Gaussian Noise

Conventional satellite remote sensing transmission follows a reconstruct-then-infer paradigm that optimizes pixel-level fidelity, creating an objective mismatch with downstream tasks such as classification and detection, especially at low SNR. This paper investigates a task-oriented framework that bypasses image reconstruction and directly transmits semantic features extracted by a multitask-pretrained backbone. A lightweight channel adaptation module (CAM) compresses feature dimensionality for bandwidth reduction, and a feature restorer recovers task-relevant structure after channel corruption. With the backbone frozen, the CAM and task-specific downstream heads are jointly optimized with task and feature-level supervision under random-SNR training. Under the adopted AWGN setting, experiments on scene classification and object detection show consistent gains over reconstruction-oriented JSCC baselines across different SNR conditions, with the largest improvements in the low-SNR regime.

Diffusion samplers reverse a learned noising process using either stochastic (DDPM) or deterministic (DDIM) updates, which represent endpoints of a single family controlled by a scalar noise-injection variance that is applied identically at every spatial location. This uniform approach neglects the geometry of natural images: high-curvature regions such as edges and textures, where the denoiser is uncertain, benefit from stochastic correction, whereas smooth regions, where the score is precise, are degraded by injected noise. This work investigates whether each pixel requires stochastic correction at a given timestep and introduces Spatially Adaptive Noise Injection (SANI), a novel sampling framework that dynamically adjusts noise application on a per-pixel basis. SANI integrates a probabilistic gating mechanism with a derived spatially adaptive variance, ensuring that noise is injected precisely where needed to refine complex features while preserving well-formed structures. Experimental results and decoupling ablations demonstrate that SANI consistently improves Fréchet Inception Distance (FID) over the vanilla DDPM and DDIM endpoint samplers across diverse sampling timesteps, while remaining competitive with variance-learning baselines, highlighting the importance of spatial adaptivity in diffusion sampling.

Noise2Noise (N2N) trains denoisers on pairs of independently corrupted observations, eliminating clean references. We stress-test two natural conjectures about why the L1 loss outperforms L2 here. First, the hypothesis that the L1 loss confers robustness via parameter sparsity confuses the loss with Lasso regularization: an explicit Lasso penalty produces the predicted sparsity yet fails to reproduce L1's cross-noise behavior, while L1- and L2-trained weight distributions are indistinguishable. Second, the population optima of the two losses coincide exactly for symmetric signal posteriors and nearly so for concentrated ones. Measured differences are therefore dominated by optimization dynamics (bounded-influence gradients), which we probe with gradient statistics and contaminated-target training. On Kodak24 with five synthetic noise families, the L1 loss holds a statistically significant edge over L2, below 1 dB PSNR, holding across three seeds on 13 of the 14 noise columns. On real camera noise the loss is not the decisive variable in distribution: on official SIDD validation blocks, synthetic-Gaussian-trained N2N models gain only 0.8 to 3.7 dB over the noisy input regardless of loss, while retraining on SIDD's own noisy pairs, never reading ground truth, gains 9.4 to 11.0 dB, far ahead of BM3D. All metrics are on raw network outputs, and the study makes no leaderboard claim. The training pair distribution, not the loss, carries the inductive bias. That design rule applies wherever clean references are unobtainable, from microscopy to industrial inspection sensors.

The energy efficiency of analog computing makes it one of the most promising candidates for deploying resource-intensive machine learning workloads on constrained platforms such as mobile and embedded devices. However, analog accelerators are inherently susceptible to noise and non-idealities arising from physical component variations, whose behavior is further sensitive to environmental factors. These effects can significantly degrade inference accuracy. In this work, we conduct a comprehensive experimental study on a representative example of analog hardware to investigate the impact of temperature. We first characterize the behavior of stochastic and systematic non-idealities across a range of operating temperatures. Following this, we compare a set of simulation-based and hardware-based mitigation strategies aimed at improving robustness against temperature-induced performance degradation. Our results suggest that temperature-induced degradation is driven primarily by systematic non-idealities rather than stochastic noise alone. Noise-aware training improves robustness, while hardware-in-the-loop training and temperature-aware calibration provide the strongest accuracy retention across varying thermal conditions.

Learning robust representations for time-series signals under noise and distribution shifts remains challenging, especially in clinical applications such as electroencephalogram (EEG) and electrocardiogram (ECG) analysis. We propose Diffusion-Conditioned Representation Alignment (DCRA), a training framework that repurposes the forward diffusion process as a structured corruption scheduler for representation learning. Different from conventional augmentation and consistency-based methods that rely on independently sampled perturbations, DCRA introduces a structured corruption trajectory via the diffusion forward process, which enables continuous and controlled representation evolution across noise levels. We introduce a feature-level consistency objective that aligns representations across noise levels while preserving class-discriminative structure. This mechanism promotes structure-preserving consistency, which enables smooth and semantically coherent feature trajectories in latent space. The proposed framework is encoder-agnostic and can be integrated with state space models and Transformer architectures. The seizure detection experiments on the CHB-MIT EEG dataset show that DCRA consistently improves performance under multiple noise conditions and achieves higher sensitivity at low false-positive rates. Analysis reveals that DCRA produces more balanced and structured representations compared to baseline and diffusion-only models. These findings highlight the benefit of combining structured corruption with representation alignment for robust time-series learning.

Stochastic gradient descent (SGD) with gradient clipping and additive noise has become a standard technique for training machine learning models, particularly in applications requiring robustness or privacy guarantees. However, clipping introduces a bias in stochastic gradients, while additive noise introduces additional variance, making the long-run behaviour of individual optimization trajectories difficult to characterize. In this work, we prove that SGD with clipping and additive Gaussian noise (SGD-CN) converges almost surely (a.s.) under smoothness and uniformly bounded stochastic-gradient noise assumptions, provided the step sizes satisfy some standard decaying conditions. Our analysis extends to momentum variants such as the stochastic heavy ball and Nesterov's accelerated gradient, where we show that careful energy constructions yield similar guarantees. These results provide stronger theoretical foundations for understanding the pathwise behaviour of clipped stochastic gradient methods and suggest that, despite the bias and noise introduced by clipping and perturbation, the algorithm remains stable in both convex and nonconvex regimes.

Large language models are increasingly used as judges to measure social bias in text, yet the passages they judge are often noisy, containing typos, informal spelling, and broken punctuation. The consequences of such surface noise for social bias measurement remain unclear. To investigate this question, we apply five realistic noise conditions at multiple intensity levels to 3,822 stereotype-related responses and compare the resulting bias judgments with those on the original text. We find that such surface noise does not degrade bias measurement symmetrically: it is far more likely to turn neutral judgments into biased ones than biased judgments into neutral ones, by up to a 120x margin. We further observe two non-obvious effects across four LLM judges: in the most fragile judge the distortion is at its purest at mild, realistic noise levels, where erasure is scarcest, and as judges grow robust it attenuates toward parity rather than reversing. Bias measured on noisy text is therefore systematically overestimated, most in the categories that matter most for fairness.

Robust speech-to-text translation systems should perform reliably across diverse acoustic conditions, yet practical pipelines lack controllable tools for systematic environment exploration. Large speech models remain sensitive to unseen acoustic conditions, as training data rarely cover the full range of real environments.We present NOPEHYPE, a structured training workflow that combines a controllable environment simulator, coverage-optimal environment reduction on Power Spectral Density (PSD) templates, and a small, interpretable hyperparameter search over simulator knobs. We show that simulator-generated noise achieves performance comparable to balanced realnoise training across Whisper and SeamlessM4T models, provide principled environment prototype sets, and identify practical default simulator configurations from a structured 27-run hyperparameter sweep.

In this paper, we consider the scalar-on-function linear regression model under a realistic sampling scheme in which the functional covariates are observed on a regular grid and contaminated by additive noise. We propose a two-step estimation procedure: first, the underlying curves are reconstructed from the discrete noisy observations using a Fourier-based projection method; second, the slope function is estimated by a penalized least-squares criterion over finite-dimensional trigonometric spaces, with data-driven selection of the model dimension. We establish oracle-type inequalities for the prediction error, both with respect to the reconstructed curves and to the true latent curves. Under regularity assumptions on the slope function and polynomial decay of the eigenvalues of the covariate, we derive convergence rates for the prediction error and show that our estimator attains the minimax rate when the number of grid points is sufficiently large. Finally, the proposed method is illustrated on simulated data and on a real meteorological dataset.

We develop a second-order theory of quantization noise in matrix multiplication in which the quantization format is characterized by the variance it assigns to each element. The constant variance profile of integer quantization recovers existing integer-noise theory, while the multiplicative profile of floating-point rounding reduces the data dependence to a scalar, the participation factor $κ$, yielding a closed-form signal-to-noise-ratio law. The resulting functional also admits a closed-form upper bound $κ^{*}$ that no function-preserving linear transform can exceed and that is attained by a recent state-of-the-art method. Building on this analysis, we introduce KBBQ (\textbf{K}appa-\textbf{B}raked \textbf{B}lockwise \textbf{Q}uantization), which parameterizes the extent to which a transform approaches this ceiling. At W4A4, across four base models and two FP4 formats, KBBQ outperforms the prior state of the art without additional deployment-time computation.

Bone-selective digitally reconstructed radiograph (DRR) synthesis depends on high-resolution encoder detail, yet static skips cannot condition reuse on the evolving decoder representation. We ask whether decoder state adds useful information beyond encoder-only self-recalibration for high-resolution skip reuse. RFS-UNet uses pooled encoder and aligned decoder statistics for bounded residual channel recalibration at the 512^2 and 256^2 skips, leaving the backbone unchanged. In the matched seed-2026 comparison isolating decoder conditioning, RFS raises validation PSNR by 0.254 dB over Self-RFS. Across three seeds, locked-test PSNR rises from 33.225+/-0.048 to 33.537+/-0.128 dB; RFS lowers MAE in 179/200 held-out CT cases and reduces mean MAE by 3.91%. It adds 0.117% parameters and 1.169% counted Conv2d operations. These results support decoder state as a useful conditioning signal for high-resolution feature reuse in controlled paired projection synthesis.

Images are important tools in various sciences. Despite the development of photo-taking tools, creating clear and image without noise remains challenging in practice. In particular, Poisson noise has an effect on medical and astronomical images, and reduces their quality. Additionally, blur is another factor that has an effect on image quality. The problem of image restoration becomes very complicated when we have no information about the Point Spread Function (PSF). These types of problems are known as blind case. However, in some images, such as some astronomical images, the type of PSF can be specified, and these types of problems are known as nonblind problems. Total Variation (TV) is a widely used method for solving such inverse problems, where the selection of the penalty function is the most critical factor that affects the method's performance. In this paper, to improve edge preservation, we employ a reweighted $\ell_1$-regularization of the fractional order derivative. Furthermore, we propose a nonblind and blind image deblurring approach under Poisson noise using the Minimax Concave Penalty (MCP), which is a continuous, sparsity promoting, and nearly unbiased regularizer. This formulation leads to a nonconvex optimization model. To solve the proposed model, we introduce an efficient numerical algorithm based on the Alternating Direction Method of Multipliers (ADMM) and provide an analysis of its convergence. Finally, the effectiveness of the proposed algorithm are demonstrated through extensive experiments on various images.

We study constrained online convex optimization with adversarial constraints and conditionally unbiased, finite-variance observations of constraint values and gradients. Under common feasibility, our \LEDGER\ algorithm attains $O(\sqrt T)$ expected regret and $O(\sqrt{T\log(eT)})$ expected budget violation, the largest cumulative overspend over any window. It uses a reflected exponential potential, clipped signed observations, and predictable adaptive regularization, with one feedback triple and one projection per round. Neither a Slater condition, independence between feedback channels, nor an absolute constraint-value bound is needed. A Gaussian testing lower bound proves that the budget rate has optimal horizon dependence under square-root regret at fixed positive noise, including the logarithm. The same obstruction holds for terminal violation, so the logarithm is not a cost of maximizing over windows; an $O(\sqrt T)$ budget bound instead forces linear regret. In contrast, fixed positive Gaussian value noise yields a joint regret--hard-violation lower bound of $Ω(\min\{σ,1\}T/\log^2 T)$, even with exact gradients in one dimension. The hard-violation construction matches arbitrarily many moments while preserving a feasible-endpoint gap and constant endpoint probabilities. Together, the bounds separate uncertainty about hard feasibility from learnable signed budgets. Deterministic restarts remove the horizon input without changing either upper rate.

Scene text recognition is reported as 89--97% accurate on the six standard benchmarks, and the problem is widely treated as saturated. We present an alternative reading. When the same test images are stratified jointly by ground-truth word rarity and character n-gram novelty against a reference corpus, accuracy at the rare-word x rare-trigram corner of the resulting 5x5 grid drops 10--18 pt below the q3/q3 centre across nine English specialised recognisers, and the same direction (corner below centre) holds on all 13 of 13 (language, model) pairs we test across four writing systems (Latin, Han, Han+kana, Arabic). The drop is not a capacity bottleneck. A 6x vision-backbone scale-up (CLIP4STR-Base 158M -> CLIP4STR-Huge 1.0B, OpenCLIP ViT-H/14 LAION-2B) leads every benchmark in aggregate accuracy yet leaves the stress corner unchanged (86.9 -> 86.5, within paired-bootstrap noise). Four converging probes--layer-wise probing, confidence-when-wrong, attention re-balancing, and a cross-script commit-vs-abstain error split--localise the failure to the autoregressive decoder's lexical prior. We then ask how much of the gap existing techniques recover. Of 16 non-architectural mitigations, the largest mean q5/q5 gain is +1.3 pt and none clears the paired-bootstrap noise floor; the only intervention that does is the architectural shift from autoregressive to CTC decoding (SVTRv2, +2.5 pt, p=0.02, n=474). A confidence-routed AR-CTC ensemble adds a directionally consistent +0.6 pt that stays within noise, and its dominant learned coefficient is each model's own minimum-softmax confidence--independently echoing the mechanism above. No configuration we test improves both the compositional corner and aggregate accuracy. The rare-input long tail thus points to architectural change rather than added capacity.

Direct Preference Optimization (DPO) simplifies alignment through pairwise comparisons but assumes all observed preferences are reliable. Real data often violates this assumption, leading to reversed, weak, or ambiguous labels that cause harmful policy updates. To address this, we propose Posterior Label Correction DPO (PLC-DPO) to robustly optimize preferences by routing each pair's training signal as a clean, flip, or tie case. The key idea is to use the calibrated policy-reference margin as online evidence to take appropriate correction actions. This reframes noisy preference learning as actively correcting supervision direction and strength rather than merely filtering suspicious examples. Across 57 dataset-model-benchmark cells, PLC-DPO obtains the best mean win rate against DPO (60.5 vs. 55.5 for the next-best method). Injected-noise and tie stress tests, human disagreement analysis, and self-confirmation diagnostics further show that the routing remains stable and distinguishes flipped from weakly directional pairs.

We propose a fidelity-constrained framework that anchors the output of a black-box denoiser to its input without retraining and with little additional computation. The method linearly blends the denoised image with the input and selects the maximum blending factor that satisfies a prescribed local fidelity constraint using Peak Signal-to-Noise Ratio (PSNR) or Structural Similarity Index (SSIM). For PSNR control, a closed-form solution is obtained under a local constant-blending assumption. For SSIM control, we derive a tractable formulation based on inverse SSIM under the same assumption and solve it efficiently using iterative root finding. Experiments on DIV2K images with synthetic Gaussian noise and outputs from Real-ESRGAN and a non-local means denoiser show that the proposed anchoring strategy provides effective fidelity control while balancing denoising performance and statistical naturalness, as measured by the excess kurtosis of residual noise. In particular, SSIM-based anchoring yields more consistent behavior across noise levels than PSNR-based anchoring.

In real-world scenarios, the training data usually contains redundant features, label noise and feature noise, which provide severe challenges for the efficiency of machine learning methods. Since standard support vector machine (SVM) adopts $l_2$-norm penalty and hinge loss function, it lacks the ability of selecting significant features and is sensitive to noise. To address these issues, this paper proposes a novel asymmetric, robust, bounded, sparse and smooth (aR) loss function for $l_1$-norm penalized geometric twin SVM (aRSGTSVM) to handle classification and regression tasks. The $l_1$-norm penalty can achieve the feature selection. The proposed aR loss function can not only effectively mitigate the impact of label noise, but also significantly enhance the stability to resampling noise, i.e., the zero-mean feature noise around the boundary hyperplanes. Furthermore, a statistical analysis of the robustness of aRSGTSVM was also conducted using the influence function. Since aRSGTSVM involves nonconvex and nonsmooth optimization, we develop a fast and stable proximal gradient descent based solving algorithm. Compared with related state-of-the-art methods, experimental results demonstrate the superiority of the proposed aRSGTSVM on both synthetic and UCI datasets. Furthermore, we apply aRSGTSVM to index tracking tasks, where results for tracking the different indices in the China stock market show that it can achieve satisfactory performance.

Accurate physical-layer modeling is increasingly essential for reliable ultra-wideband operation and capacity optimization, especially under the intensified inter-channel stimulated Raman scattering (ISRS) effect. This paper proposes the link-adaptive digital twin (LA-DT) for hybrid-amplified ultra-wideband links to overcome the generalization and speed limitations of existing methods, achieving accurate modeling and robust generalized signal-to-noise ratio (GSNR) estimation across diverse links. First, to address EDFA heterogeneity, the GSNR modeling task is decomposed into three key power predictions: ASE, NLI, and signal powers before EDFA entry. Second, to enhance cross-scenario generalization, three dedicated DT models are developed using a novel neural architecture with linear modulation layers (LMLs). Third, for rapid adaptation to unseen scenarios with limited data, three domain discriminators guide few-shot fine-tuning of the LMLs. Fourth, the LA-DT explicitly accounts for Raman amplifier (RA) insertion loss, improving practical deployment reliability. Results across 35 scenarios show that LA-DT reduces RMSE for NLI, ASE, and signal power predictions to 0.151, 0.111, and 0.113 dBm with improvements of 56.0%, 58.4%, and 52.7% over the baseline,and achieves an average GSNR estimation RMSE of 0.114 dBm (55.8% improvement). For 12 unseen scenarios, the LA-DT maintains high accuracy through few-shot fine-tuning with only 20 samples per scenario, achieving an average GSNR RMSE of 0.159 dB and demonstrating strong adaptability and robustness.

Many pipelines can pay a per-example cost to acquire an auxiliary, model-derived observation -- an LLM's structured reasoning, a slow oracle, an expensive measurement -- and then must decide when the acquired signal is worth using. Our thesis is a distinction that is easy to miss: detecting that such a signal helps on average is not the same as learning to act on it per instance, and a reward-SNR floor governs when the second is even possible. Even when the signal is faithful and an in-sample oracle picking the top-b examples by realized reward shows a sizable apparent gain, no deployable policy can learn when to acquire it: across per-impression, cluster, regime, and uplift-tree granularities, learned routing never beats random, and a matched-moment noise placebo reproduces >=100% of the oracle's apparent gain -- the apparent "learnable structure" is order statistics of noise. We explain this with one distinction, detecting a mean effect vs. learning a per-instance acquisition policy, and a reward-SNR detectability floor: routing is estimable offline only if the reward SNR rho clears rho*(N) ~= 2.8/sqrt(N), with a positive control confirming a true low-SNR limit rather than a broken pipeline. As a concrete instantiation we introduce Structured Hypothesis Embeddings (SHE): a frozen LLM turns a user history into ranked, confidence-scored, evidence-grounded intent hypotheses, fused into a recommender. On three public datasets (MIND, REES46, Amazon-Beauty), SHE is faithful and calibratable, yet its value is backbone- and regime-conditional (significant over an ordered GRU, +0.0114, 95% CI [+0.0030, +0.0209], but a global redundancy gap indistinguishable from zero), and learned acquisition collapses at every granularity because all three datasets sit below the floor. The realizable unit is a design-time regime gate, not a per-instance policy. We release code and a one-command reproduction.

Bioacoustic recordings are often degraded by ambient noise, which complicates the analysis of weak or noise-overlapped vocalizations. Convolutional neural networks, particularly U-Net architectures, have shown a strong denoising performance in speech and music processing. However, their direct application to bioacoustic signals is limited by the scarcity of clean training data. To address this issue, we propose a training set synthesis approach and develop a supervised denoising model that predicts a complex ratio mask in the time-frequency domain. The model leverages ridges, or frequency contours, that represent the fundamental frequency together with one or more harmonic partial components of vocalizations. These ridges are used both for the synthesis of training sets and to design a loss function that assigns higher weights to the ridge regions (ridge-guided loss function). This weighting step helps the network better preserve vocalization details during denoising. As a case study, we evaluate our approach using ultrasonic vocalizations (USVs) recordings of house mice, which are widely studied in behavioral biology and neuroscience. In actual field recordings, the proposed method enhances fundamental and harmonic partial ridge tracking compared to our previous signal-processing approach. In addition, a classifier trained on denoised data improves USV classification on out-of-sample, noisy recordings from wild and domesticated mice compared to classifiers trained on noisy recordings. Our proposed method also substantially improves the scale-invariant signal-to-distortion ratio on synthetic testing data across a wide range of input signal-to-noise ratios. Although we focus on USVs, the proposed approach should be broadly applicable to other bioacoustic signals with trackable ridges, and thus enables ridgebased training set synthesis and denoising.

Model learning by an eavesdropper is treated as an estimation problem in a federated environment. The Fisher Information Matrix for the eavesdropper's estimation problem is driven to singularity through a signaling design; this ensures that the eavesdropper cannot learn the model. Herein, the innovation of prior designs is that model shifts are designed to maximize the difference in the model learned by Eve and the central server while satisfying a transmission power constraint for the agents. Two shift schemes are provided. MaxModShift outperforms a prior ModShift design while requiring lesser transmission power. Compared to a noise injection scheme, MaxModShift performs better while requiring a lower bandwidth secret channel and a reduced average power consumption.

Objective. MRI provides excellent soft-tissue contrast, but long acquisition times can cause patient discomfort and lead to motion artifacts, forcing a trade-off between spatial resolution and scan time. Diffusion-based super-resolution (SR) reconstructs high-resolution (HR) images from low-resolution (LR) inputs, but typically needs many sampling steps and initializes from a Gaussian prior ill-suited to image restoration. We developed an efficient diffusion framework that reconstructs HR MRI directly from LR data. Approach. We propose super-resolution diffusion bridge model (SR-DBM), a super-resolution diffusion bridge model that casts SR as a stochastic transport between the LR and HR image distributions. Through a Doob's h-transform of a mean-reverting stochastic differential equation, SR-DBM pins the process to the paired HR and LR images at its endpoints, initializing reconstruction from the measured anatomy rather than from Gaussian noise. The HR image is recovered by a deterministic reverse trajectory in which a network predicts the clean image at each of only ten sampling steps. We evaluated SR-DBM on ultra-high-field 7T brain T1 MP2RAGE maps and pelvic T2-weighted prostate images against nine comparison methods using PSNR, SSIM, GMSD, and LPIPS. Main results. SR-DBM attained the highest PSNR and SSIM and the lowest GMSD on both datasets (brain: 27.66+-1.52 dB, 0.96+-0.02, 7.96+-1.86$; prostate: 27.87+-2.29 dB, 0.80+-0.05, 8.38+- 1.44), with statistically significant gains over every comparison method (two-sided Wilcoxon signed-rank test with Holm correction, p<0.05). The strongest baseline, SR-EMamba, ranked second. Qualitatively, SR-DBM produced the smallest residual errors and best preserved fine structures and lesions.

Probably Approximately Correct (PAC) learning [Val84] is a fundamental learning model that has been extensively investigated. In this model, $\mathcal{H} \subseteq \{0,1\}^{\mathcal{X}}$ is a concept class, and $h^*\in\mathcal{H}$ is the target concept to be learned. Having access to i.i.d. labeled examples from a distribution $\mathcal{D}$ over $\mathcal{X}\times\{0,1\}$, which admits $h^*$ as the best concept in $\mathcal{H}$, the goal is to design a learning algorithm that outputs a hypothesis having low error competitive to $h^{*}$ with high probability. This model was initially studied under the realizable setting, which assumes that $h^*$ has no error. A natural relaxation is to allow label noise, that is, the true label can be flipped with probability $η\in(0,1/2)$. In reality, certain labels might be extremely noisy, especially for those points near the decision boundary. Hence, it is natural to allow very noisy points, though only rarely. This is quantified by a noise model introduced by [MT99] and [Tsy04], now known as Tsybakov noise. For learning general concept classes, [MN06] gave the general upper and lower bounds for error guarantees under Tsybakov noise. However, their upper and lower bounds differ by a logarithmic factor. Resolving this gap has remained a well-known open question for the past twenty years. In this work, we resolve this open question by improving the upper bound to match the best known lower bound, thus establishing the optimal error guarantee for learning under Tsybakov noise. Our learning algorithm operates by adaptively partitioning the instance space into regions, roughly corresponding to different noise levels, and returning a hypothesis in the concept class satisfying a specific error constraint for each region. Our technique shares a conceptual foundation with several recent advances in non-realizable learning, such as [HLZ24] and [Han25].

Accurate user equipment (UE) localization is critical for beam management in reconfigurable intelligent surface (RIS)-assisted millimeter-wave (mmWave) based sixth-generation (6G) networks, especially if the direct base-station-UE links are unavailable. This paper proposes a beam-domain fingerprint framework that maps the received signal-to-noise ratio (SNR) across a small set of predefined RIS reflection states to the UE azimuth angle and range, without requiring channel state information (CSI). Crucially, we extend the framework to a realistic interference-impaired scenario in which a nearby cross-link interferer (CLI) corrupts the clean SNR fingerprint, yielding a signal-to-interference-plus-noise ratio (SINR) fingerprint; an interference-to-noise ratio (INR)-constrained calibration strategy keeps the interference level physically interpretable. Four machine-learning (ML) regressors are evaluated under both conditions. Simulation results at 28 GHz with a 20x20 RIS show that k-nearest neighbors (KNN) achieves the lowest angle MAE of 0.37 degrees and range MAE of 4 cm under clean conditions, rising to 1.4 degrees and 7.6 cm under interference. A key finding is that interference degrades angle estimation substantially more than range estimation across all models, a consequence of the asymmetric encoding of location information in the beam-domain fingerprint.

Autoregressive continuation provides a natural path toward minute-scale audio-visual generation by repeatedly extending a short-window generator conditioned on previously generated video and audio. However, models are trained on clean ground-truth histories, while inference relies on their own generated histories, where accumulated errors cause identity drift, over-smoothing, and audio-visual desynchronization. Recent methods reduce this mismatch by reusing prediction residuals as synthetic corruption, but we observe that the effectiveness of residual correction critically depends on the flow-matching noise level at which residuals are produced. We propose Vorch-Director, a noise-level-aware residual correction strategy that associates each residual with its originating noise level and injects residuals from matched noise regimes during training. By aligning injected errors with the denoising process, Vorch-Director produces more realistic autoregressive histories while retaining efficient teacher-forcing training. Built on the audio-visual LTX-2 diffusion transformer, Vorch-Director further introduces task embeddings to distinguish historical video, reference images, and target video, enabling unified conditioning for long-horizon generation. Together with a clean conditioning sink and mixed-task training, Vorch-Director supports multi-shot, multi-subject, reference-guided audio-visual long-video generation. We evaluate Vorch-Director on ST-Bench and introduce a new long-horizon audio-visual benchmark with metrics for quality drift and long-range consistency. Extensive experiments demonstrate improved stability and audio-visual fidelity over strong baselines.

We propose a deep learning framework for image restoration from images degraded by both multiplicative Gamma noise and blur. Unlike conventional deep equilibrium (DEQ) models that rely on implicit neural regularization, the proposed method learns an explicit and interpretable regularizer parameterized by geometric priors associated with surface area and mean curvature. To minimize the resulting variational model, we develop a mirror descent algorithm tailored to the commonly used Gamma-noise fidelity terms. Leveraging the Kurdyka-Lojasiewicz property for functions defined in $o$-minimal structures, we establish the global convergence of the generated iterates to a critical point. Experimental results on both grayscale and color image restoration demonstrate that the proposed method consistently outperforms representative model-based approaches while achieving performance comparable to state-of-the-art DEQ models based on implicit regularization, despite requiring substantially fewer trainable parameters.

Refurbishment-based noisy-label learning mixes an observed label with a model-derived pseudo target, typically using one sample-wise cleanliness score to control both branches. This creates a hidden coupling: reducing trust in the observed label automatically increases trust in the pseudo target. We show that this complementarity can replace one unreliable signal with another because a pseudo target learned from corrupted supervision may reproduce the noise it is meant to correct. Our representation diagnostics provide a consistent account of this mismatch: noisy supervision redirects deeper layers more strongly, whereas shallower relations remain comparatively stable and provide information beyond the loss posterior. We therefore propose TRACE, a Two-Source Reliability Assessment framework for Label Correction and Sample Reweighting. TRACE assesses the observed label using loss fit, shallow relation stability, and prediction agreement, while separately assessing the pseudo target using model confidence. Its source-specific scores control target correction and supervision strength without assuming complementary reliability. Across synthetic and real-world noisy benchmarks, TRACE improves representative refurbishment baselines and yields more reliable pseudo supervision.

Differentially private zeroth-order optimization (DP-ZO) enables memory-efficient private fine-tuning of large language models using only forward evaluations. Existing aggregation-based DP-ZO methods reconstruct model updates at a fixed scale, ignoring that the strength of useful signals varies throughout training. Consequently, noise-dominated updates may receive excessive weight and degrade model utility. To address this issue, we propose SAGE, a noise-aware shrinkage method that adaptively attenuates privatized estimates according to their estimated signal quality. SAGE subtracts the known Gaussian noise variance from the observed second moment to estimate the underlying signal energy, stabilizes this estimate through temporal tracking, and compares its current signal-to-noise level with a warm-up reference to derive a bounded shrinkage factor. As pure post-processing, SAGE requires neither additional privacy budget nor model queries and introduces only constant additional state. Our theoretical analysis shows that shrinkage reduces the quadratic update-risk term faster than the linear descent term, preserving useful descent while limiting the influence of noise-dominated updates. Experiments on RoBERTa-large, OPT-1.3B, and OPT-6.7B demonstrate that SAGE outperforms existing baselines in most settings under the same privacy budgets while preserving the forward-only memory efficiency of DP-ZO.

Large language models (LLMs) have become the default tool for a remarkable range of tasks, yet they have had conspicuously little success at one of the most common machine learning workloads: predictive analytics over tabular data. This gap is the founding premise of the fast-growing field of tabular foundation models, but the question of why generic LLMs fail has remained open. We study a frontier LLM in its purest inference regime - a single generation pass over a prompt containing the full training and test data, with no tools, no agentic scaffolding, and no fine-tuning - and systematically evaluate five hypotheses for the failure: (a) an inability to handle noisy or non-linearly-separable data; (b) the linearised CSV format obscuring column structure; (c) the tokenisation of numeric values; (d) the number of test points classified per query; and (e) the dimensionality of the input. Controlled experiments falsify (a)-(d). Dimensionality, in contrast, is decisive: sweeping random linear projections of thirty-one benchmark datasets, the LLM is the only method among nine whose accuracy decreases as dimensionality grows, while every classical baseline stays flat or improves. A behavioural comparison against 252 configured classical models finds that in two dimensions the LLM predicts like a local, distance-based method (up to 91.6% grid agreement), but in higher dimensions no classical model - even when augmented with tuned, dimension-dependent noise - reproduces its predictions. We do not claim to have identified the internal mechanism; our results show, more modestly, that the LLM's capability dissolves with dimension in a way no noise-corrupted classical learner mimics - which explains why LLMs, so capable elsewhere, keep losing to fifty-year-old baselines on tables, while leaving the mechanism of the prediction as an open question.

Multi-step returns accelerate reward propagation in off-policy reinforcement learning, but couple the evaluation of each decision to the suboptimal logged actions that follow it, inducing a pessimistic bias that grows with the horizon. We propose Expectile $n$-step Q-learning (ENQ), which replaces the symmetric $n$-step temporal-difference (TD) loss with an asymmetric expectile loss on the action-value error, with expectile level $τ$ as the only method-specific hyperparameter added beyond $n$-step TD. We prove that the ENQ operator is a $γ^{n}$-contraction. Under deterministic dynamics, at $τ=1$, its bias vanishes at the optimal action-value function $Q^*$ on covered in-support pairs, and the corresponding fixed point satisfies the separation-$n$ instance and its multiples of the lower-bound inequality used by Long-Horizon Q-learning (LQL). Under stochastic dynamics, the operator bias admits two-sided bounds with horizon-independent noise constants. Using a single expectile level $τ=0.8$ and a fixed backup horizon across 27 manipulation and navigation task instances, ENQ is competitive with LQL on aggregate, achieves higher measured training-step throughput in our profiling study, and benefits more from a ten-critic ensemble in a controlled scaling experiment.

Single-photon avalanche diode (SPAD) cameras are promising for low-light and high-dynamic-range intensity imaging, but their practical use is limited by complex sensor-specific noise. Unlike time-correlated single-photon counting (TCSPC) systems, SPAD cameras record whether at least one detection occurred in each gate without photon timestamps in intensity imaging mode, making explicit noise decomposition difficult. We present a practical noise modeling and calibration framework for SPAD intensity denoising. Our forward model describes binary-frame accumulation with a Binomial observation process, models signal-independent dark noise as an exposure-dependent pure dark count term plus an exposure-independent dark-frame bias term, and incorporates pixel-wise response non-uniformity. We design a dedicated calibration procedure for the proposed model and use it to build a count-domain noise-synthesis pipeline for network training. For denoising, we further design a SPAD-specific dark-shading correction (SPAD-DSC) to remove most systematic noise before network training. We construct a real-world SPAD intensity dataset for testing. Experimental results demonstrate the superiority of the proposed noise model.

Robust low-light imaging remains challenging for the community. Recent studies have explored fusing Near-Infrared (NIR) with noisy RGB to achieve improved enhancement, yet most methods depend on carefully curated training data pairs, with limited robustness under different scenarios. This paper offers a new perspective for RGB-NIR low-light imaging by incorporating 3D-aware neural modeling. Without using clean RGB supervision, a powerful model can be optimized to implicitly fuse extremely noisy RGB observations with NIR cues in 3D space, effectively recovering clean RGB images. The proposed model obviates the requirement for clean RGB data collection, generalizes across different noise levels. Extensive evaluations on synthetic and real data demonstrate its superiority. Codes available: https://github.com/MyNiuuu/3DarkFusion

Sparse identification of nonlinear dynamics (SINDy) and PDE functional identification (PDE-FIND) recover parsimonious ordinary and partial differential equations (ODEs and PDEs) from data. However, sparse and noisy temporal measurements can make derivative estimates unreliable. To address this problem, we evaluate Koopman-based upsampling techniques implemented with dynamic mode decomposition (DMD), extended DMD (EDMD), and optimized DMD. These methods learn finite-dimensional approximations of Koopman evolution on selected observables and are used to interpolate and denoise snapshots inside the observed time window before derivative estimation and sparse regression. The empirical benchmark comprises two ODE systems, Lorenz-63 and Van der Pol, and three periodic PDE systems, Burgers, Fisher-Kolmogorov-Petrovskii-Piskunov (Fisher-KPP), and linear advection-diffusion, over sparse and noisy sampling regimes. Polynomial EDMD gives the strongest ODE results, especially in coefficient accuracy. The PDE results are system-dependent: low-rank DMD-assisted reconstructions improve Burgers and advection-diffusion discovery, while the raw baseline (without upsampling) remains competitive for the Fisher-KPP data. A comparison against linear and smoothing-spline interpolation techniques shows that the selected Koopman-based preprocessors provide overall performance gains over these non-dynamical alternatives. We also demonstrate that DMD-assisted upsampling can stabilize Pareto-based non-oracle support-size selection. Overall, Koopman-based upsampling is best viewed as a dynamics-aware preprocessing step that can reduce derivative-estimation error when its observable representation and low-rank structure are appropriate for the data.

Adversarial training can improve the robustness of predictive models to bounded perturbations, often at the cost of statistical efficiency. We study this trade-off in kernel regression over a reproducing kernel Hilbert space (RKHS). It is shown that, under squared loss, adversarial training in RKHS introduces a term involving the product of the function norm with the mean absolute value of the response noise, which we call the \textit{noise premium}. Our analysis shows that the noise premium makes the prediction error of adversarial training converge strictly more slowly than the nonparametric minimax benchmark even after balancing approximation and estimation errors. Moreover, for a fixed perturbation budget, once the budget exceeds a certain threshold, the solution to adversarial training collapses to the zero function. To mitigate these effects of the noise premium, we propose noise-debiased adversarial training. The resulting noise-debiased estimator can attain the minimax optimal rate up to a logarithmic factor for the prediction error, raises the collapse threshold, and admits an explicit bound on the increase in adversarial loss. Numerical experiments on synthetic and real data support the theoretical findings and validate the effectiveness of the proposed noise-debiased method.

Structural causal models are the standard language for reasoning about interventions and counterfactuals, but they describe static variables, typically measured once, and usually forbid cyclic dependencies. Many systems we care about, such as patients, climates, and economies, instead evolve continuously in time, are observed at irregular time points, and contain feedback loops. We argue that neural operator learning provides a natural foundation for causal reasoning in this setting, and propose Orca, a framework in which each node of the causal graph is a function of time and each mechanism is a learned map between function spaces. We extend existing neural operator architectures to express causal mechanisms: a mechanism computes the function value of a node from its parent nodes by taking several parent functions as input, respects the arrow of time, and treats latent exogenous noise as a function that can be inferred and reused for counterfactuals. We formalize the model class and demonstrate counterfactual reasoning on synthetic continuous-time examples. Code is available at https://github.com/gerritgr/orca

Deep neural networks (DNNs) have achieved remarkable success in classical machine learning problems. However, they are known to be vulnerable to adversarial attacks. Countermeasures proposed in the literature, notably Information Bottleneck Distillation (IBD) introduced by Kuang et al., degrade the classification accuracy on clean inputs while improving the robustness to adversarial inputs. In this work, we extend the IBD framework by introducing an extra teacher model (clean teacher) trained with only clean inputs, into the distillation process from a robust teacher model trained by adversarial training. The features of both clean and robust teachers are transferred to the student through a cross-layer attention matrix. Experimental results on the CIFAR-10 and CIFAR-100 datasets show that the proposed method improves classification accuracy on clean samples compared to the original IBD, while maintaining similar accuracy on adversarial samples. Furthermore, our methods are competitive with state-of-the-art approaches, including the recent dual-teacher distillation framework B-MTARD, particularly in terms of the harmonic mean between clean and robust accuracy. We also analyze the impact of different training settings that have different influences on the attention module.

Low-light image enhancement (LLIE) methods involve tunable parameters that are typically fixed, often leading to performance degradation when applied across scenes. Manually selecting the best configuration, however, can be time-consuming and not always practical. Peak signal-to-noise ratio (PSNR) is the natural fidelity criterion for automating parameter selection, yet it requires a ground-truth reference that is typically unavailable. To our knowledge, no learning-based method addresses no-reference PSNR prediction for low-light image enhancement; the natural surrogate, no-reference image quality assessment (NR-IQA), targets perceptual quality rather than signal fidelity, and all seven baselines we test achieve 0% top-1 selection accuracy on our benchmark. With paired training data, the ground-truth PSNR is analytically computable, providing exact supervision without a separate teacher network. Building on this, we propose BlindPSNR, a lightweight no-reference network that fuses the enhanced image with the degraded low-light input via windowed cross-attention and estimates PSNR through heteroscedastic regression. While a scalar-regression baseline achieves top-1 accuracy of 54.4%, BlindPSNR raises this to 89.5% with regret dropping from 1.62 dB to 0.026 dB, and generalizes to unseen datasets (SRCC = 0.61-0.67).

Accurate multipath parameter estimation is critical for modern wireless communication systems, particularly in challenging low-SNR environments. Traditional Maximum Likelihood Estimation algorithms, such as CLEAN, provide high-resolution parameter extraction but suffer from prohibitive computational complexity due to exhaustive grid search. Conversely, purely data-driven deep learning approaches lack physical grounding and struggle to generalize across variable multipath densities and off-grid parameters. To address these limitations, this paper proposes Neural Network-Assisted CLEAN (NN-CLEAN), a hybrid framework that embeds a multi-head residual network directly into the iterative CLEAN extraction loop. By replacing the exhaustive grid search with rapid, parallelizable forward passes while delegating residual subtraction to exact mathematical models, NN-CLEAN isolates physical multipath parameters without accumulating non- physical errors. Extensive Monte Carlo simulations demonstrate that NN-CLEAN achieves estimation accuracy exceeding 96% at 5 dB SNR, matching the traditional Grid-Search CLEAN (GS- CLEAN) baseline, while providing a massive reduction in computational complexity and substantially outperforming subspace methods and standalone one-shot neural networks. Crucially, NN-CLEAN exhibits a near-flat scaling in execution runtime and memory consumption as batch sizes increase. This highly efficient parallelization establishes NN-CLEAN as a robust, real- time solution for channel estimation in MIMO systems.

Optimization in non-convex neural network models is strongly influenced by the geometry of the solution space: sparse, isolated, point-like clusters are typically algorithmically inaccessible, whereas wide and flat regions can be found efficiently despite being relatively rare. At zero temperature this picture has been formalized in binary perceptrons through the overlap gap property (OGP), which limits algorithmic access to configurations with zero training error above a critical constraint density $α_{\rm OGP}$. Here we extend this description to finite temperature, where a positive training error is allowed and statistically penalized. We first show that the frozen one-step replica-symmetry-breaking solution, dominating the zero temperature equilibrium measure, survives at any finite temperature. We furthermore derive a general criterion, based on the smoothness of the single-pattern Gibbs weight near the decision boundary, that determines when a finite-temperature relaxation of the loss removes freezing. We then extend the OGP construction to finite temperature and show that dense, algorithmically accessible regions of finite-energy configurations persist beyond $α_{\rm OGP}$, up to a threshold $α_{\rm OGP}(ε)$ that grows with the allowed training error $ε$. Finally, in the teacher-student setting, we show that these wide, finite-energy regions still retain good generalization. Using a finite energy message-passing algorithm, we demonstrate numerically that thermal noise enables effective generalization in the regime of constraint densities where both recovering the teacher and finding a zero temperature solution are computationally hard.

Given a model that is already trained, which features does it rely on causally versus spuriously? Existing methods require access to the training procedure and cannot answer this post-hoc. We introduce the \textbf{Normalised Sensitivity Ratio~(NSR)}, a post-hoc, model-agnostic diagnostic for this question under a structured-shift regime: environments differ primarily in the mean of spurious features while the causal mechanism and causal marginals remain stable, as in multi-site clinical data or multi-batch genomics. Within this regime, causal features induce constant model sensitivity across environments while spurious features track shift. NSR formalises this as the squared coefficient of variation of per-environment sensitivity. Under a linear structural causal model (SCM) with $K\ge3$ non-degenerate environments, NSR achieves exact identification (Theorem~1). We fully characterise failure: weak shifts ($O(\varepsilon^4)$ collapse), degenerate geometry, and proxy attenuation ($O((1-α)^4)$), giving practitioners quantitative criteria for assessing whether the regime holds. Finite-sample rates are $O_p(n^{-1})$ under the null and $O_p(n^{-1/2})$ under the alternative. Experiments confirm all theoretical predictions on synthetic data (area under the ROC curve [AUROC] $= 1.000$ under conditions satisfying the regime), show consistent rankings across five model families (Kendall $τ\ge0.529$), and recover six of eight causal features on bike-sharing data (Precision@7 $= 0.75$) without modifying any trained model.

Conformalized selection has been widely applied to select high-quality candidates from large datasets with rigorous uncertainty quantification, such as reliable labeling, drug discovery, and the alignment of large language models. Nevertheless, existing methods assume clean responses on calibration data, an assumption that rarely holds in practice. In this paper, we formulate the above tasks as selecting candidates with true predicted labels or with responses exceeding certain values. We demonstrate that existing conformal selection methods fail to control the false discovery rate (FDR) or suffer from severe power loss under contaminated calibration data. To that end, we propose Robust Conformalized Selection (RCS), a unified framework for selective classification with valid FDR control under general label contamination. The key insight of RCS lies in a novel statistical reduction: by separately conditioning on different classes, we translate the intractable label noise into a localized covariate shift problem, which then enables a covariate-adjusted empirical-Bayes-type estimate of the number of false selections. Statistical properties such as the asymptotic FDR control, power optimality, and robustness of RCS are established. We further develop an instantiation of RCS under randomized response model, and also apply RCS to the task of selecting candidates with large response values. Extensive experiments on both simulated and real-world datasets demonstrate the effectiveness of RCS.

Diffusion models typically suffer from error accumulation during iterative sampling, commonly referred to as exposure bias. We reveal systematic frequency-dependent discrepancies between training and inference, which can be interpreted as frequency-dependent SNR error. Crucially, the direction of this mismatch varies across models and timesteps, indicating that fixed correction rules do not generalize. We propose Spectral Alignment (SPA), a lightweight, guidance-based method that calibrates the power spectrum of intermediate predictions to a pre-computed prior. Our approach consists of two stages: (1) offline fitting of a parametric spectrum model from training data, and (2) inference-time guidance via efficient FFT-based gradient computation. SPA introduces minimal computational overhead (3-4%) and is complementary to Classifier-Free Guidance (CFG). We demonstrate consistent improvements across diverse architectures, from pixel-space models (DDPM, ADM) to latent diffusion models (SD2.0, SDXL) and flow-matching models (SD3.5, FLUX). Our implementation is available at https://github.com/SonyResearch/SPA.

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.

Multiplicative Gamma noise is a signal-dependent degradation in coherent imaging; synthetic aperture radar (SAR) despeckling is its most prominent real-world instance. Existing diffusion denoisers parameterize their forward process by abstract signal-to-noise schedules rather than by the physical look number $L$, so different deployment scenarios typically require separately trained models, and transfer from synthetic Gamma training to real SAR remains challenging without clean ground truth. We introduce $γ$-Bridge, a look-parametric bridge whose schedule $L(t)$ connects the noisy observation at $L_{obs}$ to the clean limit through exact multiplicative Gamma marginals. Its closed-form Gamma--Lévy reverse posterior admits both stochastic and deterministic processes, while observation conditioning and a two-step consistency loss stabilize multi-step inference in the low-SNR single-look regime. Because bridge time directly represents $L$, one conditioned network can smart-start from any admissible input look and stop at a target look number. These two orthogonal controls enable zero-shot restoration over the full admissible grid after training only at $L_{obs} = 1$ on natural images with synthetic Gamma corruption. Combined with a homogeneous-patch look estimator, $γ$-Bridge processes data from six spaceborne and airborne SAR sensors without sensor-specific fine-tuning, achieving leading results on standard synthetic benchmarks while providing physically interpretable input and output controls absent from prior denoisers. Codes are released \href{https://github.com/Teriri1999/GammaBridge}{here}.

Modeling galaxy-galaxy strong gravitational lenses to infer the brightness of the source galaxy and the mass distribution of the foreground galaxy is computationally challenging, particularly for high-resolution, high signal-to-noise ratio observations. In this regime, high-dimensional representations of both the source and the foreground mass distribution are necessary to model the data down to the noise level. This inference problem has been challenging for both traditional and machine learning-based methods because of its high dimensionality and its non-linearity in the foreground mass distribution. We present a method to generate joint posterior samples of the source galaxy and foreground mass distribution as pixelated images conditioned on observations. The method combines diffusion-based generative modeling and recurrent inference machines. It can model realistic gravitational lensing simulations with background and foreground galaxies drawn from cosmological hydrodynamical simulations down to the noise level.

Diffusion-based methods have achieved remarkable empirical success in solving inverse problems. However, many existing posterior samplers either lack rigorous theoretical guarantees or incur substantial computational overhead. We propose a simple and efficient algorithm, called \pddim, for solving linear inverse problems with diffusion priors via a DDIM-type sampler. Our method requires only lightweight, coordinate-wise modifications to the standard DDIM update, while explicitly incorporating the measurement model. The key idea is to perform posterior sampling separately along each singular direction of the measurement operator: for each direction, the sampler follows the learned diffusion prior when the observation signal-to-noise ratio (SNR) is below the corresponding diffusion SNR, and switches to a calibrated measurement-based predictor otherwise. We prove that the proposed sampler converges to the Bayesian posterior conditioned on the measurements. Empirical results show that the proposed sampler performs favorably against existing diffusion-based posterior samplers across a range of image restoration tasks, achieving the best performance on the majority of evaluation metrics considered. Overall, our results convert posterior sampling for noisy linear inverse problems to simple coordinate-wise DDIM updates, yielding an efficient, easy-to-implement algorithm with provable posterior consistency.

Neural Markov Logic Networks (NMLNs) are a flexible neurosymbolic relational model. Previous work has shown that, although NMLNs achieve strong performance as generative models for small relational structures, they underperform diffusion-based generative graph models on larger structures. In this paper, we strengthen NMLNs along two main dimensions: (i) we increase the expressive capacity of their potential functions using graph neural networks, and (ii) we develop a new training and inference algorithm inspired by parallel-tempering Markov chain Monte Carlo methods, which we name parallel noising. Together, these enhancements enable NMLNs to attain strong performance in graph generation relative to general diffusion-based generative graph models. Furthermore, they allow NMLNs to match the performance of specialized text-based recurrent models when generating small molecular structures.

In astronomical imaging surveys, repeated observations of the same sky patches are taken in order to obtain deeper images and detect new sources. This is the case in the search for many transient phenomena, such as supernovae, gravitational wave (GW) optical counterparts and other cataclysmic variables. In many such surveys some of the images are undersampled, meaning that the pixel size is too large, and the image suffers from aliasing. For undersampled images, both co-addition of the images and background subtraction are done in a non-optimal manner, which leads to reduced sensitivity and an increased rate of false alarms. We present a new method (named Linear Undersampled Transients & Addition (LUTRA)) that performs both processes in a mathematically proven optimal way, which allows improved performance for many scientific applications. It also allows easy and direct performance of measurements such as photometry and astrometry in a simple manner, while providing results in super-resolution. We demonstrate the performance of the method on public ZTF data and show $\times 1.25$ higher SNR compared to current methods. We provide an open source Python implementation.

How deep does a graph neural network need to be on a sparse graph? We study its purest statistical form: node classification on the sparse contextual stochastic block model (CSBM) with average degree $Δ=O(1)$, whose local weak limit is a broadcast-labelled Poisson Galton-Watson tree. Prior work derived a message-passing classifier $h_\ell$ that aggregates from each vertex at distance $k\le\ell$ the attenuated evidence $2\operatorname{artanh}(γ^k t(X_v))$, with $γ$ the edge signal and $t$ a bounded likelihood-ratio transform of the feature. We prove that the value of depth is governed by a single number, the Kesten-Stigum ratio $κ=γ^2Δ$. Below the threshold ($κ<1$), the error sequence is Cauchy at a geometric rate, $|\mathcal{E}(\ell)-\mathcal{E}(\ell')|\le Cκ^{(\ell+1)/3}$ for all $\ell'>\ell$, so all layers beyond depth $O(\log(1/ε))$ change the error by less than $ε$; conversely, under mild regularity each sufficiently deep layer still flips the decision with probability at least $cκ^{\ell/2}$, the empirically sharp exponent. Above the threshold ($κ>1$), depth is geometrically productive: $\mathcal{E}(\ell)$ is driven to a branching-process floor of order at most $1/(κ-1)$ at any geometric rate $κ^{-s\ell}$, $s<1$ (this bound has content only for $κ>17$). No local classifier of any depth beats the universal floor $e^{-Δ}Φ(-ζ)$ set by isolated roots ($ζ$ the feature signal-to-noise ratio), while the first layer provably helps by an explicit total-variation amount. Simulations with an exact belief-propagation baseline on the same trees show that the pairwise rule's error curve is mildly non-monotone in $\ell$, so an optimal finite depth exists (an exact instance is certified in the appendix), while BP saturates strictly faster, at an effective per-layer ratio below $κ$ that we identify.

Autoregressive video diffusion models have enabled the generation of arbitrarily long videos by removing conditioning on future frames, thus greatly improving computational efficiency. Yet, they suffer from error accumulation over time, as the denoised sequence gradually drifts away from the conditioning distribution seen during training. Recent advances attempt to reduce this error by anchoring each generated frame to the learned manifold of real ones. However, even when all generated individual frames lie close to the real manifold, there are trajectories which the model lacks sufficient knowledge to continue without exiting it, thus reaching a terminal point. To prevent the model from being trapped in terminal points, we start from the hypothesis that for well-modeled future trajectories the distribution of the predicted noise should match the one of the forward noising process. To enforce such a prior at test time, we introduce Terminal points Avoidance through Noise Guided Optimization (TANGO), which uses the diffusion model as a critic of its own outputs, by predicting one step forward and requiring an isotropic Gaussian noise prediction. We use the deviation from this expected noise distribution to search for an alternative trajectory that does not lead to a terminal point. Our approach achieves a $3.1\%$ absolute improvement on VBench over state-of-the-art, while reducing Fréchet Video Distance by $28.3\%$ on average across $15$s videos. Our code is available on https://mever-team.github.io/tango.

Noise injection is a well-known technique in stochastic optimization. We report its surprising effectiveness with an interleaved (on-off-on-off...) rather than the usual monotonic decay schedule. We present a theoretical analysis of noise injection, which confirms that corruption by impulse noise approximates a Jacobian regularization, whereas Gaussian noise acts as a curvature penalty. This regularization behavior has been invoked to explain why noise injection increases model robustness. But the interleaved nature of our proposed schedule produces superior results even for the optimization objective: mixing phases of noisy data permits the optimizer to escape local minima and increase exploration without the risk of catastrophically forgetting the important features from the clean data. To stabilize this training scheme against the rapid changes of the loss when switching between clean and noisy data, we introduce a gradient-norm stabilization technique that scales noisy updates based on clean gradient magnitudes. We compare this method with other common augmentation methods and find substantial improvements in corruption tolerance and robustness to real-world distribution shifts on CIFAR-100-C, ImageNet-C, and ImageNet-R for ResNet and ViT architectures, with the best results being achieved by stacking our method on top of other augmentations. Through saliency and attention maps we show that the effect of interleaved noise injection stems from penalizing the failure modes encouraged by the inductive bias of the models: impulse noise works against the locality bias of convolutional (ResNet) architectures, and Gaussian noise reduces the tendency of attention-based models to pick up large-scale spurious features. Interleaved noise injection is therefore an effective tool to improve the test performance on clean, noisy, and out-of-distribution data at essentially zero computational cost.

We propose a noise-robust elicit-to-optimize framework that integrates inverse reinforcement learning (IRL) and reinforcement learning (RL) for eliciting agents' risk preferences and optimizing policies under a broad class of risk objectives characterized by distortion riskmetrics. On the elicitation side, we propose an adaptive Bayesian IRL method that infers agents' latent risk objectives from their noisy observed decisions, explicitly allowing agents to take stochastic and suboptimal actions. We establish the existence of a finite set of distinguishing questions that identifies the preferred distortion riskmetric within the candidate class and prove that the convergence rate of the algorithm is of order $O(\exp(-cm+O(\sqrt{m\log m})))$ under general settings, where $c>0$ is a constant and $m$ denotes the number of algorithm iterations. On the optimization side, we develop a model-free RL algorithm for optimizing policies under conditional distortion riskmetrics. By representing the objective as an integral of the conditional cost quantile function with respect to the distortion function, the method unifies distortion-riskmetric objectives. We optimize diverse risk objectives by extending the Proximal Policy Optimization (PPO) algorithm with policy, value, and quantile neural networks, where the quantile network estimates the full conditional cost quantile function and enables numerical evaluation of general risk objectives. A comprehensive empirical study demonstrates the framework's elicitation accuracy and effectiveness in complex financial environments.

The development of smart transportation systems and the introduction of 6G wireless communication technologies have significantly changed vehicle network topologies. Future connected autonomous vehicle (CAV) networks require bandwidth-efficient, reliable, and low-latency communication for safety-critical applications such as traffic sign recognition and decision-making. Conventional communication systems transmit raw data regardless of task relevance, which is inefficient in resource-constrained satellite channels where uplink bandwidth is scarce and propagation losses are large. Semantic communication addresses this limitation by transmitting task-relevant information instead of full signal representations. It extracts and conveys essential semantic features and leverages deep learning to optimize task performance at the receiver. Therefore, we present a Variational Autoencoder (VAE)-based multi-task semantic communication framework for satellite-assisted autonomous driving. Unlike deterministic autoencoder-based methods, the proposed model uses probabilistic latent representations for more robust and efficient encoding. The learned features are transmitted over noisy wireless channels to perform traffic sign reconstruction and classification. The framework is trained end-to-end to jointly optimize both tasks. Results show that the proposed approach achieves significant bandwidth reduction of up to 87.23% to 98.17% while maintaining stable performance across varying signal-to-noise ratio conditions.

With the growing demand for satellite sensing and communication, the limited wireless resources are difficult to support multiple satellite systems. Therefore, it is desired to investigate integrated sensing and communication (ISAC) in low Earth orbit (LEO) satellite systems to enable multi-functionality within a single satellite, thereby saving both spectrum and orbital resources. In this paper, a framework for ISAC in LEO satellite systems is established, where a satellite can simultaneously sense multiple targets and serve multiple communication users (CUs) over the same spectrum. Considering the limited onboard energy of satellite, a novel robust beamforming design algorithm is developed with the goal of minimizing total transmit power while satisfying the mean squared error (MSE) requirements for sensing and signal-to-interference-plus-noise ratio (SINR) requirements for communication in presence of channel phase uncertainty which exacerbates the cross-functional interference. According to theoretical analysis, the proposed algorithm for ISAC in LEO satellite systems is effective. Moreover, extensive simulations confirm the superiority of the proposed algorithm over baselines.

Decentralized gradient descent (DGD) is widely used for solving distributed optimization problems over networks of agents. While its convergence properties are well understood, less is known about the communication and computation resources required to attain a prescribed accuracy. In this paper, we study DGD from a resource-aware perspective and characterize the communication-computation budget required to attain a target error level. We develop a bottleneck-centric framework in which different factors dominate the optimization dynamics at different error scales. Specifically, we identify operating regimes governed by initialization, objective heterogeneity and network connectivity, gradient noise, and communication noise. To capture these effects, we introduce two fundamental quantities: the gradient-Diversity-to-Network-connectivity Ratio (DNR) and the Gradient-to-Communication-noise Ratio (GCR). We show that these quantities determine the sequence of bottlenecks encountered during optimization and the corresponding budget-optimal operating strategy. Using a multi-stage analysis, we derive optimal stepsize selections and explicit budget-complexity bounds that quantify the budget resources required to attain a prescribed accuracy. The resulting expressions reveal how the overall budget decomposes into contributions associated with successive bottlenecks and provide insight into the fundamental tradeoffs among objective heterogeneity, network connectivity, gradient noise, and communication noise.

Finite Reliability Representations (FRR) certify when a cell-constant policy is sufficient for reliable decision-making in a partially observed system with a known physical noise floor. In practice, however, sensing and execution noise can be latent and context-dependent. This paper develops a certificate-aware active disambiguation framework for an unknown physical noise parameter theta = (sigma_y, sigma_u), with the sensor-only case obtained by fixing sigma_u. We define the Value of Noise Information (VoNI) as the expected excess FRR certificate gap caused by using a reliability cover calibrated to the current estimate rather than to the realized noise parameter. We bound VoNI using action-value model mismatch and FRR radius inflation, showing that noise estimation has low decision value in sub-crossover regimes where the FRR certificate is insensitive to theta, but becomes valuable when posterior uncertainty can invalidate the current cover. A bi-level decision maker uses a posterior over theta, obtained from innovation statistics, execution residuals, or another online estimator, and triggers diagnostic probing only when uncertainty threatens the FRR certificate. We also interpret VoNI as a tractable, certificate-aware approximation to a high-level finite POMDP for latent sensing-execution regime disambiguation. Under stationary, identifiable, and persistently exciting regimes, we establish posterior consistency and convergence of the induced policy loss to the FRR approximation floor. Closed-loop UGV simulations with EKF-based innovation residuals show earlier detection of abrupt sensing-noise jumps, lower drift-tracking error, and substantially fewer probing actions than posterior-entropy exploration over 50 Monte Carlo trials.

Self-supervised data splitting has emerged as a promising paradigm for sparse-view CT reconstruction, enabling training from incomplete measurements without fully sampled ground truth. However, the influence of key design choices, including partitioning strategy, preprocessing, and inference, remains insufficiently understood. In this work, we introduce a unified framework that decomposes splitting-based reconstruction into these three components, enabling controlled comparison of existing methods and two incremental extensions: multi-partition splitting and an alternative inference strategy. Experiments on simulated LoDoPaB-CT data under independent and correlated noise, together with validation on the real-world 2DeteCT dataset, show that the optimal partitioning strategy strongly depends on the measurement noise structure. Lattice-based splitting performs favorably under independent noise, whereas angular masking is more robust under correlated noise and real measured data. Multi-partition splitting consistently improves over pure projection-wise splitting in several settings. Complementary perceptual and structural metrics, including LPIPS and HaarPSI, reveal differences between masking strategies that are less apparent from PSNR and SSIM alone. These results provide practical guidelines for designing self-supervised sparse-view CT reconstruction methods and highlight the limitations of common independence assumptions in realistic imaging environments.

Rank estimation under label noise poses a fundamental challenge, as ordinal annotations often exhibit structured uncertainty rather than simple label corruption. In this paper, we reformulate rank estimation with noisy ordinal labels as a stochastic ordering problem, in which each instance is inherently associated with multiple plausible ranks instead of a single deterministic label. Based on this view, we propose stochastic order learning (SOL), a learning framework that captures ordinal label uncertainty and learns an embedding space through two complementary objectives: a discriminative loss that structures instance--centroid interactions and a stochastic order loss that enforces probabilistic ordering relations between instances. Extensive experiments across diverse datasets demonstrate that SOL enables reliable rank estimation under various types and levels of label noise. The source code is available at https://github.com/cwlee00/SOL.

The optimization of long-horizon agents increasingly relies on reflection-based mechanisms, where a large language model (LLM) acts as an optimizer to diagnose agent failures and improve agent policies. However, real execution traces are difficult to use directly for optimization: large trace collections are often redundant and heterogeneous, making optimization inefficient and prone to overfitting to low-value failures; meanwhile, each individual trajectory also contains many irrelevant steps, while naive context reduction methods such as truncation or sliding windows can discard causally important evidence and produce misleading optimization signals. To resolve this dilemma, we introduce STRACE (Structural TRajectory Analysis and Causal Extraction), a framework that constructs high signal-noise optimization contexts for more precise and effective optimization. At the batch level, STRACE mines failure patterns to filter redundant traces and retain representative failures; within each selected trace, it performs causal localization over a textual dependency graph to remove non-causal steps and identify the true root-cause module for optimization. Empirical results demonstrate that STRACE significantly outperforms standard context-filtering baselines. Notably, on a challenging formal verification task (VeruSAGE-Bench), it successfully optimizes human-expert designed agents, delivering $1.4\times$ success-rate improvement (42.5% to 58.5%). The code is available at https://github.com/moomight/STRACE .

Real-image diffusion inversion is governed by a tight quality-cost trade-off, with costs incurred in computation, storage, or per-image optimization. We study this trade-off through the forward Gaussian noise anchor that defines a diffusion trajectory and isolate two mechanisms behind effective stored-noise inversion. First, diffusion noise exhibits an element-wise compression asymmetry: int8 full-dimensional anchors preserve reconstruction, whereas low-dimensional subspace summaries are much less reliable, often collapsing even at comparable or smaller payloads; the element-wise over subspace ordering persists across five stored-noise inversion methods. Second, inversion is trajectory-bound and score-prior coupled: the matched forward anchor and a trained score network are both necessary, arguing against a purely algebraic-identity explanation. Together, these findings specify what to store and how to use it. They lead to Noise-Anchored Reverse Correction (NARC), a training-free inversion primitive that stores a single int8 latent anchor and reuses it with a fixed, noise-level-dependent anchor-weight schedule: strong anchoring when the reverse trajectory is noise-dominated, then relaxed anchoring as image detail emerges. On PIE-Bench++ with Stable Diffusion 1.5, NARC outperforms five modern non-exact baselines and improves PSNR by +3.24 dB over PnP DirectInv while using about 400x less inversion storage than PnP DirectInv. The compression asymmetry, anchor specificity, and editing plug-in also transfer to SDXL 1024^2.