Residual Learning

Machine fault diagnosis from vibration requires learning from scarce labelled fault recordings while meeting the computational constraints of edge devices for local inference. We introduce DualRes, a compact oscillatory state-space model that combines two complementary spectral views of vibration, capturing rapid changes and fine frequency structure. Time-aligned views are processed by selective oscillatory memory, which learns how long to retain temporal patterns. The encoder contains 39,528 parameters. We evaluate supervised learning across six bearing datasets and a gearbox benchmark, with an additional gearbox pilot. Recording-level splits and explicit accounting of labelled duration distinguish data efficiency from repeated exposure to correlated samples. On the main gearbox benchmark, DualRes achieves state-of-the-art performance among the nine evaluated methods at six of seven label budgets. With about six labelled seconds per class, it improves macro-F1 by 16.1 percentage points over the next strongest comparator. On the same benchmark, DualRes achieves a 1.44-fold recording-level speedup and a 24.8-fold reduction in checkpoint storage relative to a selective state-space baseline under matched hardware and runtime conditions. Bearing results reveal task-dependent trade-offs. These findings support oscillatory memory as a compact approach to vibration diagnosis under limited labelled exposure.

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.

Prohibited-item detection in X-ray imagery remains challenging due to object superposition, weak texture, and material clutter which obscure both semantic appearance and object boundaries. We propose \textbf{DERA}, a \textbf{D}etached \textbf{E}dge-\textbf{R}esidual \textbf{A}daptation framework for prohibited item detection under X-ray imagery. DERA combines hierarchical visual features with a parallel pixel-difference edge pyramid and learns an object-specific boundary prior from training-time contours of the instance masks. The detached prior gates edge-sensitive features, which are injected into the early visual stages through residual heads. This staged design preserves the foundation detector at the start of adaptation, isolates boundary supervision from semantic feature learning, and restricts the final adaptation stage to only $14.7$K trainable parameters. Evaluated on PIDray, CLCXray, and STCray, DERA improves the baseline by \textbf{3.1}, \textbf{1.6}, and \textbf{2.4} AP points, respectively.

Vision-language models such as CLIP embed images and text in a shared space, where modality-specific distributions often remain separated. Existing accounts connect this modality gap to initialization, contrastive dynamics, and information imbalance, while its distributional and pairwise contributions to retrieval remain unresolved. We introduce UOT-Gap, a training-free variational diagnostic that models frozen image and text embeddings with unbalanced entropic optimal transport (UOT). The UOT optimum separates transport, coupling complexity, and marginal mass variation; a complementary pair-aware residual compares observed image-caption pairs with the UOT soft matching. On Flickr8K and COCO-1K with frozen CLIP, OpenCLIP, and SigLIP encoders, caption degradation reduces Flickr8K Recall@1 from 0.559 to 0.003. Across six dataset-model conditions, the pair-aware residual tracks retrieval degradation with mean absolute Spearman 0.973, compared with 0.392 for the mean gap. The association remains stable across five random COCO-1K subsets at $0.954\pm0.026$, with a minimum of 0.943. UOT barycentric updates reduce the transport objective while degrading retrieval, distinguishing geometric objective descent from task improvement. These results establish UOT-Gap as a diagnostic for caption quality, modality alignment, and retrieval robustness.

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.

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.

Imbalanced time series classification is often addressed by changing the training distribution, objective, logits, or final threshold. These interventions address important biases, yet leave a representation-level question unmeasured: after minority support is reduced, does a learned feature space remain locally reliable around minority regions? We identify a training-local geometry failure: under imbalance, minority cases can lie in sparse, rest-dominated, or mixed feature-space neighborhoods, even when the representation retains useful global class structure. To diagnose and repair this failure, we propose Local Reference Geometry (LRG), a lightweight post-hoc feature augmentation module applied between a fixed feature extractor and the classifier head. Using training features only, LRG measures local exposure and class-mixture risk, then augments each fixed feature with a standardized signed displacement from nearby training geometry and an LDA-projected residual summary. On controlled UCR/Bake Off Redux imbalance benchmarks, paired raw-versus-LRG comparisons show gains for learned, pretrained, and fixed representations, including when LRG is combined with training-level interventions and post-encoder classifier corrections. Ablations show that the gain comes from the signed local residual appended to the original feature, rather than from generic prototype distances, affinity features, scalar statistics, or VLAD-style codes. Further analyses support the proposed local-geometry failure hypothesis: minority neighborhoods become increasingly rest-exposed under imbalance, training-local risk identifies error-prone regions, and LRG gains concentrate in those high-risk regions.

Learning from heterogeneous representations is usually reduced to feature concatenation, which erases which representation produced an error. We instead algebraize the residual: a representation is a typed object that owns both a coordinate system and the residual it leaves unresolved, and learning is an ordered composition of operators that preserve or deliberately erase that type. Fold realizes the objects as point-in-time conditional-mean fields on 10x10 rank grids. FPRC-PQ realizes the algebra as relax-aggregate-close: each field is relaxed by a correction fitted to its own residual in its own coordinates; corrected fields meet at a fixed mean that is the sole identity-erasure boundary; and a shared learner closes only the aggregate's fresh residual. The composition telescopes exactly into representation, local residual estimate, and residual-of-residual estimate. Its aggregate is a learned control-variate interface with population variance reduction, while refitting the closer along perturbations of the backbone yields first-order coupled-path mean orthogonality. As an analytical extension, a reflective rumination operator reads the displacement of a global reconstruction from the aggregate anchor, reflects it, and fixes its gain by a unique orthogonal projection rather than return-tuned grid search. On 3.67M Chinese A-share stock-day observations (2023-2026) under a frozen point-in-time protocol, the evaluated base algebra raises net-of-cost return from 13.52% to 19.10% and Sharpe from 1.42 to 2.09. Matched-capacity, unified-residual, identity-free two-stage, and pairwise-only controls all trail it. The gain is therefore not explained by more features or more trees, but by making residual ownership and composition explicit while representation identity is still available.

Scientific machine learning often relies on proxy targets computed from known domain factors when direct observations are limited. When those same factors are used as model inputs, however, high predictive accuracy may reflect reconstruction of the proxy-generating equation rather than robustness to degraded factor information. We study this problem in RUSLE-derived soil-loss proxy prediction under controlled degradation of the soil-erodibility factor $K$. We introduce a diagnostic framework that combines degraded-formula references, classical tree-based baselines, matched direct and formula-feature predictors, contextual ablations, tail-error analysis, and degradation robustness scoring. We then propose RASPL, a formula-preserving residual framework that retains the degraded formula estimate as the prediction anchor and learns an adaptively gated contextual correction. RASPL substantially outperforms matched direct prediction and provides stronger degradation and tail robustness than treating the formula estimate as an ordinary input feature. Within RASPL, a compact statistical encoder achieves the highest macro-averaged $R^2$ and lowest computational cost, whereas a convolutional encoder achieves the strongest degradation robustness and lowest Tail95 mean absolute error (MAE). These results establish formula preservation as the central design principle for robust learning from factor-derived proxy targets.

Modern multi-tenant Low-Rank Adapters (LoRAs) serving systems concurrently host tens to hundreds of LoRA adapters. Though powerful, this introduces a critical system dilemma between serving efficiency and task performance: higher-rank adapters generally achieve better downstream task performance, but their GPU VRAM footprint and Host-to-Device PCIe swapping overhead severely constrain scalability. Conversely, ultra-low-rank adapters ($r \le 2$) minimize both VRAM footprint and PCIe transfer overhead, but suffer from downstream task performance degradation. To solve this problem, we propose Subspace-Aligned LoRA Training (SALT), a serving efficiency-aware hierarchical fine-tuning framework. Our solution operates in three phases. First, a provider jointly trains high-capacity domain centroids on public data within the domain using a novel alignment regularizer that coheres in-domain task subspaces into a unified basis. Next, users fine-tune ultra-low-rank task residual adapters on private data atop those frozen centroids. Finally, during inference, the provider pins the centroid in GPU VRAM and dynamically swaps in each user's task residual on demand. Across LLMs of varying scales, SALT recovers high-rank accuracy using $r \le 2$ residuals, achieving up to 18.5% absolute accuracy gains over state-of-the-art compression baselines and reducing per-adapter memory by up to 16x. When integrated into vLLM, SALT improves serving throughput by up to 51% under PCIe bandwidth pressure and 28% under GPU VRAM constraints for Llama-3.2-3B.

3D scene understanding requires reasoning about entity existence, spatial layout, and object relations, yet RGB images alone often provide insufficient 3D cues. Existing 3D-VLMs commonly rely on depth or 3D-position-aware inputs at inference time, introducing additional acquisition, reconstruction, or annotation costs that limit RGB-only deployment. We therefore study how training-time 3D evidence can be converted into spatial reasoning capabilities retained under RGB-only inference. We propose a privileged-evidence distillation framework that constructs a distillable teacher through a unified evidence interface and controlled residual injection, and transfers its knowledge to a deployable student receiving only RGB images and questions through logit and structured representation distillation. To avoid imitating teacher signals unsupported by RGB, we further introduce evidence-sensitivity-guided distillation, which uses corrupted evidence to identify highly evidence-dependent targets and down-weight their supervision. We also define a recoverability decomposition based on the matched baseline, teacher, and student, separating privileged gains into RGB-recoverable improvements and residual teacher advantages. Across four benchmarks, the teacher achieves the best result on 7 of 11 reported metrics among the compared methods. The RGB-only student outperforms its matched baseline on all 11 metrics, including gains of 10.4 ScanQA CIDEr and 19.1 Scan2Cap CIDEr@0.5, without additional inference-time inputs. These results validate the effectiveness of training-time privileged 3D evidence distillation for both teacher performance and deployable RGB-only spatial reasoning. Separately, our matched baseline-teacher-student analysis characterizes privileged-gain transfer across evidence types and spatial skills.

Existing theories of neural-network width characterize asymptotic limits, but provide limited guidance on whether an expansion direction identified from finite training data remains beneficial on unseen data. We study this problem for function-preserving residual expansion and introduce the effective alignment dimension, a measurable quantity describing the signal-noise geometry of activation gradients. By deriving the exact mean and variance of the inner product between independently estimated training and test gradients, we obtain a finite-sample upper bound on misalignment probability. The bound depends only on the effective alignment dimension and an effective sample size, requiring finite second moments and a nonzero population gradient, without covariance spectral assumptions or prescribed width-growth rates. We integrate this certificate into the train-test residual-expansion framework, yielding a high-probability condition for test-risk improvement. Experiments across width-controlled LLaMA-style Transformers, Pythia, and ResNet-20 show that wider models exhibit larger effective alignment dimensions and lower empirical misalignment. Direct residual interventions confirm that the alignment statistic predicts the sign and magnitude of held-out loss changes.

We present LARA (Lightweight Additive Residual Adaptation), a method for efficient adaptation that operates in the residual stream of a frozen model rather than in its weights. Where LoRA adds an update of low rank to weight matrices, LARA reads the hidden state at a small set of layers and adds a correction of low rank back to the residual stream, leaving all base weights untouched. On a code fine-tuning task and on preference optimization (DPO), LARA matches LoRA at equal parameter counts. Because adaptation is a frozen base plus a residual, LARA exposes a scale γ, applied at inference, that interpolates smoothly between base and adapted behavior, a form of graded control that adaptation in weight space does not offer. Finally, because each behavior is a small residual module over a shared frozen base, many behaviors can be held resident at once and routed automatically per token. We place seven behaviors, six fine-tuned and one optimized for preference, on one frozen 1.5B model for roughly 33 MB of overhead, against one full model for each behavior. Because the base is untouched, behaviors are trained separately and selected per token rather than loaded on demand, which suits hosting many behaviors, and adding new ones, on a single model on a device.

Modern recommender systems are typically based on deep learning (DL) models, where a dense encoder learns representations of users and items. As a result, these systems often suffer from the black-box nature and computational complexity of the underlying models, making it difficult to systematically enhance their recommendation capabilities. To address this problem, we propose Probabilistic Residual Learning (PRL), a causal Bayesian recommendation model that models the residual between ground-truth and base predictions, enabling targeted refinement of existing systems. Specifically, PRL (1) probabilistically groups users for localized residual modeling, (2) models domain-level confounders that influence user and item representations, and (3) aggregates cluster-specific residual predictions over the confounders using do-calculus. Experiments demonstrate that our plug-and-play PRL is compatible with various base deep learning recommender systems, improving their performance while automatically discovering meaningful user clusters.

Neural surrogates are widely used in scientific machine learning for fast prediction of three-dimensional (3D) thermo-fluid fields. However, generating training data using conventional numerical solvers often incurs substantial computational and storage costs. We propose to train an attention graph neural network by minimizing the finite-volume method (FVM) residuals of the governing equations. These residuals are evaluated directly on the mesh, requiring no labeled data. We evaluate the trained surrogates against computational fluid dynamics (CFD) references and a data-supervised baseline across four scenarios. On the two steady-state benchmarks, the FVM-loss model achieves an all-field normalized root-mean-square error (nRMSE) of 2.3-2.8%. It demonstrates close agreement with the CFD references, including the buoyancy-energy coupling. On the two parametric transient cases, the FVM-loss model outperforms the supervised baseline in terms of accuracy, while avoiding the data-generation cost entirely. These results indicate that the FVM loss can provide a practical training signal for neural surrogates and reduce the model development cost.

The edge-of-chaos heuristic has long served as a guiding principle for designing reservoir computers, yet its relevance to machine performance remains elusive. Here, taking the spectral radius of the reservoir network as the control parameter, we show that the radius yielding the best forecasting performance does not coincide with the Lyapunov edge of the isolated, teacher-forced, or closed-loop generative reservoir. By analyzing the collective dynamics of the teacher-forced reservoir, we find that the target dynamics are represented mainly by stable Lyapunov modes whose finite-time stability is strongly modulated by the input. This finding motivates a stability-expressivity transfer index, which balances the stability of these modes against their expressivity in representing the target. Across chaotic and quasiperiodic targets, and for both asymmetric and symmetric reservoirs, this index accurately identifies the optimal spectral radius for autonomous forecasting.

Single-image reflection removal aims to recover a clean transmission layer from one image captured through glass. We study an explicit decomposition pipeline built on RDNet and introduce LowAux, a training-only low-pass reflection auxiliary objective. The original residual target remains the main reflection supervision, while symmetrically filtered prediction and target provide a stable low-frequency constraint. We further incorporate scene-balanced real pairs from RRW to broaden real-scene coverage and improve cross-dataset generalization. To avoid evaluation discrepancies caused by model-specific resizing, padding, output quantization, and metric code, we build a unified public benchmark over CEILNet, Real20, Postcard, Objects, and Wild. Under the same evaluator, the proposed system obtains a five-dataset macro average of 27.546 dB PSNR, 0.9220 SSIM, 0.9751 NCC, and 0.004760 LMSE, achieving the highest macro-average PSNR, SSIM, and NCC and the lowest LMSE among the compared public checkpoints and internal variants. Per-dataset and qualitative analyses show that the main benefit is a more balanced performance across diverse reflection distributions, while clear semantic reflections in Postcard remain challenging.

Rollout generation is a major bottleneck in Reinforcement Learning (RL) for Mixture-of-Experts (MoE) Large Language Models, motivating low-precision rollout acceleration such as FP8. As an emerging low-precision format, NVFP4 combines fine-grained scaling for accuracy preservation with native W4A4 FP4 GEMMs for higher throughput than FP8. However, we find that directly applying NVFP4 to MoE RL rollout is impractical. NVFP4 rollout with BF16 training collapses after roughly 150 steps, accompanied by rapidly growing rollout-trainer log-probability gaps. Through training-inference error analysis and controlled ablations, we identify activation error, rather than weight error, as the dominant source of FP4 RL instability: weights can be synchronized and aligned by a shared quantization-dequantization path, whereas activations are recomputed online and error is amplified by the coarse E2M1 grid. Therefore, to stabilize NVFP4 RL for MoE, we propose QUantization-error Alignment across Dual Sides (QUADS). On the trainer side, we introduce Asymmetric Quantization-Aware Training fake-quantizing weights while keeping activations unquantized for better alignment. On the rollout side, Residual Activation Compensation corrects high-error activation channels while preserving native W4A4 GEMMs. In our MoE RL experiments on several benchmarks, QUADS achieves BF16-level accuracy, improves average pass@1 by 21.49 points over naive NVFP4 RL, and delivers ~16% higher rollout throughput than FP8.

Quadrotors flying in tight formations are severely affected by turbulent aerodynamic interactions, such as downwash, that can cause catastrophic collisions if left unmodeled. To compensate for these effects, we propose a physics-informed residual dynamics learning framework that captures complex aerodynamic interactions while ensuring the joint multi-quadrotor system remains differentially flat. We leverage this preserved flatness to design a computationally efficient feedback linearization controller that is easily tunable with linear control techniques and cancels aerodynamic disturbances via feedforward compensation. Hardware experiments demonstrate our framework reduces average tracking errors by 31% compared to nominal baselines. Crucially, our lightweight approach matches the tracking performance of state-of-the-art nonlinear model predictive control (NMPC) while requiring an order of magnitude less computation. We are the first to show that stable, tight formation flight can be achieved with under 30 seconds of training data and a 5ms loop rate, unlocking high-fidelity aerodynamic compensation for compute-constrained flight stacks.

The rapid advancement of generative AI has enabled the creation of highly realistic deepfake media, posing significant threats, including misinformation, digital identity theft, fraud, and manipulation of public opinion. AI-generated image (AIGI) detection is reliably challenging due to the diversity of generative methods and the subtle artifacts they leave behind. In this work, we propose GenRes, a novel framework for generative residual learning via a neural tensor network, which models fine-grained relational features between original and transformed samples to enhance generalization. To address scenarios involving multiple generative transformations, we introduce GenRes++, which employs a learnable attention mechanism to aggregate relational features across multiple transformed samples and enables the model to focus on the most informative cues. Both models leverage PE-Core as a feature extractor, providing generalized and semantically rich embeddings that improve cross-domain performance and enable the detection of AIGI generated by unseen methods. Comprehensive experiments on multiple benchmark datasets demonstrate that the proposed GenRes++ approach outperforms existing methods.

Gaussian Splatting has achieved significant improvements by incorporating warping-based techniques. However, such methods suffer from pixel-level inaccuracies due to uncertain geometry. This uncertainty leads to spatial misalignments in the warped images, which disrupt residual learning used in warping-based methods and fundamentally limit the gains of correction, particularly on thin structures and high-frequency details. Driven by our insight that useful visual cues are not lost but locally preserved under slight displacement, we propose Geometry-Aware Deformable Aggregation (GADA). This method introduces an iterative refinement module with deformable offsets to actively correct spatial misalignments and recover these displaced cues. Furthermore, to address the limitations of standard pipelines where visibility checks (i.e., thresholding) often discard valid pixels and multi-view warped image fusion relies on naive mean aggregation, our module is coupled with an implicit confidence weighting mechanism that selectively suppresses unreliable evidence. Consequently, our approach outperforms prior warping-based Gaussian Splatting, preserving high-frequency quality while achieving 2.13 times faster FPS.

Chess engines have evolved from search-based systems optimized solely for strength to neural policies capable of modeling human decisions across much of the rating spectrum. Maia-3, the strongest human-like move policy for chess, models the typical moves of a given rating but does not model high Elo strength well (2500+ Lichess Elo) nor has an extensible architecture for modeling individual play style. On the other hand, search-based engines like Stockfish are far stronger than any known human but struggle to model human-like play. To solve these problems, we present Matilda, a permutation-invariant set transformer that re-ranks the full legal-move distribution produced by a frozen Maia-3 and improves it along both dimensions with one 1.7M-parameter model. Matilda uses Maia-3 to provide both global context and search candidates. Context is encoded from Maia-3's hidden representation, time control, and an optional 32-dimensional player-style vector, while the top-16 candidate moves are optionally rescored by Stockfish. A zero-initialized head scatters per-candidate adjustments back into the policy logits, so the untrained model is exactly Maia-3 and every gain is value-added under full-vocabulary NLL. On a 2500+ Elo benchmark from Lichess, Matilda improves on Maia-3 by +0.5-0.6% below 2800 but +4.3%, +11.9%, and +21.9% at 2800-2900, 2900-3000, and 3000+, respectively, and an additional +0.41% overall from player-style embeddings. Ablations show that the improvements are primarily driven by the engine-derived features, the mechanism is not engine-specific, and the gains survive memorization, sibling, and account audits while preserving Maia-3 at 1000-2500 Elo. Because search supervision is modular, Matilda naturally supports interchangeable search engines, demonstrated by replacing Stockfish with an AlphaZero-family engine.

Many dense prediction networks rely on additive feature transformations and model higher-order feature interactions only implicitly. Product units provide an explicit mechanism for multiplicative feature modeling, but their logarithmic--exponential formulation can cause numerical instability, which has limited their use in deep dense prediction networks. In this work, we propose Product-Unit U-Net (PU-UNet), a residual U-Net that integrates stable product-unit residual blocks into rich low-resolution stages for medical image segmentation. The proposed formulation combines smooth positivity mapping with log-domain clipping, enabling stable multiplicative feature learning with negligible computational overhead. On ISIC 2018, Kvasir-SEG, and BUSI, PU-UNet achieves Dice scores of 0.942, 0.959, and up to 0.925, respectively. Compared with a matched Residual U-Net baseline, PU-UNet consistently improves Dice and IoU while keeping parameters, FLOPs, and inference latency nearly unchanged, and reduces the image-level false-positive rate on normal BUSI cases from 0.077 to zero. Ablation studies suggest that the gains are associated with product-unit interactions, are strongest under low-resolution placement, and benefit from the proposed stabilization design. These results suggest that stable product-unit residual learning can be an effective way to enhance U-Net-style segmentation networks with explicit multiplicative interactions.

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

For residual learning that refines existing behavior, sample efficiency depends on two things: how much information each rollout returns, and how efficiently the learner uses that information. Reinforcement learning's standard scalar reward carries far less information than the directional task error that defines the task. Random exploration further discards whatever information each rollout returns. Through residual learning with directional task-error supervision and a task error model that drives sample selection, we achieve stable three-, four-, and five-ball juggling on anthropomorphic Barrett WAM arms. Despite planning and controlling through a simple, idealized stack, the system converges from the second attempt. The first attempt drops, after which task error decreases monotonically without further failures. In comparison, five-ball juggling typically takes humans years of practice. We compare residual learners across two ternary axes, the directional information in the learning feedback and the commitment of the analytic prior, spanning Newton-style Jacobian updates, Composite Bayesian Optimization, and stochastic search methods. Both axes prove necessary: neither directional feedback nor an informative prior suffices alone, and the simplest method that combines them, a fixed-Jacobian Newton update, is the most reliable. The learned residual tolerates substantial prior misalignment and degraded joint tracking, affecting mainly convergence speed. The bottleneck for residual learning on real robots is therefore the information content of the supervision signal and how the learner uses it, not the accuracy of the surrounding stack. Video documentation of all experiments is available at https://kai-ploeger.com/residual-juggling.

Conditional diffusion image generators can be repurposed for editing through inversion, without the need for large-scale paired fine-tuning data. However, producing high-quality, targeted edits while maintaining image identity and global consistency remains challenging, as weakly conditioned inversion often embeds conflicting image features into the noise. We demonstrate that incorporating a residual image encoding as additional conditioning enables both improved identity preservation and better editability. We optimize this residual encoding to provide a strong conditioning signal for reconstruction, thereby reducing the reliance on inversion and susceptibility to its aforementioned pitfalls. To ensure this residual does not interfere with desired edits, we incorporate a gradient reversal-based optimization strategy that disentangles the residual from the edited condition. We illustrate our method's ability to produce high-fidelity results across precise intrinsic-based editing and relighting, and show proof-of-concept text-guided manipulation.

Mixture-of-Experts (MoE) models enable efficient scaling, but training them from scratch remains prohibitively expensive. MoE upcycling mitigates this cost by converting pretrained dense models into sparse MoE models. However, existing upcycling methods typically rely on large-scale continued training and often perform poorly under data-constrained supervised adaptation, due to either homogeneous experts or overly disruptive perturbations to pretrained parameters. In this setting, effective upcycling must leverage pretrained weight structure while introducing sufficient diversity among routed experts. To this end, we propose SVD-Partitioned Residual Initialization (SPRI), which distributes SVD-partitioned residuals derived from pretrained feed-forward network (FFN) weights across routed experts, introducing controlled expert diversity grounded in pretrained spectral structure. We further introduce a two-stage training strategy to improve adaptation stability. We evaluate SPRI on multilingual speech-to-text translation, where limited supervised data challenges MoE upcycling and multiple target languages provide natural routing heterogeneity. On CoVoST2 across 15 En-to-XX directions, SPRI improves average BLEU and COMET over fully fine-tuned dense models by 2.58 and 3.32 points, respectively, and outperforms the prior best MoE upcycling baseline by 3.39 BLEU and 4.34 COMET points.

Accurate brain tumor segmentation from multiparametric magnetic resonance imaging (MRI) is critical for treatment planning, response assessment, and neuro-oncology research. However, automated segmentation remains a difficult task in computer vision because of variation in tumor appearance and MRI protocols across patient scans. Moreover, clinically important regions such as enhancing tumor and tumor core are often small relative to the full brain volume, further increasing the difficulty of achieving high voxel-level precision. These challenges are amplified in multi-site datasets, where differences in scanner hardware and acquisition parameters can introduce non-biological variation. To address this, networks must learn tumor-specific features while remaining robust to site-dependent noise. In this paper, we show that an ensemble of multi-fold predictions from a modern 3D convolutional segmentation network with corrective diffusion (CorrDiff) post-processing improves brain tumor segmentation across datasets. We propose CoMNet, an ensembled MedNeXt-CorrDiff framework for accurate multi-site brain tumor segmentation. In this framework, we use MedNeXt as the primary segmentation model for feature learning, while a corrective diffusion block learns to refine the residual errors in the individual prediction maps before probabilistic thresholding. This process reduces the variance across fold predictions by correcting fold-specific residual errors and aggregating them into a consensus mask that is less sensitive to site-dependent imaging variability. Our proposed framework achieved the highest Dice score compared to two baseline models on the UTSW-Glioma and BraTS-SSA datasets. Experimental results support the use of corrective diffusion and fold-level probability ensembling as meaningful additions to existing state-of-the-art models for accurate glioma segmentation on multi-site datasets.

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

Lossy compression is essential for massive spatiotemporal data from scientific simulations. Learned compressors can achieve high compression ratios at moderate accuracy targets, but their aggregate reconstruction losses do not guarantee accuracy for each block. Existing Guaranteed Autoencoder (GAE) methods add a per-block residual correction by retaining SVD/PCA-style coefficients until the target is met. This works at moderate tolerances, but in the high-fidelity regime with block-level NRMSE from 10^-6 to 10^-4, the number of retained coefficients grows quickly and the correction stream dominates the total rate. We propose a residual-centric view: the learned residual is structurally different from the original scientific field and should be coded with a representation designed for that residual. We introduce two residual coders. LBRC is a deterministic, training-free pipeline that adaptively quantizes the learned residual to the target NRMSE and losslessly encodes the resulting integer residual using 3D Lorenzo differencing, zigzag mapping, bit-plane coding, and entropy coding. NGLR adds a causal neural predictor that outputs a normalized bias for an integer-rounded Lorenzo prediction in the same deterministic integer pipeline, reducing the entropy of the remaining residual code while preserving deterministic decoding. The predictor weights are serialized and counted in the bitstream. Across E3SM, JHTDB, and ERA5 at block-level NRMSE targets from 10^-6 to 10^-4, LBRC improves compression ratio over GAE by 30-60% and is broadly competitive with SZ. NGLR adds a further 10-40% over LBRC and outperforms SZ in the evaluated high-fidelity regime. These results show that residual representations tailored to learned-compressor residuals can preserve the advantage of learned compression when global residual correction becomes rate-dominant.

Inverting a robotic task requires more than reversing symbolic state transitions or rewinding motor trajectories. In robot manipulation tasks, symbolic inverse plans often fail to fully restore the effects of forward executions under continuous interaction dynamics. We present a hybrid framework for inverse manipulation that derives inverse-skill objectives from STRIPS-like operators automatically extracted from demonstrations through soft geometric predicates. For each extracted operator, we construct an inverse restoration objective that preserves preconditions, restores delete effects, and negates add effects. A task planner first attempts to satisfy this objective using available action primitives. Unresolved symbolic predicates then induce a residual operator learning problem solved through Reinforcement Learning (RL). We evaluate the framework on the ManiSkill3 PushCube task. For a forward pushing skill, the symbolic inverse performs a coarse pick-and-place restoration, while a residual Soft Actor-Critic policy refines the cube pose to satisfy the remaining inverse predicates. Our results show that predicate-derived residual control can turn an approximate symbolic inverse into a physically grounded inverse skill.

Spatio-Temporal Video Grounding aims to localize object tubes based on textual queries. While recent methods have achieved remarkable success, they mainly focus on high-quality(HQ) inputs, neglecting the widespread presence of low-quality(LQ) videos in real-world scenarios. Although tuning methods like LoRA can adapt to degraded inputs, they inevitably disrupt pre-trained knowledge. To address this, we propose Null-Space Tuning (NST). This framework exploits the geometric property that adding vectors within the null-space of frozen weights to the layer input does not affect the output. Leveraging this, NST injects learnable residuals into input features that can be selectively invisible to the pre-trained backbone. Specifically, NST combines the Quality-Adaptive Unit and Dual-Space Reparameterization to synthesize these residuals by confining components for HQ inputs to the null-space, while directing restoration components for LQ inputs to the non-null space. As the frozen weights eliminate null-space components, we effectively rectify degraded inputs while preserving pre-trained knowledge for HQ inputs. Extensive experiments show that NST outperforms state-of-the-art methods on our Mixed-Quality benchmark.

Neural operators are often reported to exhibit zero-shot super-resolution, a phenomenon in which a model trained on coarse grids produces accurate predictions on finer testing grids without additional retraining. Despite strong empirical evidence, the theoretical foundations of this phenomenon remain unclear. In this work, we provide a systematic theoretical study of zero-shot super-resolution in operator learning. We first show that zero-shot super-resolution can be information-theoretically impossible even in benign settings such as when the input functions are available over the entire continuum and the ground truth is a simple rank-one linear operator. We then identify H{" o}lder smoothness of the output functions as a sufficient condition for zero-shot super-resolution and derive corresponding generalization bounds. Finally, we also validate the identified failure modes through experimental results.

Reconstruction-based inference assigns a class by comparing class-wise reconstruction residuals; Sparse Representation Classification (SRC) is a canonical instance whose reliability depends on the geometry of the learned representation. We adopt a strict training-inference separation: SRC is used only as a fixed test-time rule and is never differentiated, unrolled, or optimized during training. In a span-level idealization based on class-conditional spans and their associated projection residuals, we formalize residual-ordering stability through a residual margin and characterize geometric obstructions -- span overlap, dominance, and near-overlap via small principal angles -- that can collapse this margin in worst-case directions. This span-level theory is primary: it specifies when the idealized residual family is well-separated, and it provides a conditional solver-level interpretation for practical residual approximations (e.g., OMP) insofar as they remain close to the span-level residual ordering. Under explicit coverage and separation assumptions, we derive a quantitative lower bound on the (idealized) residual margin. Guided by these targets, we propose geometry-shaping objectives that promote masked within-class self-expressiveness, discourage cross-class reconstruction pathways and inter-class span alignment, and prevent collapse -- without invoking SRC residuals or predictions during training. Experiments on images (COIL-100), text (TREC), and EEG connectivity evaluate all representations under identical fixed SRC/OMP inference and report residual margins and geometric diagnostics; cross-entropy is included only as a reference geometry under the same evaluation protocol.

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

Recent studies on long-term time series forecasting have shown that simple linear models and MLP-based predictors can achieve strong performance without increasingly complex architectures. However, many competitive baselines still rely on structural priors such as frequency-domain modeling, explicit decomposition, multi-scale mixing, or sophisticated cross-variable interaction modules, while paying less attention to how simple temporal mappings should be trained and organized. In this paper, we propose STAIR, short for Stagewise Temporal Adaptation via Individualization and Residual Learning, a training paradigm for long-term time series forecasting that aims to unlock the capacity of simple temporal mapping models without introducing complex architectural modules. STAIR decomposes forecasting ability into three progressive stages: it first learns common temporal dynamics across variables through a shared temporal mapping, then adapts the shared model to each variable via channel-wise fine-tuning to capture variable-specific patterns, and finally complements the backbone with cross-variable information through residual learning. We further introduce Shared-to-Individual Fine-tuning and alpha-RevIN to mitigate the limitations of strict channel independence and the overly strong normalization prior induced by standard RevIN. This design gradually increases modeling flexibility while keeping the core temporal predictor as a shallow MLP in the main experiments, with linear variants analyzed separately. Experiments on nine long-term forecasting benchmarks show that STAIR matches or outperforms recent strong baselines while preserving a simple temporal backbone, providing a concise and effective modeling perspective for long-term time series forecasting.

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

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

Accurate dynamical modeling is essential for simulation and control of embodied systems, yet first-principles models of electromechanical systems often fail to capture complex dissipative effects such as joint friction, stray losses, and structural damping. While residual-learning physics-informed neural networks (PINNs) can effectively augment imperfect first-principles models with data-driven components, the residual terms are typically implemented as unconstrained multilayer perceptrons (MLPs), which may inadvertently inject artificial energy into the system. To more faithfully model the dissipative dynamics, we propose DiLaR-PINN, a dissipative latent residual PINN designed to learn unmodeled dissipative effects in a physically consistent manner. Structurally, the residual network operates only on unmeasurable (latent) state components and is parameterized in a skew-dissipative form that guarantees non-increasing energy for any choice of network parameters. To enable stable and data-efficient training under partial measurability of the state, we further develop a recurrent rollout scheme with a curriculum-based sequence length extension strategy. We validate DiLaR-PINN on a real-world helicopter system and compare it against four baselines: a pure physical model (without a residual network), an unstructured residual MLP, a DiLaR variant with a soft dissipativity constraint, and a black-box LSTM. The results demonstrate that DiLaR-PINN more accurately captures dissipative effects and achieves superior long-horizon extrapolation performance.

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.

We propose Self-Augmented Residual 3D Gaussian Splatting (SA-ResGS), a novel framework to stabilize uncertainty quantification and enhancing uncertainty-aware supervision in next-best-view (NBV) selection for active scene reconstruction. SA-ResGS improves both the reliability of uncertainty estimates and their effectiveness for supervision by generating Self-Augmented point clouds (SA-Points) via triangulation between a training view and a rasterized extrapolated view, enabling efficient scene coverage estimation. While improving scene coverage through physically guided view selection, SA-ResGS also addresses the challenge of under-supervised Gaussians, exacerbated by sparse and wide-baseline views, by introducing the first residual learning strategy tailored for 3D Gaussian Splatting. This targeted supervision enhances gradient flow in high-uncertainty Gaussians by combining uncertainty-driven filtering with dropout- and hard-negative-mining-inspired sampling. Our contributions are threefold: (1) a physically grounded view selection strategy that promotes efficient and uniform scene coverage; (2) an uncertainty-aware residual supervision scheme that amplifies learning signals for weakly contributing Gaussians, improving training stability and uncertainty estimation across scenes with diverse camera distributions; (3) an implicit unbiasing of uncertainty quantification as a consequence of constrained view selection and residual supervision, which together mitigate conflicting effects of wide-baseline exploration and sparse-view ambiguity in NBV planning. Experiments on active view selection demonstrate that SA-ResGS outperforms state-of-the-art baselines in both reconstruction quality and view selection robustness.

We develop a new and general encode-approximate-reconstruct operator learning model that leverages learned neural representations of bases for input and output function distributions. We introduce the concepts of numerical operator learning and discretization independence, which clarify the relationship between theoretical formulations and practical realizations of operator learning models. Our model is discretization-independent, making it particularly effective for multiresolution learning. We establish theoretical approximation guarantees, demonstrating uniform universal approximation under strong assumptions on the input functions and statistical approximation under weaker conditions. To our knowledge, this is the first comprehensive study that investigates how discretization independence enables robust and efficient multiresolution operator learning. We validate our method through extensive numerical experiments involving both local and nonlocal PDEs, including time-independent and time-dependent problems. The results show that multiresolution training significantly improves accuracy and computational efficiency. Moreover, multiresolution training further enhances empirical discretization independence.

Scaling factors in residual branches have emerged as a prevalent method for boosting neural network performance, especially in normalization-free architectures. While prior work has primarily examined scaling effects from an optimization perspective, this paper investigates their role in residual architectures through the lens of generalization theory. Specifically, we establish that wide residual networks (ResNets) with constant scaling factors become asymptotically unlearnable as depth increases. In contrast, when the scaling factor exhibits rapid depth-wise decay combined with early stopping, over-parameterized ResNets achieve minimax-optimal generalization rates. To establish this, we demonstrate that the generalization capability of wide ResNets can be approximated by kernel regression associated with the Neural Tangent Kernel (NTK). Our theoretical findings are validated through experiments on synthetic data and real-world classification tasks, including MNIST and CIFAR-100.