Residual Connections

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2 papers in the last four weeks, down 50% on the four weeks before. 0.0% of all new papers.

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Latest papers 34

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

Residual Connections Phase Space

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

Ultra-Low Bitrates Autoregressive Image Generation Residual Connections Diffusion Transformers

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

Residual Connections Short-Horizon Forecasting Long-Horizon Task Planning

Sep 22, 2026cs.LG

Geometry-Aware Hyperbolic Residual Quantization

Residual Vector Quantization turns continuous representations into discrete, multi-level token sequences. Yet most methods operate in Euclidean space, despite the coarse-to-fine structure of the resulting codes and the latent hierarchies present in many data domains. Hyperbolic geometry offers a natural alternative for hierarchical representations, but naive hyperbolic extensions introduce geometric inconsistencies: non-associative hyperbolic addition prevents consistent residual aggregation, while standard straight-through gradient estimation ignores the geometry of the latent space. We propose a geometry-aware hyperbolic residual quantization that addresses these issues in both the forward and backward passes. In the forward pass, Hyperbolic Residual Aggregation restores the telescoping behavior of residual quantization on the Poincare ball. In the backward pass, a discounted Hyperbolic Straight-Through Estimator routes the reconstruction gradient through the quantizer as a single geometric block, avoiding unstable recursive gradient transport across residual stages. Evaluations on hierarchical prediction, recommendation, image tokenization, and neural audio coding tasks show that our method improves the stability and structural organization of hyperbolic residual codes over naive hyperbolic baselines. At the same time, we observe a clear structure-compression trade-off: Euclidean residual quantization remains preferable for pure compression, while geometry-aware hyperbolic quantization is most useful for hierarchically organized discrete latent spaces.

Alessio Colombo, Melika Ayoughi

Universiteit van Amsterdam, Amsterdam, Netherlands

Hyperbolic Space Residual Connections Hierarchical Wasserstein Gradient Flows

Sep 8, 2026cs.CR

ZK-Trace: Certified Collusion Tracing with Zero-Knowledge Credentials for Federated GNSS Interference Monitoring

Federated global navigation satellite system (GNSS) monitoring distributes a proprietary classifier to partly trusted stations, any of which may leak its copy. ZK-Trace combines public identity marks, recipient-specific Tardos fingerprints, and zero-knowledge credential verification. The registry supports offline tracing without the leaker's cooperation. We establish conditional false-accusation bounds for arbitrary recovered bit patterns, a finite completeness bound under a hidden-bias residual channel, and a deterministic tracing-score bound for correlated feature-distillation errors. An interval-arithmetic checker makes the conditional bound executable and allocates a common budget across accusation and tamper decisions. Under innocent-row independence, the certificate-based evaluation uses a false-naming budget of 0.001 per investigation. It isolates all 160 single-owner copies and traces 712 of 720 two-owner mixtures without naming an innocent. Experiments use a simulated GNSS federation and CIFAR-10. Feature matching preserves the feature mark in 20/20 runs and cross-architecture transfer in 19/20, at copy-accuracy costs of 4.8 and 6.1 percentage points on GNSS and CIFAR-10. Function-only distillation erases the feature mark, and distillation also removes weight-space marks. These results support verifiable tracing under explicit statistical and cryptographic assumptions. Credential knowledge and recipient evidence serve distinct roles.

Redwanul Karim, Nisha L. Raichur, Lucas Heublein +3

Fraunhofer Institute for Integrated Circuits IIS, 90411 Nürnberg, Germany

Global Navigation Satellite System Zero-Knowledge Proofs Secure Aggregation Traces Collusion Residual Connections

Aug 8, 2026cs.LG

TEMPER: Tensorized Efficient Manifold-constrained Parameterization for Expressive Residual Routing

Residual connections rely on a static residual pathway, and are essential for training deep neural networks. Hyper-connections (HC) increase the expressivity of residual routing by incorporating multiple residual streams and learning dynamic information flow, while manifold-constrained (mHC) variants stabilize training through doubly stochastic residual mixing. However, a generator-level bottleneck remains in existing methods: they use dense, unstructured generators for pre-branch aggregation, residual mixing, and post-branch redistribution, which results in parameter count growing rapidly with the number of streams. To address this issue, we propose \underline{\textbf{T}}ensorized \underline{\textbf{E}}fficient \underline{\textbf{M}}anifold-constrained \underline{\textbf{P}}arameterization for \underline{\textbf{E}}xpressive Residual \underline{\textbf{R}}outing (\textbf{TEMPER}), which represents these generators as multi-way tensors over the input-stream, feature, and output-stream modes, and parameterizes them using tensor networks. Such a structured low-rank formulation is shown to preserve token-dependent manifold-constrained routing interface while substantially reducing parameter growth. It also promotes interpretability and intuition, as: i) tensor ranks control the dimensionality of the learned routing subspace, with full ranks recovering dense routing; while ii) the generator approximation errors bound differences in routing logits and, consequently, in the routed-block outputs. Comprehensive experiments show that TEMPER matches or outperforms existing methods across language modeling and commonsense reasoning tasks, while requiring substantially fewer additional parameters. At eight residual streams, TEMPER achieves the best CORE score while using about

84\%

fewer additional parameters than mHC, thus showing a stronger performance-parameter efficiency trade-off.

Yuxuan Gu, Wuyang Zhou, Huijun Xing +1

Department of Electrical and Electronic Engineering, Imperial College London

Residual Connections Reparameterization Tensor Networks Parameter-Efficient Fine-Tuning Methods Concept Bottleneck Models

Aug 6, 2026cs.CV

Dense-Cast: A lightweight ensemble of deep learning architectures for precipitation nowcasting

Proper short-term forecasting of precipitation is crucial in disaster management and preparedness. Nonetheless, the variability and nonlinearity of precipitation make short-term forecasting challenging for meteorologists. Moreover, capturing temporal dependencies in spatiotemporal data is a challenge in precipitation nowcasting. In this article, we introduce a lightweight deep learning model for half-hourly precipitation nowcasting. This model has been designed by incorporating the DenseNet architecture, residual connections, and transformer encoders for effective precipitation nowcasting with reduced model parameters. The North-Eastern region of India has been selected as the area of interest for our study. The region receives the highest precipitation during the months of June-September due to the monsoon season. The proposed model takes the previous five time-steps of half-hourly precipitation as inputs and predicts the precipitation in the next two half-hours. The GPM IMERG precipitation dataset with a 30-minute cadence has been used in this study for training and testing the model. The proposed architecture achieves best MAE of 0.235 millimetres, RMSE of 0.735 millimetres, and KGE score of 0.816 at an interval of 30 minutes.

Gourav Jyoti Kalita, Hidam Kumarjit Singh

Department of Electronics and Communication Technology, Gauhati University, Guwahati-781014, Assam, India

Precipitation Nowcasting Rainfall Short-Horizon Forecasting Deep Learning Dense Ensemble+1

Aug 6, 2026cs.SD

Beyond Residual Connections: Manifold-Constrained Hyper-Connections for Robust Speaker Representation Learning

Residual connections are fundamental to deep speaker recogni- tion models, such as ECAPA-TDNN and ResNet. However, standard identity mapping limits information flow to a sin- gle path, constraining representation capacity. We introduce Manifold-Constrained Hyper-Connections (mHC), reformulat- ing residual paths as a multi-stream evolution where informa- tion is mixed through a doubly stochastic matrix. By employing Sinkhorn-Knopp iterations, mHC ensures energy conservation by preserving signal intensity and feature mean, which stabi- lizes gradients and mitigates signal degradation in complex net- works. We evaluate mHC by replacing standard residual con- nections in backbones including ECAPA-TDNN, ResNet-34, Res2Net, and E-Res2Net. Extensive experiments on VoxCeleb1 demonstrate that mHC connections consistently enhance per- formance across all architectures, highlighting its effectiveness for robust speaker representation learning.

Zezhong Jin, Xiaoyu Wang, Zhe Li +4

Dept. of EEE, The Hong Kong Polytechnic University · Baidu Inc. · Speech, Language, and Cognition Laboratory, The University of Hong Kong, Hong Kong SAR

Residual Connections Discrete Speech Representations

Aug 5, 2026cs.LG

Training Crossroads for Recurrent Vision Transformers: Recurrence, Neural ODEs, and Deep Supervision

Vision Transformers (ViTs) achieve strong image-recognition performance, but their parameter count grows linearly with depth when each block is independently parameterized. Single-block recurrent ViTs (bViT) remove this growth by repeatedly applying one shared block. Rather than proposing a new architecture, we fix a bViT and provide a controlled empirical characterization of three training and inference regimes under a common CIFAR-100 protocol, asking: (i)~when does recurrence beat independently parameterized depth---at matched FLOPs or at matched parameter memory? (ii)~when a residual recurrent block is trained through an ODE solver, does solver order act as numerical refinement or as an architectural bias? and (iii)~what does robustness beyond the training horizon cost in nominal accuracy? We find that standard ViTs remain preferable when FLOPs are the primary constraint, whereas recurrent ViTs offer a better accuracy--parameter trade-off under memory constraints. Consistent with the standard view of residual networks as Euler discretizations of ODEs, the continuous-time analogue of a residual recurrent block is the state-subtracted vector field

\dot{z}=F_θ(z)-z

; although known in principle, this distinction is easy to violate when the block is wrapped as a black-box vector field, and we qualify the cost at few accuracy points. Because the vector field is learned jointly with the solver, higher-order solvers act as a solver-induced architectural bias rather than a numerical-accuracy improvement, and their gains are not uniform. Finally, stage-wise deep supervision traces an accuracy--robustness frontier: it does not improve nominal accuracy, but degrades gracefully far beyond the training horizon, where naive recurrence collapses to near-random performance.

Grzegorz Gruszczynski, Pawel Olszowiec, Michal Byra +2

Samsung AI Center, Warsaw, Poland · Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland

Self-Supervised Vision Transformers Vision Transformer Residual Networks Residual Connections Recurrence Neural Ordinary Differential Equations+1

Aug 2, 2026cs.LG

Sphere Retraction Normalizations

Residual connections are the de facto mechanism for training deep neural networks stably. Geodesic Normalization (GeoNorm) recasts them on a Riemannian manifold, orthogonalizing each layer output against the current hidden state and applying the resulting update through the Riemannian exponential map. Every hidden state thus keeps a constant

\ell_{2}

-norm, confining the residual stream to a hypersphere. The exponential map, however, is only one member of a broad family of retraction maps. We show that on the hypersphere this entire family collapses to a single scalar design choice. What distinguishes one retraction from another is only how the magnitude of an update is converted into a rotation angle within the plane spanned by the hidden state and the update. This view places Euclidean residual connections and GeoNorm in one framework. Instantiating it with the metric projection retraction and the Cayley retraction yields Proj-SpheretNorm and Cay-SpheretNorm, which are exactly norm-preserving yet require only algebraic operations. Both prove to be members of a one-parameter family of angular retractions,

p

-SpheretNorm, whose rotation angle saturates rather than growing without bound. The two methods above are recovered exactly at

p = 1

and

p = 2

, while the identity map and GeoNorm arise only as limits at either end. On nanoGPT, all three methods outperform existing lightweight deep connection schemes, and the best validation loss is attained at finite

p

, indicating that the exponential map is not the preferred retraction for spherical residual streams but merely one end of a spectrum.

Jie Zhang, Cheng-Fang Su, Yi-Jui Huang +1

Department of Computer Science and Information Engineering, National Central University, Taiwan · Department of Applied Mathematics, National Yang Ming Chiao Tung University, Taiwan · Department of Mathematics, National Central University, Taiwan

Residual Connections Geodesic Residual Stream

Jul 16, 2026cs.LG

Certifying Residual Architectures from Their Primitives: A Sharp Stability Threshold

Whether a deep residual architecture trains stably is usually determined by training it, which is expensive and answers the question only for the architecture, depth, and floating-point format tested. In practice, stability is secured by heuristics for where to place normalization and which type to use, supported by experiments but lacking a common principle. We show that stability can instead be certified before training, directly from the architectural primitives of a residual block, as an explicit function of depth and floating-point format. The certificate has two elements: (a) a power-law growth bound,

|v(x)|\le c|x|^q+b

, whose exponent

q

is computed from the block's primitives by an arithmetic of exponents (forward); and (b) gradient bounds from a Lipschitz condition on the block over reachable states (backward). The certificate determines when the state can reach the largest finite floating-point value

M

: for

q\le1

, overflow requires at least order

\log M

layers, whereas for

q>1

it can occur within order

\log_q\log M

layers; the threshold

q=1

is sharp. Every normalization and bounded activation sets

q=0

, and the arithmetic identifies minimal modifications that bring a block from

q>1

to

q=1

without normalization. Empirically, in forecasting, only

q>1

blocks blow up, as predicted by the forward certificate. In GPT-2 on OpenWebText,

q=1

blocks without normalization also diverge: the forward certificate holds, while the backward one fails in the attention block with the largest query-key coefficient. Relaxing normalization from

q=0

to

q=1

improves out-of-distribution generalization in operator learning and accuracy in time-series forecasting. As deep models become more complex and costly to train, our results provide a way to assess the trade-off between stability and representational flexibility directly from block primitives, before training.

Hyemin Gu, Michael Tyrrell, Tuhin Sahai +1

University of Massachusetts Amherst · SRI International

Residual Networks Residual Connections Exponents Certification Velocity Field

Jul 1, 2026cs.LG

Muon as a Residual Connection

Muon has recently emerged as one of the most effective optimizers for training large neural networks, yet its empirical success has been explained from several different perspectives. In this paper, we propose a simple mechanistic interpretation: Muon can be understood as an implicit residual connection during training. Specifically, orthogonalizing the update can sacrifice some immediate gradient fidelity while improving representation preservation for downstream layers. We study this trade-off in controlled linear optimization settings, where Muon can learn representations that are slower to fit a local target but easier for downstream layers to exploit. Our results suggest a conceptual explanation for Muon and a design perspective for optimizers that balance local descent with downstream usability.

Hao Huang

College of Computer Science and Technology Zhejiang University Hangzhou, Zhejiang, China

Muon Residual Connections Neural Network

Jun 30, 2026cs.LG

Review Residuals: Update-Conditioned Residual Gating for Transformers

Residual connections add every sublayer's proposed update with a fixed coefficient of one; the network never evaluates whether an update is reliable before committing it. Drawing on the human-factors principle of independent verification, we introduce Review Residuals, which scale each update by a learned, input-dependent gate conditioned on both the current state and the proposed update: h_l = h_{l-1} + r_l * u_l with r_l = sigmoid(W[RMSNorm(h_{l-1}), RMSNorm(u_l)]). Conditioning the gate on the update is the property that distinguishes it from prior gated and scaled residuals. We report two findings. First, a depth-stability result: a convex (Highway-style) form of the gate reintroduces vanishing gradients and fails to train beyond ~20 layers, whereas the additive, identity-preserving form trains stably at all depths we tested. Second, an emergence-with-scale result: trained from scratch across five sizes (60M-1B parameters, multi-seed), Review Residuals show no advantage at small scale but at 590M significantly outperform both a parameter-matched Highway gate and a parameter-matched standard residual (p<0.05), with a larger advantage at 1B. The benefit grows with model size rather than shrinking.

Kyle Kramer

NeraTech LLC

Residual Connections Batch Normalization Transformer Architectures Review

Jun 23, 2026cs.CV

MambaRaw: Selective State Space Modeling for Efficient 4K Raw Image Reconstruction

In-camera JPEG previews are ubiquitous in raw image formats and provide an sRGB reference at negligible storage cost. Although existing metadata-based reconstruction frameworks can exploit this side information when recovering raw images, their context models often become computationally expensive especially at high resolution, eg, 4K raw image, given that attention mechanisms scale quadratically with feature maps, hindering its practical application. To address these limitations, we propose MambaRaw, a JPEG-conditioned metadata-based raw image reconstruction framework that uses State Space Models (SSMs) to estimate entropy parameters efficiently. Our key contribution comprises a Spatial-Energy Coupled Context Modeling mechanism with two lightweight modules: (1) TileMambaBlock, which performs Mamba-style selective scanning only on information-dense tiles to improve the efficiency; and (2) Energy-Aware Refinement (EAR), an identity-initialized residual module that enhance feature representation to match the long-tail energy distribution of raw signals. Extensive experiments on three camera datasets (Sony, Olympus, Samsung) show consistent improvements over strong metadata-based baselines and set a new state of the art for JPEG-guided raw reconstruction with great efficiency. Notably, at low metadata bitrates, MambaRaw increases PSNR by 1.2--1.4 dB and reduces end-to-end coding latency by about 9%. Code is released at https://github.com/Peizeli1/MambaRaw.

Peize Li, Fanhu Zeng, Tongda Xu +5

Institute for AI Industry Research (AIR), Tsinghua University · King’s College London · Dalian University of Technology +3

Image Reconstruction Topomamba State Space Models Residual Connections Energy-Efficient

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 Connections Gradient Lyapunov Function Impact Analysis

Jun 8, 2026cs.CV

A Large Scale Open-Source Image and Video Dataset for Robust Wildfire Detection and Classification

Wildfire detection and monitoring are critical for mitigating fire spread and reducing environmental and infrastructural damage. In this work, we introduce GWFP (Global Wildfire Prevention Dataset), a large-scale, open-source dataset of wildfire images and videos designed to support early fire and smoke detection research. GWFP contains geographically diverse wildfire scenes, including flames, smoke, Waterdog/Fog environmental conditions, Near Infrared (NIR) imagery, Ember, and challenging negative samples collected from real-world scenarios worldwide. To evaluate dataset robustness and cross-domain generalization, we benchmark multiple convolutional and transformer-based architectures across both in-domain and cross-dataset settings. Additionally, we explore lightweight frequency--spatial feature interaction using Hadamard-enhanced residual connections (HTE-ResNet) to analyze representation robustness under domain-shift conditions. Experimental results demonstrate strong cross-dataset generalization and practical utility for real-world wildfire monitoring applications. The dataset and source code will be publicly released upon acceptance.

Emadeldeen Hamdan, Yingyi Luo, B. Ugur Toreyin +4

Department of Electrical and Computer Engineering, University of Illinois Chicago, Chicago, IL, USA · Informatics Institute, Istanbul Technical University, ˙Istanbul, Türkiye · USDA Forest Service Pacific Wildland Fire Sciences Laboratory, Washington, USA +1

Wildfire Detection Wildfire Df-Wild Dataset Vision Datasets Video Dataset Residual Connections

Jun 7, 2026cs.CV

Classifying galaxies in the Galaxy10 DECals dataset using Inception and Residual CNNs

Image data regarding galactic morphology is expected to increase both in quantity and quality for the next foreseeable years; thus it is important to explore which deep learning architectures adapted for image classification tasks are cost-effective. Residual and Inception networks are ideal for exploring classification convolutional neural networks (CNNs) due to their computational efficiency, achieved through techniques such as residual connections and parallelized inception modules, enabling deeper networks without excessively increasing computational complexity. In this work, we analyze the performance of ResNet101 and InceptionV4 on a spatially-augmented Galaxy10 DECals dataset. Retaining the ten-class classification of galaxies, we modify the image count of each class. We find that ResNet101 and InceptionV4 models achieved accuracies of

\sim

90%, comparable with reported performance in the literature. In terms of performance metrics, ResNet101 is superior to InceptionV4. Our results indicate that either of these CNN architectures could serve as a robust foundation for specialized pipelines for classification of galaxy images from upcoming surveys.

Lanz Anthonee A. Lagman, Prospero C. Naval, Reinabelle C. Reyes

Data Science Program, College of Science, University of the Philippines - Diliman, Philippines · Department of Computer Science, College of Engineering, University of the Philippines - Diliman, Philippines · National Institute of Physics, College of Science, University of the Philippines - Diliman, Philippines

Convolutional Neural Networks Astronomical Images Residual Networks Residual Connections Query Image

Jun 5, 2026cs.LG

Modeling Nonlinear Feature Interactions with Product-Unit Residual Networks

Understanding nonlinear feature interactions is crucial in science and engineering, yet standard multilayer perceptrons (MLPs) often capture such interactions only implicitly, leading to entangled representations that can impair robustness and interpretability. We investigate product-unit residual networks (PURe) that integrate multiplicative product units with residual connections to explicitly model cross-feature couplings while stabilizing optimization. We conduct a systematic evaluation on an interaction-driven synthetic benchmark and two real-world datasets, assessing predictive accuracy, robustness to Gaussian feature noise, and performance under limited training data, and we compare real- and complex-valued variants under a matched parameter budget. Beyond accuracy, SHapley Additive exPlanations (SHAP)-based interaction analyses show that PURe learns more concentrated and structurally coherent interaction patterns than MLP baselines. Overall, PURe achieves competitive or improved performance, better robustness and sample efficiency in low-data regimes, and enhanced interaction-level interpretability.

Ziyuan Li, Uwe Jaekel, Babette Dellen

Department of Mathematics, Informatics and Technology, University of Applied Sciences Koblenz, Joseph-Rovan-Allee 2, 53424 Remagen, Germany · Technical University of Munich, Munich, Germany

High-Order Correlations Multilayer Perceptrons Residual Connections Residual Networks Interpretability Entanglement

Jun 2, 2026cs.SD

Speech Emotion Recognition using Attention-based LSTM-Network with Residual Connection

Speech emotion recognition is an important component of modern human-computer interaction systems. However, many state-of-the-art approaches rely on large pretrained models with high computational and memory requirements, limiting their applicability. This paper proposes ResLSTM-SA, a lightweight architecture that integrates residual connections with soft attention within an LSTM-based framework. Evaluated on the RAVDESS dataset under strict speaker-independent partitioning, the proposed model outperforms conventional attention-based LSTM baselines and several previously reported CNN- and hybrid CNN-LSTM architectures in terms of unweighted average recall (UAR). The best-performing variant (ResLSTM-SA-h64) achieves a maximum UAR of 0.6517 with only 46.8k trainable parameters, delivering competitive accuracy with three orders of magnitude fewer parameters than large-scale self-supervised alternatives, thereby enabling efficient deployment on edge devices and real-time voice assistants. The source code is available at https://github.com/Mak-Sim/ResLSTM-SER.

Daniil Krasnoproshin, Maxim Vashkevich

Embedded System Department of Belarusian State University of Informatics and Radioelectronics 6, P. Brovky st., 220013, Minsk, Belarus

Cnn-Lstm Bidirectional Long Short-Term Memory Residual Connections Partitioning

May 29, 2026cs.LG

Student Capacity Moderates Knowledge Distillation Effectiveness: A Systematic Study Across ResNet Teacher-Student Pairs on CIFAR-10

We investigate how teacher-student capacity relationships modulate knowledge distillation (KD) effectiveness in ResNet-based image classification on CIFAR-10. Across four teacher-student pairs (R50->R18, R34->R18, R50->R34, and R101->R34) we compare Logit-KD and Feature-KD under a strict evaluation protocol: hyperparameters and checkpoints are selected on a held-out validation split, selected configurations are re-run with five seeds, and the test set is used exclusively for final reporting. Beyond accuracy, we measure distillation fidelity directly via teacher-student agreement and KL divergence. We report four findings. First, the student-capacity pattern survives the corrected protocol at reduced magnitude: the only statistically significant gains occur for R34 students under Feature-KD (+0.19 and +0.21 pp, p<0.05), in two pairs whose teachers differ two-fold in parameters but not in accuracy, localizing the moderating variable on the student side, while no KD gain for R18 students is distinguishable from zero. Second, Feature-KD matches or outperforms Logit-KD in all four pairs, and its students land closer to the teacher's output distribution (KL at T=1) than Logit-KD students despite never observing teacher logits. Third, top-1 teacher-student agreement is flat across all pairs, decoupling fidelity from accuracy gains. Fourth, architecture dominates KD: correcting the ResNet stem for 32x32 inputs is worth +5.5 to +7.2 pp, more than 25x the largest KD gain. We also retract an attribution made in v1: a controlled re-run shows the reported gradient-clipping bug had no measurable effect, and v1's larger gains are explained by test-set selection. Code and results: github.com/umutonuryasar/kd-capacity-gap (tag v2.0).

Umut Onur Yasar

Knowledge Distillation Teacher Residual Connections Residual Networks Logit Lens Systematic Study

May 26, 2026cs.LG

SparseOpt: Addressing Normalization-induced Gradient Skew in Sparse Training

Dynamic Sparse Training (DST) methods train neural networks by maintaining sparsity while dynamically adapting the network topology. Despite the promise of reduced computation, DST methods converge significantly slower than dense training, often requiring comparable training time to achieve similar accuracy. We demonstrate both analytically and empirically that Batch Normalization (BN) adversely affects sparse training, and propose SparseOpt, a sparsity-aware optimizer, to address this. Experiments on ResNet models across CIFAR-100 and ImageNet demonstrate consistently faster convergence and improved generalization with our proposed method. Our work highlights the limitations of current normalization layers in sparse training and provides the first systematic study of the interaction between Batch Normalization, sparse layers, and DST, taking a significant step toward making DST practically competitive with dense training.

Mohammed Adnan, Rohan Jain, Tom Jacobs +4

University of Calgary · 2Vector Institute · 3CISPA Helmholtz +2

Batch Normalization Neural Network Optimization Residual Connections

May 26, 2026cs.CV

CodecCap: High-Fidelity Codec-Inspired Residual Modeling for Dense Video Captioning

Existing video captioning methods struggle to balance visual fidelity and redundancy: holistic captions are compact but lose fine-grained evidence, whereas segment-wise captions improve coverage but introduce heavy redundancy. We propose CodecCap, a codec-inspired framework for high-fidelity dense video captioning. Analogous to video codecs, CodecCap represents videos using keyframe and residual captions. Keyframe captions exhaustively encode stable visual context, while residual captions capture temporally only localized actions, motions and changes. This effectively preserves fine-grained visual evidence while reducing redundant descriptions. To quantify the fidelity of captions, we introduce VidCapQA, a caption-then-QA benchmark with 1,000 questions across 14 capability dimensions. Results on VidCapQA show that captions directly generated by strong VLMs still miss many visual details, highlighting caption representation as a critical bottleneck. Experiments show that CodecCap significantly surpasses direct captioning with the same underlying VLMs, suggesting keyframe-residual captioning a way for high-fidelity video-language supervision. We further use CodecCap to construct CodecVDC-100K, a large-scale dense captioning dataset with anchor, residual, scene-level, and video-level supervision.

Zihan Lin, Songhe Deng, Shuwei He +6

ERNIE Team, Baidu · College of Artificial Intelligence, Inner Mongolia University

Video Captioning Captions Vision Encoders High-Fidelity Residual Connections

May 24, 2026q-bio.NC

Interpretation, Learning, and Empathy as One Constraint: A Residual-Adequacy Architecture with Accountable Abstention

An agent must act on the situation before it, learn what it cannot yet represent, and model other agents well enough to coordinate. These faculties are usually realized by separate mechanisms, yet they share a failure mode: the situation can exceed what the agent can currently represent, and the honest response is then a principled refusal that says what was missing. We develop a small cognitive architecture in which these limits arise from a single quantity. An Interpretation-Decision Unit (IDU) interprets a content vector through a family of regimes - local representational frames with private bases - and decides which actions it licenses; a scalar residual of the content against the active regimes' representational scope drives the unit. Low residual with a clean licensing emits an action; otherwise the unit re-interprets, attempts a description-length-justified expansion, or halts with a typed, witnessed terminal. We prove the unit is total and deterministic: for any content and fixed configuration it halts in finitely many bounded-cost steps with a unique terminal witness, so abstention carries its cause by construction. By binding the architecture's open parameters without changing its mechanics, the same residual-against-scope constraint recovers three documented phenomena at three scopes: the typology of not-knowing (typed abstention); a forced misunderstanding between agents, localized to one shared concept and invisible to the agent committing it (bounded empathy); and prerequisite dependence in learning derived from a bounded focus window rather than posited (developmental prerequisites). Each instantiation is worked for a natural and an artificial agent and states a falsifiable prediction, so one constraint can model limits in both human and machine cognition. The account contributes a unification and a notion of accountable abstention, typed and witnessed by construction.

Chainarong Amornbunchornvej

National Electronics and Computer Technology Center (NECTEC), 112 Phahonyothin Road, Khlong Nueng, Khlong Luang, Pathum Thani 12120, Thailand

Abstention Abductive Reasoning Interpretation Representational Capacity Empathy Residual Connections

May 10, 2026cs.LG

The Transformer as a Polar State Estimator

We show that the core components of the Transformer---attention, residual connections, and normalization---arise naturally from a single geometric state estimation problem. Modeling the latent state in polar coordinates naturally separates radial and hyperspherical dynamics, yielding a precision-weighted filtering procedure in which normalization enforces the hyperspherical constraint, attention aggregates directional evidence, and the residual connection implements an incremental state update. The standard Transformer block with rotary positional encodings is recovered by discarding the geometric correction terms of the resulting state estimator, showing that its architecture follows from the underlying estimation problem rather than from independent design choices. The proposed \textit{Polar Transformer} retains these geometric corrections.

Peter Racioppo

Independent Researcher Los Angeles, CA

Energy-Based Transformer Transformer Architectures State Estimation Residual Connections

May 9, 2026cs.CV

L2A: Learning to Accumulate Pose History for Accurate 3D Human Pose Estimation

Existing 2D-3D lifting human pose estimation methods have achieved strong performance. But the utilization of historical pose representations across network depth was overlooked. In current pipelines, information is propagated through fixed residual connections, which restricts effective reuse of early-layer features such as fine-grained spatial structures and short-term motion cues. However, naively incorporating historical features across layers is non-trivial. We further identify that maintaining a consistent representation space across layers is a prerequisite for effective cross-layer feature aggregation. To address this issue, we propose a history-aware framework that enables effective network cross-layer history feature utilization. Specifically, we adopt a spatial-temporal parallel Transformer backbone to prevent alternating spatial-temporal transformations during sequential processing, thereby maintaining a consistent representation space. Building upon this, we introduce a History Pose Accumulation (HPA) mechanism that adaptively aggregates features from all preceding layers to enhance current representations. Furthermore, we propose a Layer Pose History Aggregation (LPA) module that transforms layer pose features into a compact and structured form, reducing redundancy and enabling more stable aggregation. Extensive experiments demonstrate that our approach achieves state-of-the-art performance on benchmarks.

Zehua Wang, Changwang Mei, Huaijiang Sun +2

Nanjing University of Science and Technology · Lenovo

Wifi-Csi 3D Human Pose Estimation Spatio-Temporal Transformers Depth History Residual Connections

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

Residual Connections Orthogonality Transformer Architectures Geodesic Antibody

May 6, 2026cs.LG

Why Geometric Continuity Emerges in Deep Neural Networks: Residual Connections and Rotational Symmetry Breaking

Weight matrices in deep networks exhibit geometric continuity -- principal singular vectors of adjacent layers point in similar directions. While this property has been widely observed, its origin remains unexplained. Through experiments on toy MLPs and small transformers, we identify two mechanisms: residual connections create cross-layer gradient coherence that aligns weight updates across layers, and symmetry-breaking nonlinearities constrain all layers to a shared coordinate frame, preventing the rotation drift that would otherwise destabilize weight structure. Crucially, a nonlinear but rotation-preserving activation fails to retain continuity, isolating symmetry breaking -- not nonlinearity itself -- as the active ingredient. Activation and normalization play distinct roles: activation concentrates continuity in the leading singular direction, while normalization distributes it across multiple directions. In transformers, continuity is projection-specific: Q, K, Gate, and Up (which read from the residual stream) develop input-space (

\mathbf{v}_1

) continuity; O and Down (which write to it) develop output-space (

\mathbf{u}_1

) continuity; V alone, lacking an adjacent nonlinearity, develops only low continuity.

Kyungwon Jeong, Won-Gi Paeng, Honggyo Suh

Hyntel

Residual Connections Deep Network Rotation Equivariance Symmetry Continuum Cross-Layer Interactions

Apr 26, 2026cs.LG

Can an MLP Absorb Its Own Skip Connection?

We study when a skip connection around a single-hidden-layer MLP can be absorbed into a residual-free MLP of the same width. We first show that for any architecture whose skip branch is an invertible linear map (including Hyper-Connections and their manifold-constrained variants), the problem reduces to the identity skip case. For homogeneous activations of degree

k \neq 1

, such as ReLU

^2

and ReGLU, absorption is unconditionally impossible by a degree argument. For gated activations whose gate is differentiable at the origin with

g(0) = 0

, including SwiGLU and GeGLU, a linearization argument gives the same conclusion. These impossibility results extend to arbitrary depth: a composition of

L

residual blocks using such activations cannot be replicated by any composition of

L

residual-free blocks of the same width. For ungated ReLU and GELU, the situation is richer. For generic weight matrices, absorption holds at the single-block level if and only if there exists an index set

S

of size at least

d

such that

W_{\mathrm{down}}[:,S]\,W_{\mathrm{up}}[S,:] = -I_d

. This condition is non-generic (it fails with probability one under continuous weight distributions), so skip-connected and residual-free MLPs of the same width represent generically disjoint function classes. Whether this disjointness persists for deep compositions of ReLU or GELU blocks remains open.

Antonij Mijoski, Marko Karbevski

IRMA, Universit´e de Strasbourg, France · Independent Researcher

Residual Connections Residual Networks Rectified Linear Unit Skip Multilayer Perceptrons

Apr 21, 2026cs.CL

Discovering a Shared Logical Subspace: Steering LLM Logical Reasoning via Alignment of Natural-Language and Symbolic Views

Large Language Models (LLMs) still struggle with multi-step logical reasoning. Existing approaches either purely refine the reasoning chain in natural language form or attach a symbolic solver as an external module. In this work, we instead ask whether LLMs contain a shared internal logical subspace that simultaneously aligns natural-language and symbolic-language views of the reasoning process. Our hypothesis is that this logical subspace captures logical reasoning capabilities in LLMs that are shared across views while remaining independent of surface forms. To verify this, we employ Canonical Correlation Analysis on the paired residual activations from natural-language and symbolic-language reasoning chains, learning a low-dimensional subspace with maximum cross-view correlation. Furthermore, we design a training-free approach that steers LLMs reasoning chain along this logical subspace, thereby leveraging the complementary reasoning signals from both views. Experiments on four logical reasoning benchmarks demonstrate the effectiveness of our approach, improving accuracy by up to 11 percentage points and generalizing well on out-of-domain problems.

Feihao Fang, My T. Thai, Yuanyuan Lei

University of Illinois Urbana-Champaign, Champaign, IL · Computer & Information Science and Engineering, University of Florida, Gainesville, FL

LLM Reasoning Strategies Reasoning Chain Reasoning Benchmark Symbol-Natural Language Subspace+1

Apr 21, 2026cs.CV

Feature Perturbation Pool-based Fusion Network for Unified Multi-Class Industrial Defect Detection

Multi-class defect detection constitutes a critical yet challenging task in industrial quality inspection, where existing approaches typically suffer from two fundamental limitations: (i) the necessity of training separate models for each defect category, resulting in substantial computational and memory overhead, and (ii) degraded robustness caused by inter-class feature perturbation when heterogeneous defect categories are jointly modeled. In this paper, we present FPFNet, a Feature Perturbation Pool-based Fusion Network that synergistically integrates a stochastic feature perturbation pool with a multi-layer feature fusion strategy to address these challenges within a unified detection framework. The feature perturbation pool enriches the training distribution by randomly injecting diverse noise patterns -- including Gaussian noise, F-Noise, and F-Drop -- into the extracted feature representations, thereby strengthening the model's robustness against domain shifts and unseen defect morphologies. Concurrently, the multi-layer feature fusion module aggregates hierarchical feature representations from both the encoder and decoder through residual connections and normalization, enabling the network to capture complex cross-scale relationships while preserving fine-grained spatial details essential for precise defect localization. Built upon the UniAD architecture~\cite{you2022unified}, our method achieves state-of-the-art performance on two widely adopted benchmarks: 97.17% image-level AUROC and 96.93% pixel-level AUROC on MVTec-AD, and 91.08% image-level AUROC and 99.08% pixel-level AUROC on VisA, surpassing existing methods by notable margins while introducing no additional learnable parameters or computational complexity.

Yuanchan Xu, Wenjun Zang, Ying Wu

School of Information Engineering, Sichuan University, China

Defect Detection Feature Pyramid Area Under The Receiver Operating Characteristic Curve Residual Connections

Apr 16, 2026cs.CV

Class Unlearning via Depth-Aware Removal of Forget-Specific Directions

Machine unlearning aims to remove targeted knowledge from a trained model without the cost of retraining from scratch. In class unlearning, however, reducing accuracy on forget classes does not necessarily imply true forgetting: forgotten information can remain encoded in internal representations, and apparent forgetting may arise from classifier-head suppression rather than representational removal. We show that existing class-unlearning methods often exhibit weak or negative selectivity, preserve forget-class structure in deep representations, or rely heavily on final-layer bias shifts. We then introduce DAMP (Depth-Aware Modulation by Projection), a one-shot, closed-form weight-surgery method that removes forget-specific directions from a pretrained network without gradient-based optimization. At each stage, DAMP computes class prototypes in the input space of the next learnable operator, extracts forget directions as residuals relative to retain-class prototypes, and applies a projection-based update to reduce downstream sensitivity to those directions. To preserve utility, DAMP uses a parameter-free depth-aware scaling rule derived from probe separability, applying smaller edits in early layers and larger edits in deeper layers. The method naturally extends to multi-class forgetting through low-rank subspace removal. Across MNIST, CIFAR-10, CIFAR-100, and Tiny ImageNet, and across convolutional and transformer architectures, DAMP more closely resembles the retraining gold standard than some of the prior methods, improving selective forgetting while better preserving retain-class performance and reducing residual forget-class structure in deep layers.

Arman Hatami, Romina Aalishah, Ilya E. Monosov

Johns Hopkins University

Exact Unlearning Unlearning Method Retraining Residual Connections Video Object Removal

Jan 12, 2026cs.LG

ARCQuant: Boosting NVFP4 Quantization with Augmented Residual Channels for LLMs

The emergence of fine-grained numerical formats like NVFP4 presents new opportunities for efficient Large Language Model (LLM) inference. However, it is difficult to adapt existing Post-Training Quantization (PTQ) strategies to these formats: rotation-based methods compromise fine-grained block isolation; smoothing techniques struggle with significant 4-bit quantization errors; and mixed-precision approaches often conflict with hardware constraints on unified-precision computation. To address these challenges, we propose ARCQuant, a framework that boosts NVFP4 performance via Augmented Residual Channels. Distinct from methods that compromise block isolation or hardware uniformity, ARCQuant maintains a strictly unified NVFP4 format by augmenting the activation matrix with quantized residual channels. This design integrates the error compensation process directly into the matrix reduction dimension, enabling the use of standard, highly optimized GEMM kernels with minimal overhead. Theoretical analysis confirms that the worst-case error bound of our dual-stage NVFP4 quantization is comparable to that of standard 8-bit formats such as MXFP8. Extensive experiments on LLaMA and Qwen models demonstrate that ARCQuant achieves state-of-the-art accuracy, comparable to full-precision baselines in perplexity and downstream tasks. Furthermore, deployment on RTX 5090 and RTX PRO 6000 GPUs confirms practical benefits, achieving up to 3x speedup over FP16. Our code is available at https://github.com/actypedef/ARCQuant.

Haoqian Meng, Yilun Luo, Yafei Zhao +3

School of Computer Science and Technology, Tianjin University

Full-Precision Performance Efficient Large Language Model Residual Connections

Nov 8, 2025cs.LG

Hard-constraint physics-residual networks for hydrogen crossover prediction and high-pressure extrapolation in PEM water electrolysis

Hydrogen crossover is a critical safety and efficiency constraint in high-pressure polymer electrolyte membrane water electrolysis (PEMWE), but accurate prediction remains difficult because data are limited, transport physics are strongly coupled, and industrial operation requires reliable extrapolation beyond observed conditions. This study develops a hard-constraint physics-residual network (PR-Net) for hydrogen crossover prediction in PEMWE and compares it with a purely data-driven neural network (NN) and a soft-constraint physics-informed neural network (PINN). PR-Net embeds Henry's, Fick's, and Faraday's laws as a deterministic backbone and learns only a residual correction for unmodelled nonlinear effects. The benchmark includes 184 observations from eight peer-reviewed sources across six membrane types, covering 1-200 bar,

25-85°C

, and

0.05-5.0 A cm^{-2}

. PR-Net achieves

R^2 = 99.57 \pm 0.16%

, with 9-fold lower prediction variability than NN and PINN. In pressure-axis extrapolation, PR-Net attains

R^2 = 94.02 \pm 0.92%

at 200 bar, 2.5 times beyond the training pressure range, compared with

68.06 \pm 5.52%

for PINN and

58.00 \pm 8.60%

for NN (p < 0.001). Residual analysis indicates that the learned correction captures part of the high-pressure gas-phase non-ideality and recovers a transport-regime transition near

0.23 A cm^{-2}

between Fickian diffusion-dominated and Faradaic production-dominated transport. With a computation time of

1.08 \pm 0.34 ms

on low-power embedded hardware, PR-Net provides a practical framework for real-time crossover monitoring, adaptive process control, and safer high-pressure green-hydrogen operation.

Yong-Woon Kim, Jihyeok Lee, Chulung Kang +1

Department of Computer Engineering, Jeju National University, Jeju, 63243, South Korea · Faculty of Applied Energy System, Jeju National University, Jeju, 63243, South Korea · Department of Mechanical System Engineering, Jeju National University, Jeju, 63243, South Korea +1

Hydrogen System Components Polymer Property Prediction Residual Connections Extrapolation

Date pendingcs.LG

RDQ: Residual Distribution Quantization for Large Language Models

Post-training quantization (PTQ) of large language models degrades sharply below 4-bit precision. We identify the root cause as residual stream distributional drift: quantization noise injected at each transformer layer accumulates in the shared residual representation, causing KL divergence from the FP16 baseline to grow super-linearly with depth (Pearson r=0.999 with log-perplexity, p<0.001, confirmed across all tested methods and bit-widths). We discover that 84% of LLaMA-3-8B layers exhibit non-Gaussian residual distributions (KS test, p<=0.05), and that per-layer residual stream variance grows 6,548x across depth. We propose RDQ (Residual Distribution Quantization), a PTQ framework whose central contribution is Cascaded Error Compensation (CEC): a sequential calibration procedure that captures the actual drifted activations each layer receives (computed by running calibration data through already-quantized upstream layers) and fits per-channel AWQ-style scales against those drifted inputs, with scales folded into preceding RMSNorm weights for exact mathematical equivalence at zero inference overhead. RDQ achieves state-of-the-art results on all three tested architectures: LLaMA-3-8B: 7.55 / 5.62 PPL (W3/W4); Qwen-2.5-7B: 7.46 / 6.38 PPL; Mistral-7B: 6.88 / 5.73 PPL. RDQ beats the best published baseline (LeanQuant/SpinQuant) at every model and bit-width combination, with gains up to -46.4% vs. RTN at W3A16 on LLaMA-3-8B. All output is standard group-128 asymmetric quantization, deployable on Qualcomm AIMET, GGUF, and any standard inference stack at zero runtime overhead.

Prateek Singh

Large Language Model Quantization Residual Connections