Symbolic Regression (SR) seeks to find succinct mathematical expressions that represent the fundamental relationships within data, providing interpretability and scientific understanding that exceeds that of black-box models. Nevertheless, traditional methods like Genetic Programming face challenges with scalability and are highly sensitive to noise, while sparse regression techniques such as SINDy rely significantly on predetermined feature libraries. In this work, we present a Neural Symbolic Regression (NSR) framework that treats neural networks as functional preconditioners for symbolic discovery. Our approach uses a decoupled pipeline: a neural network first learns a smooth, noise-robust approximation of the target function in an interaction- aware nonlinear feature space. LASSO is then applied to extract sparse, interpretable closed-form expressions. To improve predictive accuracy and symbolic fidelity by integrating distributed hyperparameter optimization with Ray Tune and ASHA scheduling. Experiments on the Nguyen benchmark suite show that our approach consistently outperforms SINDy and non-tuned neural baselines in RMSE, noise robustness, and out-of-distribution generalization. Ablation studies confirm the significance of feature interactions, neural depth, and tuning strategies. In general, this study presents a scalable and understandable neural-symbolic framework, creating a solid link between neural approximation and the discovery of sparse equations for scientific machine learning.
Joonyong Park, Shinnosuke Takamichi, David M. Chan +3cs.CL cs.SD
Neural audio codecs (NACs) convert speech into discrete token sequences, and prior work has reported that these sequences follow language-like statistical laws. This paper analyzes the token statistics of 13 NACs spanning multi-codebook residual vector quantization (RVQ), single-codebook VQ, and non-VQ designs, evaluated on three corpora under clean, white-noise, and real-world DEMAND-noise conditions. Zipf and Heaps parameters, unigram entropy, codebook occupancy, and Jensen-Shannon divergence (JSD) are estimated from matched token samples with explicit fit-validity safeguards and family-conditional $n$-gram orders. Corpus identity explains little variance in any metric, whereas acoustic condition and quantizer meta-category dominate in a metric-dependent way, and unigram entropy is the metric most strongly associated with meta-category. Clean-to-noise JSD computed at a common unigram order is associated with mel-cepstral distortion most clearly under DEMAND noise. The collapse and explosion degradation signatures previously reported for RVQ codecs concentrate in RVQ cells under white and DEMAND noise, respectively; explosion also occurs in non-VQ codecs, and single-codebook VQ codecs shift in occupancy and distribution shape without either signature. These results provide architecture-conditioned conventions for applying language-statistical analysis to NAC tokens.
Broad Learning System (BLS) offers an efficient alternative to deep architectures by enabling fast learning through randomized feature mapping and closed-form solutions. However, its reliance on squared error loss makes it highly sensitive to noise, outliers, and corrupted labels, limiting its reliability in real-world scenarios. To address this limitation, we propose Wave-BLS, a robust broad learning framework that integrates the wave loss function, which is asymmetric, bounded, and smooth, enabling controlled penalization of large errors. The proposed formulation replaces the standard least-squares objective with a wave-loss-based optimization problem, solved efficiently using a Nesterov accelerated gradient (NAG)-based scheme without requiring matrix inversion, thereby improving scalability. Extensive experiments on 30 UCI benchmark datasets demonstrate that Wave-BLS consistently outperforms classical BLS and several robust variants. Statistical validation using Friedman and Nemenyi post-hoc tests confirms the significance of the observed improvements. Furthermore, robustness evaluations under controlled noise and outlier injection reveal that Wave-BLS exhibits substantially slower performance degradation compared to BLS, even in challenging contamination settings. These results establish Wave-BLS as a stable and robust alternative to existing broad learning models for learning under data uncertainty.
Kolmogorov-Arnold Networks (KANs) replace fixed activations in deep architectures with learnable univariate edge functions, making the choice of edge parametrisation central. Existing variants rely on fixed bases such as splines, polynomials, or Fourier features, which impose a function-space geometry before data are observed. We introduce geometry-constrained KANs, a family of edge activations derived from Banach duality maps in which the geometry itself is learned through a scalar exponent $p > 1$ per edge. This exponent controls the qualitative response: sub-Euclidean values produce sharp, threshold-like behaviour reminiscent of the $\ell_1$ (LASSO) geometry, $p = 2$ recovers the linear regime, and larger values produce flatter responses near the origin. Across 50 symbolic-regression targets ($40$ from the AI Feynman benchmark plus $10$ synthetic stress tests), geometry-constrained KANs match or beat every fixed-basis baseline on median NRMSE (Banach-KAN $0.030$, tying Chebyshev and improving on splines); on average rank Banach-KAN is best on the $18$-equation core ($2.00$) and statistically tied with the strongest spline on the full benchmark ($2.32$ vs. $2.34$). The clearest gains appear under measurement noise: as $σ$ grows from $0$ to $1$, $\ell^p$-KAN degrades only $3.7\times$ -- below even a cross-validated spline ($\approx 11\times$) -- while an unregularised spline degrades $21.6\times$; Banach-KAN degrades $8.8\times$, comparable to a tuned spline but far more stable than the unregularised one. Banach-KAN also takes the most per-equation wins in the small-sample regime, with fixed-basis models catching up only as the training set grows. Learned exponents provide an interpretable, relative signal: at a fixed initialisation they reveal a consistent, target-dependent geometric ordering across equation families and input dimensions.
YoungChae Kim, Da-Hee Yang, Joon-Hyuk Changcs.SD cs.CV eess.AS
Large language model (LLM)-based audio-visual speech recognition (AVSR) systems are robust under noise. Contrastive decoding (CD), originally introduced to stabilize LLM generation by contrasting a weaker model against a stronger one at inference time, adjusts predictions without additional training. In this work, we apply CD to AVSR by contrasting audio-only conditioning with full audio-visual conditioning within the same underlying model. However, using a fixed contrastive strength introduces a trade-off across noise levels: stronger intervention helps under severe noise but may over-correct reliable predictions in clean conditions. We propose reliability-aware scaling of CD for AVSR. Instead of using a fixed strength, we adaptively modulate the contrastive influence at each token based on reliability signals derived from attention dynamics and inter-model predictive divergence. Experiments on LRS3 show consistent improvements across clean and low-SNR conditions.
Baptiste Rossigneux, Inna Kucher, Vincent Lorrain +1cs.CV cs.LG
Recent Visual-Language Models (VLMs) have enhanced the capabilities of pre-trained LLMs by adding vision tokens alongside text, with approaches like LLaVA showing impressive results. However, the computational burden of processing up to 576 or 729 visual tokens makes edge deployment challenging. While various token pruning techniques require retraining, some are training-free and thus can easily adapt to architecture changes. We introduce ClustRS, a two-part, training-free algorithm for robust token pruning. Its first component is an attention-weighted, clustering algorithm that selects representative tokens from each semantic cluster. The second component, Residual Shrinkage, is a one-pass denoising step on the selected tokens. These training-free lightweight steps make LLaVA ready for real-world data, improving robustness to a wide range of image-noise types and intensities. Experimental results on the ScienceQA-IMG and MM-VET benchmarks show our method outperforms attention- and diversity-based methods by up to 20\% under extreme noise and token conditions (reducing tokens by 97\%, down to 16 tokens) on LLaVA 1.5 7b and achieves exceptional results on LLaVA-OneVision, where we match baseline performance with fewer than one-third of their tokens under mild noise conditions. Our study demonstrates a simple yet powerful alternative to both score-only and diversity-only pruning rules, paving the way for compute-efficient and noise-resilient VLM deployment.
Ashish Anand Shukla, Rini Smita Thakur, Aryan Das +1cs.SD cs.LG
Audio-Text Foundation Models (ATMs) fail catastrophically under severe acoustic noise, yet existing adaptation strategies either rely on gradient-based Test-Time Adaptation (TTA), which reinforces noise rather than signal, or on prompt tuning that requires privileged noise annotations unavailable at inference. We address these failures with PRISM (Prototype-Rectified Iterative Self-supervised Manifold Denoising), a training-free, source-free TTA framework grounded in the Affine Noise Hypothesis: severe acoustic noise induces a low-rank affine shift in the multimodal latent space, with more than 90% of distortion energy confined to the leading 60 principal components. PRISM estimates and reverses this distortion from an unlabeled target batch using frozen text prototypes as geometric anchors via three closed-form geometric corrections compiled into a single static projection matrix by Affine Bias Regression. At inference, adaptation reduces to one matrix-vector multiplication in 0.0009 ms, making it substantially faster than gradient-based TTA while requiring no additional training. On UrbanSound8K, PRISM improves over the zero-shot baseline by 12.94 percentage points and surpasses an oracle-assisted TTA baseline by 9.41 percentage points, despite never observing its privileged augmented noise prompts. We further identify the Polyphonic Trap, a principled failure mode of subspace deflation for broadband classes, and resolve it via Confidence-Aware Regression (CAR), recovering up to 8.16 percentage points for the worst-affected class.
The efficient-KAN literature---covering Chebyshev, wavelet, and radial-basis-function variants of the original Kolmogorov-Arnold Network---has been benchmarked almost entirely on clean data. We show that this choice conceals a large capability difference between architectures: ChebyKAN's test MSE (evaluated against clean ground truth) increases by a factor of 10.6x when training data is corrupted with sigma=0.1 noise, versus 7.9x for vanilla KAN, 1.7x for a standard MLP, and just 1.4x for our proposed ER-KAN. ER-KAN combines three design choices targeting the noisy, data-scarce setting: shared Gaussian RBF bases across all edges in a layer (providing locality and efficient parameterisation), curriculum noise injection during training (explicitly teaching noise robustness), and entropy-weighted adaptive regularisation (preventing overfitting at small N). The result is a 595-parameter network that matches MLP accuracy at moderate noise while degrading far more gracefully as noise grows. We evaluate on eight analytic functions (N in {50, 200, 500}, sigma in {0, 0.03, 0.1}), on a damped harmonic oscillator physics-informed neural network where ER-KAN achieves 4.2x lower solution MSE than MLP, and on a Burgers' equation PINN where all models fail to converge---a genuine limitation we report rather than suppress. We introduce the noise degradation ratio as a simple complementary metric and recommend it become a standard reporting requirement for efficient-KAN papers.
Passive acoustic sensing offers a critical, cost-efficient, and, crucially, passive alternative for detecting small unmanned aerial vehicles. However, the practical deployment of acoustic systems is discouraged by extreme environmental noise and sensor-induced domain shift caused by heterogeneous hardware. This paper addresses these challenges by introducing a robust framework optimized for real-world battlefield conditions. We propose the integration of Per-Channel Energy Normalization (PCEN) and attention-based pooling to enhance feature extraction under low signal-to-noise ratio scenarios. We further propose a domain-aware training strategy that leverages auxiliary classes and multi-microphone data to mitigate cross-domain performance degradation. Evaluated on a unique dataset of combat-zone recordings from the Ukrainian frontlines, our approach significantly outperforms existing baselines, increasing the F1 score from 55.4% to 78.6%. This paper was originally presented at the International Conference on Military Communication and Information Systems (ICMCIS), organized by the Information Systems Technology (IST) Scientific and Technical Committee, IST-224-RSY - the ICMCIS, held in Bath, United Kingdom, 12-13 May 2026.
Fractional partial differential equations describe nonlocal dynamics, but discovering them from noisy data is difficult because fractional differentiation amplifies high-frequency measurement noise and the derivative orders are unknown. We propose Weak-Pareto, which combines an adjoint-consistent weak formulation of fractional terms with Pareto-based subset selection over discrete term types and continuous fractional orders. For linear right-hand-side terms, the adjoint transfers fractional operators from measured fields to smooth test functions, replacing noise-sensitive pointwise differentiation with smoothing integration; for nonlinear terms, the noise-suppression effect is partial yet useful. Coefficients are fitted by ridge regression within a branch-aware differential-evolution search over the orders. The support size is then selected at the validation-error-complexity elbow. We show that the variance of fixed linear right-hand-side weak features vanishes under grid refinement, whereas noise amplification in pointwise fractional features increases with derivative order. Across fractional advection-diffusion, reaction-diffusion, and Burgers benchmarks, Weak-Pareto recovers parsimonious structures from clean and noisy measurements. In controlled advection-diffusion and Burgers comparisons, it retains the correct support at every tested multiplicative-noise level, whereas the unregularised strong-form counterpart largely fails once noise is introduced; this advantage persists under additive Gaussian noise. Ablations show that the weak library drives noise robustness and that continuous-order Pareto search avoids the support-selection failure of a dense fixed dictionary. On the advection-diffusion benchmark, Weak-Pareto yields more consistent operator recovery and substantially lower measured runtime than a contemporary neural baseline.
To address the degradation of bearing fault diagnosis accuracy under strong noise, this paper proposes a time-frequency dual-domain multi-scale convolutional neural network. The time-domain branch employs three parallel convolutional kernels to capture multi-scale impulse features, while the frequency-domain branch applies the Fast Fourier Transform to extract noise-robust spectral structure information. Features from both branches are fused for fault classification, yielding a compact model of 110,122 parameters. Experiments on the CWRU bearing dataset across seven signal-to-noise ratio levels demonstrate that the proposed method achieves 99.75% accuracy under clean conditions and maintains 92.50% at -4 dB SNR, representing a 7.25 percentage-point improvement over the single-domain baseline with monotonically increasing gains under stronger noise. Ablation experiments validate the independent performance contributions of the time-domain multi-scale branch and the frequency-domain branch. Comparative experiments against WDCNN, DRSN-CW, MCNN, and 1D-LeNet confirm the superiority of the proposed method under strong noise conditions.
Changshuo Liu, Yanzheng Jin, Shangfeng Cai +3cs.MA cs.AI cs.MM
With increasingly diverse and heterogeneous information sources, effectively leveraging multimodal data is becoming pivotal for high-quality financial trading. Although recent advancements in Large Language Model (LLM)-based agents have enabled the ingestion of multimodal inputs, existing methods fail to capture nuanced cross-modal dependencies and remain vulnerable to market noise, due to limited multimodal modeling, ineffective fusion mechanisms, and inadequate robustness. To address these challenges, we propose F$^2$Agent, a novel multimodal agentic paradigm driven by the Financial Fusion of Agentic Intelligence. F$^2$Agent first deploys a hierarchy of specialized agents to comprehensively extract modality-specific signals. It further introduces a modality-aware adaptive fusion mechanism coupled with noise-robust consistency regularization to dynamically capture fine-grained inter-modality dependencies and generate noise-resilient trading signals. Extensive experiments on six stocks and cryptocurrency assets demonstrate that F$^2$Agent consistently outperforms 16 competitive baselines across multiple trading metrics, with over 20% relative improvement in annualized return on average. Notably, F$^2$Agent delivers returns of 120.48% on GOOG and 148.41% on TSLA, demonstrating its efficacy and robustness in varying market dynamics.
We propose Sen-Cap, a Sensor-Flexible and Noise-Resilient 3D human motion Capture framework that integrates multi-modal data from LiDAR and camera. While multi-modal sensors provide richer information than single-modal sensors, existing approaches still suffer from two core challenges. First, multi-modal alignment/matching across arbitrarily deployed sensors is typically handled by explicit calibration, which propagates errors under changing viewpoints and in turn constrains deployment to fixed, highly overlapped layouts. Second, prior methods degrade under severe noise or partial sensor failures, which are common in real-world environments. To address these challenges, Sen-Cap introduces a Unified Across-Sensor Motion Estimator that reconstructs local pose and shape in a human-centric space without calibrations between sensors, supporting a flexible number of sensors, as well as a Noise-Resistant Trajectory Tracker that maintains robustness under severe point cloud noise through iterative refinement. These sensor-flexible and noise-resilient features make Sen-Cap more practical in real-world deployment. Notably, operating in real time, Sen-Cap achieves state-of-the-art performance on major metrics on Human-M3 and FreeMotion, as well as strong cross-domain performance on LiDARHuman26M and RELI11D. This combination of flexibility and robustness opens new opportunities for motion capture in real-world scenarios, e.g. sports analytics, field robotics, and large-scale immersive environments.
Adrian Urbański, Gabriel della Maggiora, Artur Yakimovichcs.CV
Generative models learn the statistical properties of their training data, so high-quality generation depends on clean and representative datasets. In scientific imaging, acquisition often yields noisy measurements, while collecting clean references can be costly, impractical or even unattainable. Training directly on these measurements results in a model that reproduces the corrupted data. This can be circumvented by learning the clean population distribution directly from the noisy data. Conditional flow matching (CFM) combines a simple regression objective with stable training, efficient sampling, and strong image-generation performance, making it a natural framework for this setting. We introduce Noise-Robust Conditional Flow Matching (NR-CFM), an unconditional generator that learns from one corrupted observation per image. NR-CFM provides a closed-form clean endpoint correction for additive white Gaussian noise and learns a data-driven correction for general Gaussian corruptions with more complex covariance structure. Across the evaluated corruption settings, NR-CFM outperforms NR-GAN in most cases and remains competitive with Ambient Diffusion in the high-noise regime. We further evaluate NR-CFM on scientific data at signal-to-noise ratios as low as $0.001$, where it generates plausible particle images from severely corrupted measurements.
Andreas Maier, Lucas Kachelriess, Siming Bayer +4physics.med-ph cs.AI cs.CV
Comparing CT reconstruction methods fairly is labor-intensive and largely manual, and many benchmarks use idealized data. We ask whether a large language model (LLM) agent can do the labor of reconstruction research on its own, and whether a ranking measured on ideal data predicts behavior under realistic noise. We built an agentic loop: the agent edits a solver, runs a short cluster job, reads one frozen metric, and revises. The metric is a calibrated headroom score against the FBP baseline, inside the field of view; every method shares the same differentiable fan-beam projector. We benchmarked 26 methods on Mayo low-dose CT (noise-limited) and a 128-view sparse-view breast task from the noiseless DL-Sparse-View Challenge, with validation-selected iterations scored on a held-out test set. Every trained breast model was then re-scored on noisy inputs (I_0 = 10^5 photons) without retraining, and separately retrained on matched noise. The agent independently implemented, tuned, and benchmarked all 26 methods, and recombined them into a compact solver of 969 parameters that ties the top Mayo tier at the 1% level using 0.4% of the champion's parameters. Benchmarking gives a tier of statistically indistinguishable top methods, not one winner. Mild input noise nearly inverts the breast ranking: the noiseless champion (a supervised image denoiser, hr 0.89) collapses to 0.00, while a learned primal-dual method rises to champion (0.72 to 0.93). An ideal-data leaderboard therefore does not predict robustness. The inversion is a transfer effect, not a permanent deficit: retraining on matched noise restores much of the clean ranking (Spearman rho 0.04 to 0.61). Noise is only the easiest confounder in an open-ended set (beam hardening, scatter, anatomy, disease), so no single-factor challenge certifies generality. Benchmarks should model a broad spectrum of realistic factors at once.
Most existing nonlinear adaptive filtering algorithms only account for output noise, neglecting the fact that input noise is also prevalent in practice. Although the recently proposed bias-compensated kernel least mean square (BCKLMS) algorithm addresses input noise in the nonlinear errors-in-variables (EIV) model, it still suffers from two major limitations. First, the use of a fixed-size dictionary restricts network growth but also prevents it from fully capturing the characteristics of the input signal. Second, as an least mean square (LMS) based algorithm, it exhibits poor robustness in the presence of non-Gaussian noise in the output signal. To overcome these issues, this paper proposes the random Fourier bias-compensated filter under general adaptive function (RFFBCGA) algorithm. Within the random Fourier feature based bias-compensated (RFFBC) framework, the proposed algorithm not only maintains a fixed network structure and effectively mitigates input noise interference through the BC term, but also achieves improved characterization of the input signal. Moreover, by leveraging the flexible form of the general adaptive (GA) function, the algorithm's robustness across various noise scenarios is further enhanced. Extensive simulations, including real-world time series prediction tasks, demonstrate the superiority of the proposed method.
Lance Kennedy, Hossein Amiri, Yueyang Liu +9cs.LG cs.CG
Detecting staypoints from raw trajectory data is fundamental to numerous spatial computing applications. This process transforms raw numeric sequences of geolocations into semantically meaningful locations, such as homes, workplaces, or restaurants. Despite its importance for semantic trajectory analysis, staypoint detection lacks standard benchmarks, and existing algorithms have never been systematically evaluated. This gap persists because no publicly available datasets provide both raw individual trajectories and ground-truth staypoint annotations. This benchmark paper addresses this limitation with two key contributions: (1) we introduce 16 large-scale simulated datasets capturing thousands of agents with annotated staypoints across varying trajectory noise levels, and (2) we evaluate nine staypoint detection algorithms-including both state-of-the-art and novel methods-to analyze their robustness to noise. Our evaluation reveals that existing state-of-the-art algorithms perform poorly under realistic noise conditions. Conversely, our proposed unsupervised methods yield substantial improvements, while supervised approaches drastically outperform existing baselines. While these results are very promising, these datasets and methods are only meant as starting points for future research in staypoint detection.
Xuming Chen, Deniz Najafi, Mehrdad Morsali +5cs.AR cs.AI
Silicon-photonic (SiPh) accelerators have emerged as a promising platform for Vision Transformer (ViT) inference by performing matrix multiplications on microring-resonator (MRR) banks with high throughput and energy efficiency. Extending these platforms to support on-chip fine-tuning remains challenging because backpropagation requires large activation storage, frequent weight write-back to MRRs, and tolerance to device-level noise. We present Opto-ViT-v2, the first framework for parameter-efficient fine-tuning (PEFT) on a near-sensor SiPh ViT accelerator. Our tensorized low-rank decomposition separates pretrained optical weights from a small set of trainable electronic factors (as few as 8K parameters for ViT-Base), greatly reducing activation storage and weight updates while enabling practical on-chip training. We further introduce a gradient-accumulated sparse classifier that freezes low-importance weights through one-shot top-k gradient masking, reducing classifier training cost by about 40 percent. We also develop the first system-level noise model for photonic on-chip training, capturing the effects of MRR crosstalk, thermal drift, and laser amplitude noise during both forward and backward propagation. Calibrated using measurements from more than 200 fabricated MRR devices, the model shows that low-rank factor updates are more robust than full fine-tuning and conventional layer-wise low-rank adaptation under identical noise conditions. Experiments on VTAB-1K (19 tasks) and FGVC few-shot benchmarks demonstrate that Opto-ViT-v2 recovers within 0.3 to 0.8 percent of clean software accuracy under measured photonic noise while achieving more than 100 KFPS/W, enabling practical on-chip domain adaptation for photonic edge vision systems.
Infrared small target detection (IRSTD) commonly relies on pixel-level mask supervision. Such annotations, however, are costly and inherently uncertain because infrared targets have blurred boundaries and weak textures. We formulate box-supervised IRSTD as a problem distinct from generic box-to-mask segmentation and point-supervised IRSTD. Its central challenge is to construct stable pixel-level soft supervision from highly contaminated boxes. To this end, we propose Hotspot-Anchored Label Optimization (HALO). HALO localizes a radiometric anchor inside each box under local background-statistics constraints, then synthesizes a Physically Anchored Gaussian (PAG) soft label around the anchor. This turns noisy box supervision into continuous, pixel-level soft labels. The entire process is performed offline before training, remains decoupled from the detector backbone, and requires no online label updates. Experiments on public datasets show that HALO is competitive with representative box-supervised methods under standard tight boxes. Under looser or shifted box annotations that better approximate real scenarios, HALO is substantially more robust while remaining consistent across backbones. We further introduce a contamination-aware operating-regime analysis to characterize the effective boundary of this class of methods and reveal how intrinsic signal-to-clutter ratio relates to performance.
Discovering governing partial differential equations (PDEs) from noisy observational data is a fundamental challenge in scientific machine learning. Traditional symbolic regression (SR) methods often struggle to identify accurate equations within vast combinatorial search spaces, largely due to their inability to incorporate essential domain-specific prior knowledge. Furthermore, reliance on pointwise evaluations and discrete finite differences inherently amplifies high-frequency noise, creating deceptive fitness landscapes that derail the optimization process. To resolve these bottlenecks, we propose LLM-PDESR, a framework that integrates the structural hypothesis generation of Large Language Models (LLMs) with a mathematically rigorous evaluation environment. By employing C^4-continuous quintic splines for robust differentiation and subdomain weighted residuals as natural low-pass filters, our approach effectively mitigates the fitness landscape distortion that plagues existing methods. A Pareto-driven feedback loop then enables the LLM to iteratively refine candidate equations, balancing predictive accuracy with structural parsimony. We evaluate LLM-PDESR on 23 canonical PDEs and five structurally novel equations (including a multivariate system) specifically designed to preclude dataset memorization and test true discovery capabilities. Demonstrating real-world applicability, the framework successfully extracts a consistent structural skeleton for an interpretable 1D dynamical surrogate (1D-CACE) directly from noisy ERA5 reanalysis data. Extensive experiments and out-of-distribution testing confirm that LLM-PDESR significantly outperforms state-of-the-art methodologies in structural recovery, noise resilience, and the avoidance of spurious complexity and equation bloat.
Max Kreider, John Harlim, Daning Huangcs.LG math.DS
Accurate prediction of complex dynamical systems from noisy measurements remains a significant challenge in scientific computing. Kernel ridge regression learning strategies are often effective when applied to clean data, but have limited success with noisy data. Recent work has observed that a weak formulation can act to filter noisy data, and different learning strategies have achieved increased noise robustness with a weak-form framework. In this manuscript, we give an overview of the filtering mechanism behind the weak formulation and provide a bias-variance error decomposition. Using these insights, we combine a weak formulation with a kernel learning strategy to propose Weak-form Kernel Ridge Regression (WKRR) for learning dynamical systems. The proposed framework is simple to implement, effective for both clean and noisy data, and outperforms several baseline methods. We demonstrate the performance of WKRR on chaotic benchmark systems in up to 64 dimensions, as well as 15,000-dimensional real-world fluid data.
Audio-Visual Speech Recognition takes two input modalities, acoustic and visual streams, where visual information from lip movements aids recognition when audio is noisy. Recently, LLM-based AVSR models have emerged as a promising paradigm by connecting pre-trained audio-visual encoders to an LLM, achieving strong results in clean conditions. However, these models are predominantly optimized for clean acoustic conditions, with limited attention to making the LLM backbone robust to noise. No explicit mechanism is employed to produce stable representations under corrupted audio, leading to performance degradation in noisy environments. To address this, we propose VIB-AVSR, which integrates Variational Information Bottleneck layers at targeted positions within the LLM backbone to regularize representations. VIB-AVSR reduces degradation under noisy conditions across multiple SNR levels and noise types, without requiring architectural modifications or additional training data.
Samuel Ahnert, Esther Lagemann, H. Jane Bae +4cs.CE cs.LG physics.flu-dyn
Extracting interpretable, localized physical mechanisms from complex spatiotemporal data is a foundational challenge across physics, biology, and engineering, but has remained out of reach on real measurements. The central obstacle is obtaining high-quality gradients of data via numerical differentiation, which amplifies noise, diverges for high-order equations, and falters on irregular geometries, limiting the scope of existing approaches to clean simulations of low-order systems. Here, we present weak dominant balance, a derivative-free framework that projects governing equations into a weak (integral) formulation, offloading differentiation onto smooth analytical test functions and leaving the data untouched. The method sustains accurate regime identification under severe noise where existing approaches categorically fail, delivers the first data-driven decomposition of a third-order partial differential equation applied to turbulent duct flow, and produces matching decompositions across direct numerical simulation and particle-image velocimetry measurements of a wavy channel flow, uncovering a previously uncharacterized dynamical regime. Weak dominant balance brings mechanism-level analysis out of simulation and onto measured data, and opens complex physical systems to direct, equation-grounded interpretation.
Shahab Salehi, Luca Lusvarghi, Miguel Sepulcre +1cs.AI cs.LG cs.RO
Trajectory prediction allows autonomous vehicles to anticipate the future behavior of surrounding objects (or agents) and, accordingly, maximize the safety and efficiency of their driving. State-of-the-art Transformed-based interaction-aware trajectory prediction models, which rely on attention mechanisms to capture multi-agent interactions and maximize prediction accuracy, are commonly trained and evaluated on long-range high-quality datasets. These datasets are typically obtained by aggregating data from multiple vehicles or drones and removing any object detection or tracking noise offline. Yet, information about a surrounding object's state (its position, speed, heading) is far from being noiseless in real-world deployments. Object state estimation is affected by perception uncertainties and localization errors that can be particularly large for objects received via Vehicle-to-Everything (V2X) communications. In this paper, we analyze the impact of noisy object state information on the trajectory prediction accuracy of a state-of-the-art Transformer-based interaction-aware trajectory prediction model. Our study demonstrates that trajectory prediction accuracy can rapidly deteriorate as the noise intensity increases. Numerical results show that the prediction accuracy can reduce by a 1.3x factor under small noise levels and by as much as a 3.9x factor under the highest (yet realistic) noise conditions. These findings reveal the strong sensitivity of trajectory prediction models to noisy data, underscoring the need for more realistic training and evaluation datasets as well as noise mitigation strategies.
M. E. P. Silva, L. S. Araujo, F. T. Colombo +2physics.comp-ph cs.LG eess.SP physics.class-ph
Thermal monitoring in practical applications is often constrained by sparse sensing, measurement noise, and limited spatial resolution, which hinder the identification of heat transfer dynamics. In such settings, calibrating high-fidelity physical models is computationally demanding, motivating data-driven approaches. Dynamic Mode Decomposition (DMD) provides a framework for extracting spatiotemporal structures from measurement data, but its standard formulation is sensitive to noise and degraded observations. This chapter examines the use of DMD under these constraints, focusing on preprocessing and truncation strategies that affect stability and interpretability. Two cases are considered: forced convection with thermocouple data and transient heat conduction from degraded thermal images. The number of retained modes is treated as a modeling parameter that governs the trade-off between reconstruction fidelity and noise sensitivity. The results indicate that DMD recovers dominant thermal behavior from both sparse and degraded datasets when the truncation level is appropriately selected. Low-rank models provide stable but simplified descriptions, while higher-rank models improve spatial detail at the cost of increased noise sensitivity.
Modular neural network pipelines suffer from error compounding: noise at any module boundary propagates and potentially amplifies through subsequent modules. We introduce energy conservation as a hard physical constraint on inter-module information flow. Activation energy (the squared L2 norm of feature vectors) is enforced to be exactly preserved at every module boundary. Unlike soft energy penalties, conservation is an inviolable law: the network may redistribute energy across neurons but cannot create or destroy it. Four experiments on CIFAR-10 demonstrate: (1) conservation retains 77.4% of clean accuracy at noise sigma=0.2, versus 35.1% for baselines and 30.9% for energy-penalized models (p<0.001, 5 seeds); (2) pipelines become depth-invariant, retaining 93.3% at depths 2 through 5 with noise at every boundary; (3) the advantage generalizes to systematic bias (+45.1%), Gaussian (+40.4%), and adversarial noise (+4.8%), with a principled non-effect on dropout (-0.3%); (4) on ResNet-18, the conservation advantage scales inversely with intrinsic normalization: +0.3 pp with BatchNorm, +26.2 pp without at sigma=0.2, reaching +58.0 pp at sigma=0.5. Experiment 5 validates the operator on a real modular robotic pipeline (MuJoCo physics, Franka Panda). Across three independent runs on separate machines (90 trials per cell), conservation provides +18.9 pp average advantage on monocular-depth-style noise. A formal bound proves conserved noise energy is strictly less than input noise energy.
Self-supervised methods that learn representations and predict dynamics fully in the latent space, such as JEPA, have been shown to confuse slowly varying noise with the dynamical signals they aim to capture. Specifically, when noise features remain approximately constant within each trajectory, contrastive predictive objectives preferentially encode these features instead of the true latent variables governing the system. The learned representation then becomes dominated by trajectory-specific noise, so downstream performance degrades with noise strength and does not improve even as the number and duration of training trajectories increase. We argue that this failure is a property of the objective itself, shared by a long line of contrastive predictive objectives that sample negatives across trajectories. To illustrate this generality, we study the failure mode and its remedy in two settings: a standard SimCLR-style JEPA on a synthetic moving-dot dataset, and DySIB, a recently introduced method designed for extracting physically interpretable representations of dynamics, on movies of a rigid-body pendulum. When negatives are instead sampled within a single trajectory, the slow noise can no longer distinguish frames within that trajectory, removing the predictive shortcut. Training one encoder simultaneously on many such trajectories then forces it to encode the variables relevant for the dynamics, with longer trajectories yielding better representations even for strong slow noise. Our results point toward principles for designing contrastive predictive objectives in dynamical representation learning, especially for physical systems with noisy experimental observations.
Tao Zhong, Jiajun Deng, Nikita Kuzmin +6cs.SD cs.AI eess.AS
Full-duplex spoken dialogue models allow voice agents to listen and speak concurrently, enabling natural interaction with real-time overlap. However, end-to-end dual-channel models that jointly encode user and agent streams may degrade in realistic acoustic environments: interfering speakers leaking into the user microphone can be encoded as part of the user query, corrupting the LLM's conditioning and causing unstable turn-taking and reduced response quality. We propose Interference-Resilient Adaptive Fusion (IRAF), a lightweight, streaming-compatible module that modulates the contribution of user audio to the LLM frame by frame. IRAF predicts a scalar reliability gate from target-speaker and user audio embeddings and rescales user representations before fusion with agent embeddings. Experiments on MS-MARCO and InstructS2S-200K show consistent gains in response quality and full-duplex interaction under interfering-speaker conditions.
Contrastive audio-language models such as CLAP enable zero-shot audio classification: a sound is labelled by matching its embedding to text prompt embeddings, with no labelled audio. This matching breaks down under acoustic noise, where accuracy and mAP fall by 12-30 percentage points at 0 dB SNR on standard benchmarks. We propose Drift Augmented Scoring (DAS), a small per-class bonus added to the cosine score. The bonus rewards a class when the noisy audio embedding drifts in the direction that the class's noise-conditioned text prompts predict. It is derived from text alone, computed once and cached, and adds a single inner product per class at inference, with no gradients and no test-time batch. On a LAION CLAP backbone, we compare DAS against the four variants of Acevedo et al.'s concurrent method on UrbanSound8K and the full FSD50K eval set, mixing each clip with urban acoustic scene noise across a range of SNRs. DAS improves the metric on every test condition: by +2.60 to +5.75 accuracy points on UrbanSound8K and +1.50 to +1.74 mAP points on FSD50K.