimation), a lightweight plug-in that enhances any deterministic forecaster without architectural redesign. Operating in parallel with the base model, CARE resamples historical context to match the forecast horizon, learns residual correction patterns from this aligned history, and applies scale-aware bounded updates modulated by per-coordinate sigmoid risk gates. A multi-objective loss jointly optimizes forecast accuracy, residual tracking, risk alignment, and base-model anchoring. Across eight benchmarks with three representative backbones, CARE improves accuracy with marginal parameter and latency overhead. Its risk gates reliably identify high-error regions: on Weather, the highest-gate tertile exhibits nearly four times the error of the lowest-gate tertile, offering planners an interpretable per-step trust signal. Code is available at https://github.com/CG-BNYC/CARE.

Guo Cheng, Changlong Lv, Jingyi Hou

School of Artificial Intelligence, University of Science and Technology Beijing, Beijing 100083, China · Institute of Artificial Intelligence, University of Science and Technology Beijing, Beijing 100083, China · Key Laboratory of Intelligent Bionic Unmanned Systems, Ministry of Education, University of Science and Technology Beijing, Beijing 100083, China

Multivariate Time Series Forecasting Long-Term Time Series Forecasting Residual Learning

Oct 7, 2026cs.CV

Temporal Residual Bottleneck for Robust Asynchronous Collaborative Perception

Collaborative perception extends the sensing range of autonomous vehicles, but its performance degrades when shared features arrive stale or incomplete. Most latency-robust methods compensate delayed collaborator features through flow-guided alignment or direct feature transport. In this work, we formulate asynchronous collaborative perception as temporal residual prediction. Our Temporal Residual Bottleneck keeps a deterministic pose-warped collaborator feature as a conservative anchor and uses a

Δt

-conditioned xLSTM to extract residual temporal evidence from the available history. A detector-facing residual bottleneck then applies only gated, regularized corrections before ego-side fusion, reducing the risk of overwriting reliable static structure when temporal correspondence is uncertain. Experiments on DAIR-V2X and OPV2V show that our method is especially effective under severe fixed/irregular delays and packet drops. On DAIR-V2X, the reported checkpoint trades a small amount of synchronized peak accuracy for better robustness under stronger communication degradation. Controlled diagnostics further indicate that direct feature transport has oracle headroom but can become unreliable when deployed without accurate correspondence. These results support temporal residual fusion as a practical alternative for asynchronous and incomplete collaborative perception. Code will be publicly released at https://url.fzi.de/8dk38.

Melih Yazgan, Ahmed Abouelazm, J. Marius Zöllner

FZI Research Center for Information Technology · Karlsruhe Institute of Technology

Cooperative Perception Autonomous Driving Perception Residual Learning

Oct 7, 2026q-fin.ST

Residual Learning in Empirical Asset Pricing

Shallow models are special cases of deep models, and deep models theoretically have the potential to outperform the shallow ones. However, the existing empirical asset pricing literature provides strong benchmarks for shallow models. Residual learning allows neural network models in asset pricing to go deeper by preserving and refining their shallow counterparts. The out-of-sample Sharpe ratio for value-weighted long-short portfolios of deep residual models (2.07) is higher than that for the corresponding shallow ones (1.92) and more than twice that of the deep feedforward models (0.89). We show that model depth is a source of additional economic value in asset pricing. Residual learning can be used to deepen other neural-network-based asset pricing models if they contain intermediate layers. Our design also provides one way to scale asset pricing models, making native "large asset pricing models" more feasible.

Dexin Peng, Xiaoyu Wang

FinTech Thrust, Hong Kong University of Science and Technology (Guangzhou)

Quantitative Finance Residual Learning

Sep 30, 2026cs.LG

LARC: Low-Rank Adaptive Residual Connections for Learning in Frozen Models

Low-Rank Adaptive Residual Connections (LARC) give a frozen model a compact numerical state that can learn from feedback. The map

h+BAh

adds a low-rank correction to a hidden representation. A slow state

ρ

learns starting factors across tasks; a private fast state

Φ

copies them, changes with feedback, and resets to the trained initialization. This report specifies an input-side realization of the numerical policy carrier in Memory-Mediated Learning Architecture and examines its factor-space dynamics and learning lifetime. We study a rank-4 input residual with 12,288 trainable parameters on a frozen MiniCPM5-1B-SFT substrate. In a four-candidate program-selection task, two feedback-gradient steps reduce expected query execution error by 24.65 and 36.65 percentage points relative to resetting to the respective trained static and post-adaptation initializations. These development results cover 16 parameter groups and three paired training seeds. A direct support-loss selection rule is much more accurate, reaching 0.78125% error. In a repository-balanced chronological replay of public continuous-integration jobs, retaining online updates raises half-Brier loss from 0.1274 to 0.1808. A fixed follow-up intervention records same-batch non-descent and inconsistent future benefit from shrinking updates. Together, the algebra and measurements distinguish residual capacity, adaptation relative to a starting point, and usefulness on later decisions.

Junyi Zou, Avrova Donz

MMLA-org · Communication University of China (CUC), No. 1 Dingfuzhuang East Street, Chaoyang District, Beijing 100024, China

Meta-Learning Residual Learning Low-Rank Adaptation Online Learning

Sep 30, 2026cs.LG

RACE: Residual-Aware Test-Time Adaptation for Neighbor-Rich Time-Series Foundation Model Forecasting

Time-series foundation models (TSFMs) perform strongly across forecasting tasks, but their per-series inference is ill-suited to neighbor-rich forecasting, where each query has access to related but nonidentical historical series. Continuous glucose monitoring (CGM) and Web/cloud workloads exemplify this setting: CGM trajectories share physiological patterns but vary across individuals, devices, and conditions, while Web/cloud workloads combine common operating regimes with non-stationarity, heavy tails, and bursts. These histories share useful structure, yet neighbors are not equally relevant. Existing methods either fine-tune TSFMs for each target domain, incurring additional costs and offering limited transferability across backbones, or append retrieved series without verifying whether they support the current forecast. The key challenges are conflicting residual evidence from neighboring series and residual patterns that vary across TSFMs and forecasting tasks. We formulate test-time neighborhood scaling: using same-domain neighbor evidence without modifying the backbone. We propose RACE (Residual-Aware Correction of Forecasting Errors), a two-stage framework for using historical neighbors. We first retrieve query-compatible neighbors, align their residuals to the query scale, and aggregate coherent evidence into the training-free RACE-TF correction. Full RACE then uses a lightweight, domain-specific Gate to determine when applying the correction is beneficial, with a reusable training workflow across TSFM backbones. Across four TSFMs, RACE improves all three domain-aggregate metrics on both primary domains, with the largest gains on high-error queries. Within each domain, a Gate trained on one TSFM transfers to other backbones without adaptation, and the resulting pipeline improves all 72 cross-backbone metric comparisons over the matched frozen targets.

Hao-Nan Shi, Tong Wu, Chen-Cong Sun +3

School of Artificial Intelligence, Nanjing University · National Key Laboratory for Novel Software Technology, Nanjing University · Nanjing, China

Residual Learning Time Series Forecasting Time-Series Foundation Models

Sep 30, 2026cs.CV

ResARC: Residual-Aware AutoRegressive Coding for Ultra-Low Bitrate Image Compression

Progressive autoregressive image codecs provide an appealing paradigm for generative compression by quantizing continuous latents into discrete tokens, transmitting coarse-to-fine prefix tokens and generating the remaining suffix tokens at the decoder. However, their reconstruction quality is fundamentally limited by two residuals introduced along this pipeline: the quantization residual, arising from information loss during discrete tokenization, and the generation residual, resulting from imperfect autoregressive generation of the suffix tokens. To address these limitations, we introduce ResARC, a residual-aware autoregressive codec that explicitly compensates for both residuals at the decoder. Specifically, we generate the quantization residual with a diffusion transformer conditioned on the autoregressive decoding context, while requiring no additional side information. In parallel, we compute the generation residual at the encoder and employ a learned Generation Residual Codec to efficiently compress and transmit it for decoder-side correction. The recovered residuals are then integrated with the reconstructed latent representation and decoded through an adapted VAE decoder. Extensive experiments demonstrate that ResARC achieves competitive perceptual similarity while substantially improving distributional fidelity over leading generative codecs across the ultra-low bitrate regime. Code and models will be released soon.

Qin Yan, Ruixiao Dong, Yutao Xie +5

University of Science and Technology of China · Alibaba Group

Learned Image Compression Residual Learning Generative Image Compression

Sep 29, 2026cs.AI

Task-Relevant Null-Space Residuals for Non-Injective Neural Mappings

Non-injective mappings in neural networks map distinct inputs to the same representation, thereby implicitly inducing equivalence relations in the input space. However, the input differences eliminated by these mappings may still be required by downstream tasks, creating a mismatch between operator-induced indistinguishability and task-required distinctions. For non-injective linear operators realized in the current forward pass, their null spaces exactly characterize these invisible input variations. We propose Task-Relevant Null-Space Residuals (NSR), a general residual framework for non-injective linear mappings. NSR combines null-space component extraction from pre-mapping representations, member-level encoding and gating, and application-specific integration to exploit potentially task-relevant information under downstream supervision while preserving the original aggregation or merging rules. We evaluate NSR in two structurally different settings: token merging and graph aggregation. In token merging, NSR achieves higher semantic segmentation performance than the corresponding compressed baselines in 34 out of 36 evaluated configurations, with a maximum observed gain of 31.51 mIoU points under strong compression. In graph aggregation, NSR achieves 100% training accuracy on Tree-NeighborsMatch at depths d=2--6 across three backbones, alongside gains on heterophilic node classification and molecular graph regression. Together, these results support null-space residuals as a practical complement to non-injective linear mappings, enabling downstream models to learn from input distinctions invisible in the original operator's output.

Bizu Feng, Zhimu Yang, Shuming Wang +4

Institute of Artificial Intelligence Innovation and Industry, Fudan University, Shanghai, China · Shanghai Academy of AI for Science, Shanghai, China · Human Phenome Institute, Fudan University, Shanghai, China +1

Residual Learning

Sep 28, 2026cs.LG

LLN: Learnable Lens Networks for Parameter-Efficient Long-Horizon Dynamical Prediction

Explicit residual connections of the form (x+f(x)), often combined with normalization layers, have become a standard strategy for training very deep neural networks. However, residual addition primarily provides an algebraic shortcut for gradient propagation, while leaving the evolution of feature geometry across layers largely unconstrained. We introduce Learnable Lens Networks (LLN), a physics-inspired architecture that replaces direct feature-space residual accumulation with learnable optical transport in an augmented position-angle phase space. Each layer alternates between free propagation, which provides an implicit transport path, and a learnable lens field that performs nonlinear trajectory transformation and focusing. Theoretically, we establish that LLN transport is globally invertible and volume-preserving for any differentiable lens field, with the implemented coordinate-wise Gaussian transport further satisfying symplecticity. Importantly, these structural constraints do not limit expressivity: with unrestricted embeddings and readouts, LLN retain universal approximation of continuous end-to-end maps. Experiments across diverse dynamical systems demonstrate that LLN improves long-horizon prediction while using substantially fewer parameters than same-depth comparators. Further analysis reveals stable depth-wise gradient transport and interpretable learned dynamics under the coupled propagation and refraction design.

Binbin Yong, Zhao Su, Lan Guo +3

Lanzhou University · Monash University · University of Wollongong

Invertible Neural Networks Residual Learning Neural Network Training Dynamics

Sep 27, 2026cs.CV

Residual-Stream Burden Shapes Representation Learning in Diffusion Transformers

In diffusion-based generation, a neural network can be trained to predict the clean data, the noise, or the velocity from a noisy input. These prediction targets are interconvertible and describe the same generative process, yet plain Diffusion Transformers operating on large pixel patches succeed with clean prediction and fail with noise or velocity prediction. We argue that this asymmetry arises because noisy targets require the residual stream to preserve noise-dependent input variation through depth for the final readout, forcing subsequent layers to compute on noisy representations. A spectrally concentrated clean target imposes a lighter demand, leaving greater freedom to organize hidden representations for subsequent computation. We call this preservation requirement residual-stream burden and show how it shapes representation learning in Diffusion Transformers. Controlled experiments indicate that the exploitable structure is spectral concentration in patch space and that the bandwidth of the persistent residual state is a key resource for noisy prediction. We further show that this account is consistent with recent decoupled pixel-space architectures, whose diverse designs all reduce the residual-stream burden on the main pathway. To examine this understanding from a complementary direction, we expand and reorganize the residual-stream bandwidth directly, introducing Spatially Indexed Hyper-Connections (SiHC) that reach FID 1.71 on ImageNet

256^2

. Together, these results identify residual-stream burden as a mechanism through which prediction targets and architecture jointly shape representation learning in Diffusion Transformers.

Tongtong Liang, Siqi Kou, Ziqiao Xi +6

UC San Diego · Shanghai Jiao Tong University · Aether AI

Diffusion Transformer Residual Learning Hyper-Connections Diffusion-Based Image Generation Diffusion Models

Sep 25, 2026cs.LG

EPOC: Endpoint-Preserving Online Correction With Compressed Residual State for Multi-Horizon Time Series Forecasting

Completed forecasts provide residual feedback, but retaining full residual blocks increases auxiliary state. We propose Endpoint-Preserving Online Correction (EPOC) with a compressed residual state. It stores low-order discrete cosine transform (DCT) coefficients and the final value of the preceding residual block. Each channel shares the endpoint across component-wise online ridge regressions using current-forecast coefficients. We evaluate eight multivariate series, DLinear and PatchTST, three seeds, and two training variants: 96 matched fixed-base conditions at a 24-step horizon. EPOC achieves mean condition-wise reductions in mean squared error (MSE) and mean absolute error (MAE) of 15.40% and 9.35% from the uncorrected base, respectively, with a median of 6,352 B in retained auxiliary arrays. EPOC also outperforms the

δ

-Adapter, COSA, FAC, and OMPB in paired MSE on most conditions while retaining less state. Full ELF achieves the largest mean MSE reduction, 19.29%, but its median retained state is 474,048 B (

\times

75 relative to EPOC). Equal-size summary controls favor the endpoint by 1.65--2.20% in paired MSE; a coefficient-reconstructed endpoint yields similar accuracy to the observed endpoint, highlighting its role as a shared input. Increasing the retained DCT component count from 4 to 8 adds 1.00 percentage point of MSE reduction for 5,728 B. On jointly trained bases, EPOC lowers MSE by 16.69--20.15% relative to globally blended TEFL-style adapters applied to the same base. Code and numerical records are available at https://github.com/keiotakmin/endpoint-preserving-residual-correction.

Takumi Fujimoto, Hiroaki Nishi

School of Science for Open and Environmental Systems, Graduate School of Science and Technology, Keio University, Yokohama 223-8522, Japan · Department of System Design, Faculty of Science and Technology, Keio University, Yokohama 223-8522, Japan

Multivariate Time Series Forecasting Residual Learning Time Series Forecasting

Sep 23, 2026cs.LG

The Mechanics of Delta Learning: Target Design for Generalizable Scientific Machine Learning

In scientific machine learning,

Δ

-learning trains models on residual errors relative to physical baselines, assuming that more accurate baselines with smaller residual scales inherently improve downstream performance. Here, we demonstrate that residual scale alone is an insufficient heuristic for learnability. Evaluating molecular graph neural networks on total energy targets, we show that complex local descriptor baselines can yield small residual targets that are disproportionately rough within architecture-informed proxy spaces and harder to learn relative to their scale. Conversely, semi-empirical baseline reduces both scale and normalized roughness, improving in-domain and out-of-domain prediction. We introduce scale-normalized graph Dirichlet roughness (

D_{\text{IQR}}

) as a pre-training diagnostic for residual learnability and establish baseline complementarity as a core target-design principle, elevating target space formulation alongside model architecture as a key axis for scientific machine learning.

Kareem M. Gameel, Ihor Neporozhnii, Sjoerd Hoogland +1

Department of Physical and Environmental Sciences, University of Toronto Scarborough Alliance for AI-Accelerated Materials Discovery (A3MD) Toronto, Ontario, Canada · Alliance for AI-Accelerated Materials Discovery (A3MD) Toronto, Ontario, Canada · Department of Chemistry, University of Toronto Department of Physical and Environmental Sciences, University of Toronto Scarborough Alliance for AI-Accelerated Materials Discovery (A3MD) Toronto, Ontario, Canada

Residual Learning Scientific ML Molecular Property Prediction

Sep 23, 2026cs.CV

M-plicits: Neural Implicit Surfaces via Nested Multiscale Residuals

Encoding input coordinates with sinusoidal functions into multi-layer perceptrons (MLPs) has proven effective for implicit neural representations (INRs) of surfaces defined as zero-level sets. However, existing methods often struggle to balance training efficiency, rendering speed, and noise robustness: single-MLP approaches are expensive at inference, grid-based representations are fast but can limit surface smoothness and overfit input noise, and previous multiscale approaches frequently capture noise and produce artifacts due to hard spectral truncation. To address these limitations, we propose M-plicits, a multiscale framework that models surfaces as a residual sum of MLPs trained via a sequence of nested neighborhoods. Unlike existing residual approaches that rely on standard domain-wide sampling and require costly mesh extraction for visualization, our method strictly localizes supervision to narrow bands around the previous zero-level sets. This nested design naturally provides robustness against noisy input data: the coarse network acts as a low-pass filter that establishes a clean geometric prior, while subsequent residuals progressively refine the geometry without fitting to high-frequency artifacts. We further introduce a multiscale sphere-tracing algorithm and a GEMM-based analytical normal computation that bypasses auto-differentiation entirely, yielding high-fidelity real-time rendering. On Stanford and Thingi32, M-plicits achieves the best mean Chamfer distance in the coarse configuration and the best median Chamfer distance and IoU in the fine configuration, with substantially better noise robustness than iNGP, BACON, and IDF, while using an order of magnitude fewer parameters than grid-based baselines. Code, models, and data will be released at https://github.com/dsilvavinicius/m-plicits.

Vinícius da Silva, Isabelle Melo, Matheus Bessa +8

PUC-Rio · Universidade Federal de Santa Maria · Google DeepMind +2

Implicit Neural Representations 3D Reconstruction Residual Learning Neural Rendering

Sep 22, 2026cs.RO

Shaft-Configuration-Adaptive Catheter Tip Position Estimation via Motor-History Conditioned Residual Learning

Tendon-driven continuum manipulators are widely used in medical applications, where accurate tip-position estimation is essential for precise navigation and instrument positioning. However, patient anatomy and procedural setup impose task-dependent unknown shaft configurations, while friction, slack, and compliance introduce hysteresis, making tip estimation challenging. This paper presents a motor-history-conditioned gated recurrent unit (GRU) residual estimator for three-dimensional catheter tip estimation without direct shaft-configuration sensing. First, an initial multidirectional sweep strategy is applied to calibrate a geometric catheter model backbone, and encode the motor-angle and drive-torque response into a shaft-configuration context vector. During subsequent motion, the context conditions a GRU that predicts a task-space residual correcting this backbone, relying on motor measurements alone. The context remains fixed for the current shaft configuration, while the recurrent state captures the evolving actuation history. Across four disposable intra-cardiac echocardiography catheters and 16 bent shaft configurations, the method achieves 3.3mm open-loop tip RMSE, a 59% reduction relative to the constant-curvature baseline.

Peihan Zhang, Michael C. Yip, Ankur Kapoor +1

Digital Technology & Innovation, Siemens Healthineers, Princeton, NJ, USA. · Department of Electrical and Computer Engineering, University of California San Diego, United States.

Residual Learning Robotics Tendon-Driven Actuation Robot State Estimation

Sep 16, 2026cs.RO

Task-Oriented Active Learning of Residual Dynamics for Model Predictive Path Integral Control

Online residual learning can reduce model mismatch in predictive control, but passive data collection may fail to adequately cover states that become important later in the task. Task-agnostic active learning targets uncertain or informative regions, but information acquired in such regions does not necessarily improve task performance. This paper introduces Task-Oriented Information Acquisition (ToIA), an active-learning criterion for model predictive path integral control (MPPI) with online Gaussian process (GP) residual learning. For each sampled control sequence, ToIA estimates how much an observation obtained early in the rollout would reduce predictive uncertainty at later states on the same rollout, and weights this reduction by the rollout's relevance to the task. The score is evaluated over the existing MPPI rollout batch without sampling future observations or re-optimizing control under hypothetical posterior updates. In simulated off-road navigation across held-out maps with heterogeneous terrain, ToIA improved the goal-reaching success rate over passive GP learning by 19.3 and 27.4 percentage points and outperformed task-agnostic active-learning baselines across dense and sparse online-learning intervals. An ablation study indicates that task relevance is particularly important under sparse model updates. The implementation supports online control at 20 Hz on an NVIDIA RTX 2080 Ti.

Nobuaki Aoki, Hojin Lee, Stefan Sosnowski +1

Chair of Information-oriented Control (ITR), Department of Electrical and Computer Engineering, Technical University of Munich, Munich, Germany · Munich Institute of Robotics and Machine Intelligence (MIRMI), Technical University of Munich, Munich, Germany

Residual Learning Residual Dynamics Learning Active Learning MPPI Control

Sep 15, 2026cs.CV

ResLRP: The Role of Residual Cancellation in Attribution Instability in Vision Transformers

Vision Transformers (ViTs) are central to most modern vision models, yet obtaining input attributions that are fine-grained, faithful, and stable remains challenging. Layer-wise Relevance Propagation (LRP) has been adapted to transformer attention, but in ViTs it often produces noisy, unfaithful explanations. We show that the missing ingredient is the treatment of residual connections: cancellation effects in residual pathways lead to attribution explosion. Moreover, we find that these cancellations are substantially stronger in ViTs than in language transformers. To address this issue, we introduce Residual-aware Layer-wise Relevance Propagation (ResLRP), a simple extension of LRP whose propagation rules explicitly account for cancellations in residual branches, are exactly conservative, and provably bound relevance explosion. Causal channel-wise interventions confirm that residual cancellation, not a generic regularization effect, drives the instability. ResLRP substantially improves attribution quality across faithfulness and localization, evaluated on ViT architectures spanning supervised, self-supervised, contrastive, hierarchical, and multimodal families, as well as on the ground-truth-controlled FunnyBirds benchmark. The largest gains arise in modern Vision Language Models (VLMs), with +27-29% localization and up to 3.4x faithfulness scores. Beyond benchmarks, ResLRP localizes Sparse Autoencoder (SAE) features in input space, and our residual amplification measure serves as an architecture-level diagnostic predicting where attribution degrades.

Jim Berend, Reduan Achtibat, Daniel Schäffer +4

Fraunhofer Heinrich Hertz Institute · DSC ScaDS.AI, Leipzig University · ICT Cluster, Singapore Institute of Technology, Singapore +3

Transformer Interpretability Residual Learning Vision Transformer VLM Interpretability Explanation Stability Layer-Wise Relevance Propagation

Sep 14, 2026cs.LG

Task-Directed Residual AddUNet:Perfect-Reconstruction Routing for Full-Rate Representations

This paper establishes a perfect-reconstruction (PR) interpretation of AddUNet and its full-rate realization, and introduces a Residual Full-Rate PR architecture for task-directed representation learning. The survivor--skip structure of a constrained additive U-Net is shown to be exactly equivalent to a critically sampled multirate PR filter bank. The full-rate formulation removes the complementary-subband restrictions of the critically sampled system while preserving PR. A Residual Full-Rate PR architecture is then proposed to progressively route task-irrelevant, nuisance, or redundant structure away from the task-facing survivor while retaining the routed information explicitly. Exact reconstruction is guaranteed for arbitrary shape-compatible linear or nonlinear routing operators, without requiring invertibility, a matched synthesis bank, reconstruction loss, or learned decoder. The resulting architecture decouples representation design from reconstruction design: conservation is structural, while learning is devoted to task-directed routing. The same formulation identifies an identity-shortcut ResNet with its residual output retained as a full-rate PR system. Experiments verify exact single-channel routing of linearly separable factors to machine precision. On TIMIT, the proposed front-end improves test PER from

28.60\pm2.09\%

to

25.76\pm0.41\%

with the recognizer and training protocol held fixed, while maintaining exact reconstruction. Speaker probing further shows that structural conservation does not itself imply task-specific invariance.

Vikram R. Lakkavalli

International Institute of Information Technology Bangalore, India

Audio Representation Learning Representation Learning Residual Learning U-Net

Sep 10, 2026eess.SP

Rethinking Radiomap Blind Prediction with Limited Environment and Configuration Representations

Radiomap blind prediction infers radiomaps from observable representations of the propagation environment and base station (BS) configuration without field measurements. These representations are inherently incomplete and cannot uniquely determine the target radiomap. Under squared loss, we identify the conditional-mean radiomap as the population-optimal deterministic target and decompose domain risk into target-approximation error and irreducible uncertainty. The train-test risk gap motivates propagation priors as cross-domain guidance, although their partial or simplified forms may bias the attainable predictor. We therefore propose RadioDecomp, which treats a prior-guided predictor as a correctable base and uses deterministic residual refinement to learn its remaining predictable discrepancy. We instantiate RadioDecomp as RadioLSR (LoS-Shadow-Residual). Experiments under cross-configuration and cross-environment settings show that RadioLSR is especially effective for cross-configuration generalization and provides overall gains over a controlled monolithic counterpart under cross-environment generalization.

Xiaojie Li, Yu Han, Han Fang +3

School of Information Science and Engineering, Southeast University, Nanjing 210096, China · National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China · School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China +2

Residual Learning Cross-Domain Generalization Radio Propagation Modeling

Sep 10, 2026cs.LG

Toward Reliable Railway-Bogie Response Prediction Using Multifidelity TDNN and Physics-Informed Residual Learning

Railway engineers need simulation models that predict vehicle responses across operating scenarios that cannot be tested exhaustively. Agreement with representative measurements provides essential evidence, but calibration at a limited set of conditions does not guarantee accuracy elsewhere. We present a multifidelity railway-bogie response-correction method that treats multibody simulation histories as low-fidelity information and roller-rig measurements as high-fidelity evidence. This method combines an experiment-anchored fidelity assignment with physics-informed discrepancy learning for multichannel bogie-response histories. A time-delay neural network (TDNN) represents the condition-dependent simulation trend, and development-fitted amplitude alignment defines the low-fidelity baseline. A residual-correction network then models the reproducible response component not explained by this baseline and adds it to the baseline. An effective dynamic-balance equation constrains the learned discrepancy by representing differences in inertia, damping, stiffness, and external forcing between the simulated and physical systems. The training objective combines this constraint with residual matching, temporal smoothness, and a combined channel-2 acceleration loss selected using displacement-acceleration consistency evidence. For the evaluated reconstruction case, the corrected response gives a mean coefficient of determination of 0.8197, a mean normalized root-mean-square error (NRMSE) of 4.6055 %, and a mean normalized mean absolute error (NMAE) of 1.9297 %. These results provide initial evidence of accurate response prediction at the held-out 385 km/h condition.

Gyeolhee Lee, Moosun Kim, Taewook Kwon +3

Department of Automotive Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea · Korea Railroad Research Institute, 176 Cheoldobangmulgwan-ro, Uiwang-si, Gyeonggi-do 16105, Republic of Korea · Department of Future Mobility, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea

Surrogate Modeling Residual Learning Multifidelity Modeling Vehicle Dynamics Physics-Informed ML

Sep 7, 2026cs.LG

Structured Extrema Errors in Classical Surrogates for Viscous Burgers: A Physics-Consistent Interpretation

We study the local errors of classical machine-learning surrogate models, which approximate the time evolution of the one-dimensional viscous Burgers equation. Four models are compared on the same prediction task, using the spatial grid values directly: radial basis function (RBF) kernel ridge regression (KRR), linear Ridge, ExtraTrees, and Random Forests. Across all four models, the one-step residual, defined here as the true value minus the predicted value at each grid point, forms clear curved branches near predicted maxima and minima. A more detailed analysis of KRR shows that these errors are much more strongly related to the second spatial derivative, which measures local curvature, than to the first spatial derivative. Near a smooth extremum, predicted value and curvature form a local two-branch fold. Under our local curvature-based model of the residual, this fold predicts a leading-order near-parabolic relation between predicted value and residual. This geometric result motivates a direct test of the Burgers advection (transport) and diffusion (smoothing) terms. For KRR and Ridge, regression tests on held-out trajectories, a control that breaks the spatial alignment of the diffusion term, and a spectral test of high-frequency content are consistent with insufficient viscous smoothing at moderate and high viscosity. In this case, the surrogate retains more small-scale structure than the true future state. The same physical explanation is much weaker for the tree models. Finally, a correction that uses only predicted quantities reduces both one-step error and error during recursive rollout, where each prediction is used as the next input.

Youssef Oubari

IMT Atlantique, France

Kernel Ridge Regression Surrogate Modeling PDE Solving Residual Learning PDE Surrogate Modeling

Sep 7, 2026cs.AI

ResLearn-XR: Residual Learning for Network Traffic and Quality-of-Experience-Aware Modeling in Extended Reality

We present ResLearn-XR, a residual learning framework for predicting eXtended Reality (XR) network traffic and estimating Quality-of-Experience (QoE) risk. ResLearn-XR adopts a two-stage temporal learning structure comprising a base sequence prediction model augmented with task-specific residual learning components to improve adaptability to bursty, non-stationary XR traffic dynamics. The residual learning stages operate in the value space for continuous XR traffic forecasting and in the logit space for probabilistic QoE risk estimation. \rev{For the QoE-risk branch, we introduce a Data Descriptor Algorithm (DDA), a causal feature-construction module that converts packet-level application-layer observables into frame-timing-aware descriptors suitable for encrypted traffic analysis. We also construct an XR Traffic-QoE dataset that pairs continuous XR traffic traces with session-level user-reported QoE labels. ResLearn-XR reduces SMAPE by up to 17.84% across frame-count, frame-size, and inter-arrival-time prediction, while reducing QoE-risk estimation SMAPE by up to 87.8% over single-stage baselines.

Yoga Suhas Kuruba Manjunath, Jie Gao, Lian Zhao

School of Information Technology, Carleton University, Ottawa, ON, K1S 5B6, Canada · Department of Electrical, Computer and Biomedical Engineering, Toronto Metropolitan University, Toronto, ON M5B 2K3, Canada

Residual Learning Encrypted Network Traffic Analysis Traffic Forecasting

Sep 3, 2026cs.LG

RATL: Learning from Retrieved Residuals for Robust Multivariate Time-Series Forecasting

Retrieval-augmented generation (RAG) complements parametric models with retrieved external evidence. The same idea is attractive for continuous-output regression, but directly reusing retrieved target values is often not robust when samples differ in output level, numerical scale, or local dynamics. Moreover, conventional forecasting pipelines generally use residuals for model optimization and error diagnosis, but do not retain individual historical residual examples as memory that can be accessed at inference time.For multivariate time-series forecasting, we propose RATL, a plug-in residual-retrieval and feedback-correction method. RATL freezes a base forecaster to construct retrieval keys and turns its historical forecast residuals into a train-only memory specific to that base model. At inference time, RATL retrieves residual trajectories from similar historical contexts subject to causal availability constraints, then uses a set-aware router operating over forecast blocks and variables to select and combine these trajectories. Experiments show that historical residuals matched to the current context contain reusable forecasting information and that RATL improves frozen base forecasters in most experimental settings. Ablations further show that learned routing strengthens raw residual feedback, while validation-based correction-strength selection limits residual over-injection.On real-world benchmarks, we use iTransformer as the primary frozen base forecaster, compare against multiple strong forecasting baselines, and test transferability across backbones. The results show that RATL can further improve base-forecaster performance in most settings.Overall, RATL shifts the retrieved object from historical target values to base-model-specific historical forecast errors, providing a plug-in, residual-memory-based paradigm for learned feedback correction in continuous-output forecasting.

Yuchen He, Yueyang Cang, Zhiyuan Ning +2

Department of Automation, Tsinghua University · State Key Laboratory of Hydroscience and Engineering, Tsinghua University

Multivariate Time Series Forecasting Residual Learning Retrieval-Augmented Time Series Forecasting

Sep 3, 2026math.NA

Residual neural networks overcome the curse of dimensionality for semilinear heat equations

Rigorous results show that feedforward neural networks can overcome the curse of dimensionality in the numerical approximation of high-dimensional partial differential equations (PDEs), but comparatively little is known about residual neural networks (ResNets) in the nonlinear PDE setting. We prove that ResNets overcome the curse of dimensionality in the numerical approximation of solutions of semilinear heat equations with globally Lipschitz continuous, gradient-independent nonlinearities: under polynomial growth and network approximability hypotheses on the PDE data, there exist

η\in(0,\infty)

and ResNets

Ψ_{d,\varepsilon}

,

d\in\mathbb{N}

,

\varepsilon\in(0,1]

, with at most

ηd^η\varepsilon^{-η}

parameters whose realizations approximate the solution in dimension

d

with an

L^2

-error of at most

\varepsilon

. The proof represents one deterministic realization of a multilevel Picard estimator by a ResNet whose shortcut connections transmit the spatial variable and a scalar accumulator, while the residual branches successively add the summands of the estimator. For ridge-sum initial conditions, admissible sigmoidal activations, and globally Lipschitz truncations of the nonlinearity, we obtain, for every

ξ>0

, the explicit bound

C_ξd^{4+ξ}\varepsilon^{-(3+ξ)}

on the number of parameters.

Ilkhom Mukhammadiev, Diyora Salimova

Department of Applied Mathematics, University of Freiburg, Germany

Neural PDE Solvers PDE Solving Residual Learning Neural Network Approximation Theory

Sep 3, 2026math.PR

Correlated initialization of deep residual networks

We study the large-depth behavior of residual networks whose weights are correlated across layers at initialization. Our results confirm and extend a conjecture of Marion et al. [2025], according to which correlated initializations should interpolate continuously between the Brownian stochastic differential equation arising from independent initialization and the ordinary differential equation arising from perfectly correlated initialization. When the initialization is obtained from the application of a feature function to a stationary Gaussian sequence with regularly varying correlation, we prove that there exists a unique critical scaling such that the infinite-depth limit is the solution of a Young differential equation driven by a Hermite process. Hermite processes reduce to the fractional Brownian motion if the feature function generating the initialization has Hermite rank one, which is the case for the identity function, for example. We show that the critical scaling and asymptotic limit are uniquely determined by the decay of correlations together with the Hermite rank of the feature function. Consequently, the correlation structure and Hermite rank of the initialization represent meaningful hyperparameters in the asymptotic regime. By contrast, under finite-variance iid initialization, the asymptotic driver is universally Brownian up to normalization regardless of the choice of distribution. Our proofs rely on a collection of novel results establishing a robust stability theory for Young differential equations in Banach spaces.

Felix Benning, Ivan Nourdin, Giovanni Peccati

Neural Network Initialization Residual Learning

Sep 2, 2026cs.CL

oHC: Orthogonal Hyper-Connections on SO(4) via Quaternions

Hyper-Connections (HC) replace the single residual stream of a Transformer with

n

parallel ones, mixing them at every layer with a learned

n \times n

residual matrix. Leaving that matrix unconstrained places no limit on the factor by which the mixing step rescales the residual streams, and that factor compounds across layers, which destabilizes training. Manifold-constrained Hyper-Connections (mHC) address this by restricting the matrix to the doubly stochastic matrices. That caps the factor at one, so the mixing can no longer amplify any direction, but nothing bounds it from below. We prove that inside this set the mixing step can reduce the norm of the residual streams only by shrinking the differences between the streams, while their mean is left unchanged; and since the reduction accumulates over layers, the streams grow more alike and their diversity is spent with depth. We therefore propose Orthogonal Hyper-Connections (oHC), restricting the residual matrix to the rotation group

SO(n)

, so that the mixing step can neither amplify nor attenuate the residual streams in any direction, which keeps training stable and no longer forces the differences between the streams to contract. Specifically, at the four streams used by recent HC models we parameterize the group in closed form by a pair of unit quaternions, which adds no parameters, replaces the iterative projection with a fixed pattern of signed additions, and can be constructed faster than mHC. We evaluate oHC across a comprehensive set of downstream tasks, where it outperforms the single-stream residual baseline, mHC and iHC, which fixes the residual matrix to the identity.

Haoqiang Guo, Xuyi Chen, Bo Ke +5

The Hong Kong University of Science and Technology · Baidu Inc.

Hyper-Connections Transformer Residual Learning

Sep 1, 2026cs.CV

Residual Kalman Dynamics for Event-Based UAV Forecasting

We study short- and mid-horizon UAV bounding-box forecasting on the FRED event-camera dataset. We use a constant-velocity Kalman filter over a full center-size box state as a strong physical baseline, and train a residual model to predict acceleration-like corrections from recent box history, filtered state features, and local event representations. This simple residual formulation consistently improves over the Kalman baseline, with event-conditioned models giving the strongest results among the evaluated methods. We further show that part of the residual target is predictable from anchor position and velocity alone, indicating that canonical FRED results can reflect both visual evidence and dataset-specific motion priors. To analyze this effect, we introduce decorrelated subsets as a diagnostic stress test, showing that event-conditioned residual models retain useful predictive signal even when measured position- and velocity-based shortcuts are weakened.

Per Nyblom, Hannes Ovrén, David Gustafsson

Swedish Defence Research Agency (FOI), Linköping, Sweden

Event-Based Vision Kalman Filtering Residual Learning UAV Trajectory Optimization Trajectory Prediction

Aug 31, 2026cs.LG

PRIME: Mitigating Subgroup Optimization Competition in Shared CTR Top Networks with Plug-in Residual Input-Conditioned Mixture of Expert

Click-through rate (CTR) models vary in feature-interaction design, yet their top networks usually remain a single multilayer perceptron shared by all examples. Heterogeneous user, item, and context subgroups therefore update the same parameters; weakly aligned learning signals make the aggregate gradient a compromise among competing directions. We study the competition on Avazu with 4 models and 4 semantic fields. Across all architectures, semantic subgroups show lower Top-NN gradient cosine similarity than random groups matched by sample size and label ratio, with reductions of 0.23-0.37. This competition motivates input-conditioned experts, but directly replacing an established Dense mapping changes its initial function, sharing pattern, and capacity, obscuring the source of gains. We introduce PRIME (Plug-in Residual Input-conditioned Mixture of Experts), a Dense-anchored mixture of low-rank residual experts. PRIME anchors the original prediction and uses zero-residual initialization to match the Dense baseline exactly at training onset. Input-dependent routing weights low-rank experts for example-specific logit corrections; multi-bag aggregation and EMA load biases stabilize conditional estimation. We evaluate PRIME on held-out Avazu and Criteo test sets across 13 CTR architectures and five paired seeds. Median paired AUC gains are +0.0022 and +0.0066, with LogLoss reductions of 0.0011 and 0.0081, respectively. On FiBiNET and DCNv2, PRIME outperforms APG in all ten seed-level AUC comparisons while using fewer parameters and lower inference latency on both backbones. These results show that function-preserving conditional residuals add input-dependent capacity while preserving the Dense path and its optimization stability. Code is available at https://github.com/YH-learning/PRIME.

Heng Yao, Siyun Hou, Tianying Liu +8

Ant Group · Henan Polytechnic University · Independent Researcher +1

Residual Learning Gradient Interference CTR Prediction Mixture-of-Experts Models

Aug 11, 2026cs.LG

Two-stage Odd Residual Flows for Mean-Preserving Probabilistic Time Series Forecasting

Probabilistic forecasting plays an essential role in risk-sensitive decision-making, particularly in long-horizon settings. However, existing approaches often face a fundamental trade-off between distributional flexibility and accurate mean prediction. Traditional parametric methods, such as Mean Variance Estimation (MVE), can suffer from degraded point accuracy when trained under joint Negative Log-Likelihood (NLL) objectives, while modern-flexible generative models, including Normalizing Flows and Diffusion Models, typically rely on costly Monte Carlo sampling and may yield suboptimal mean estimates. To address this limitation, we propose Two-stage Odd Residual Flows (TORF), a framework that decouples mean forecasting from uncertainty estimation. In the first stage, a pre-trained deterministic model is used to produce an accurate mean prediction. In the second stage, a Restricted Normalizing Flow, with strictly odd functions learns flexible residual distributions around the point forecast, guaranteeing mean preservation from the first stage without sampling. Experiments show that TORF achieves state-of-the-art deterministic accuracy (NMAE) while providing strong density estimation performance (CRPS) on short and long-horizon forecasting.

Kiran Madhusudhanan, Christian Klötergens, Lars Schmidt-Thieme +1

Institute of Computer Science University of Hildesheim Hildesheim, Germany

Long-Term Time Series Forecasting Normalizing Flows Residual Learning Probabilistic Forecasting Probabilistic Time Series Forecasting