Daily Papers

Recently, 3D Gaussian Splatting (3DGS) greatly accelerated mesh extraction from posed images due to its explicit representation and fast software rasterization. While the addition of geometric losses and other priors has improved the accuracy of extracted surfaces, mesh extraction remains difficult in scenes with abundant view-dependent effects. To resolve the resulting ambiguities, prior works rely on multi-view techniques, iterative mesh extraction, or large pre-trained models, sacrificing the inherent efficiency of 3DGS. In this work, we present a simple and efficient alternative by introducing a self-supervised confidence framework to 3DGS: within this framework, learnable confidence values dynamically balance photometric and geometric supervision. Extending our confidence-driven formulation, we introduce losses which penalize per-primitive color and normal variance and demonstrate their benefits to surface extraction. Finally, we complement the above with an improved appearance model, by decoupling the individual terms of the D-SSIM loss. Our final approach delivers state-of-the-art results for unbounded meshes while remaining highly efficient.

Anomaly Detection (AD) in images is a fundamental computer vision problem and refers to identifying images and image substructures that deviate significantly from the norm. Popular AD algorithms commonly try to learn a model of normality from scratch using task specific datasets, but are limited to semi-supervised approaches employing mostly normal data due to the inaccessibility of anomalies on a large scale combined with the ambiguous nature of anomaly appearance. We follow an alternative approach and demonstrate that deep feature representations learned by discriminative models on large natural image datasets are well suited to describe normality and detect even subtle anomalies in a transfer learning setting. Our model of normality is established by fitting a multivariate Gaussian (MVG) to deep feature representations of classification networks trained on ImageNet using normal data only. By subsequently applying the Mahalanobis distance as the anomaly score we outperform the current state of the art on the public MVTec AD dataset, achieving an AUROC value of 95.8 pm 1.2 (mean pm SEM) over all 15 classes. We further investigate why the learned representations are discriminative to the AD task using Principal Component Analysis. We find that the principal components containing little variance in normal data are the ones crucial for discriminating between normal and anomalous instances. This gives a possible explanation to the often sub-par performance of AD approaches trained from scratch using normal data only. By selectively fitting a MVG to these most relevant components only, we are able to further reduce model complexity while retaining AD performance. We also investigate setting the working point by selecting acceptable False Positive Rate thresholds based on the MVG assumption. Code available at https://github.com/ORippler/gaussian-ad-mvtec

This work addresses the challenge of high-quality surface normal estimation from monocular colored inputs (i.e., images and videos), a field which has recently been revolutionized by repurposing diffusion priors. However, previous attempts still struggle with stochastic inference, conflicting with the deterministic nature of the Image2Normal task, and costly ensembling step, which slows down the estimation process. Our method, StableNormal, mitigates the stochasticity of the diffusion process by reducing inference variance, thus producing "Stable-and-Sharp" normal estimates without any additional ensembling process. StableNormal works robustly under challenging imaging conditions, such as extreme lighting, blurring, and low quality. It is also robust against transparent and reflective surfaces, as well as cluttered scenes with numerous objects. Specifically, StableNormal employs a coarse-to-fine strategy, which starts with a one-step normal estimator (YOSO) to derive an initial normal guess, that is relatively coarse but reliable, then followed by a semantic-guided refinement process (SG-DRN) that refines the normals to recover geometric details. The effectiveness of StableNormal is demonstrated through competitive performance in standard datasets such as DIODE-indoor, iBims, ScannetV2 and NYUv2, and also in various downstream tasks, such as surface reconstruction and normal enhancement. These results evidence that StableNormal retains both the "stability" and "sharpness" for accurate normal estimation. StableNormal represents a baby attempt to repurpose diffusion priors for deterministic estimation. To democratize this, code and models have been publicly available in hf.co/Stable-X

Machine learning demand forecasts optimize statistical accuracy yet leave excess operational volatility that inflates safety stock and amplifies the Bullwhip effect. We introduce Contextual Deconvolution (CD), a two-stage estimator that reframes demand sensing as a convex decomposition: a kernel-modulated banded operator separates transient promotion-driven shocks from a smooth structural baseline, and hierarchical partial pooling enables catalog-scale deployment without per-SKU training. The operator is data-derived, not imposed---it reduces to the identity wherever the promotional response is impulsive (most of M5, all of Favorita) and contributes only where genuine multi-day carryover exists, so the gains rest on the structural decomposition itself. Evaluating strictly out-of-sample on 30,490 M5 SKUs and 2,845 Favorita items, with calendar-aware baselines given CD's identical future calendar, we anchor the contribution on a full inventory-cost accounting: CD lowers safety stock, holding cost, and order variance but under-provisions event spikes, reducing total cost only when holding costs exceed sim20\% of stockout costs (95\% CI [17%,25%]); otherwise it is an operational-stability and inventory-capital layer, not an expected-cost minimizer. Its accuracy contribution is reliability rather than central tendency: across eleven baselines, CD attains the lowest cross-sectional dispersion of per-SKU error and mis-forecasts by more than 200\% on 0.8\% of SKUs versus 9.9--20.6\% for every baseline, ranking first on both in all four M5 draws. Because the Variance Ratio and std-based safety stock are minimized by any sufficiently smooth forecast, we treat them as diagnostics, not objectives. A supporting analysis shows the learned demand operators are non-normal, yet CD's compact parametric kernel matches their operational performance interpretably.

The Cox proportional hazards model is widely used in survival analysis to model time-to-event data. However, it faces significant computational challenges in the era of large-scale data, particularly when dealing with time-dependent covariates. This paper proposes a moment-assisted subsampling method that is both statistically and computationally efficient for inference under the Cox model. This efficiency is achieved by integrating the computationally efficient uniform subsampling estimator and whole data sample moments that are easy to compute even for large datasets. The resulting estimator is asymptotically normal with a smaller variance than the uniform subsampling estimator. Additionally, we derive the optimal sample moment for the Cox model that minimizes the asymptotic variance in Loewner order. With the optimal moment, the proposed estimator can achieve the same estimation efficiency as the whole data-based partial likelihood estimator while maintaining the computational advantages of subsampling. Simulation studies and real data analyses demonstrate the promising finite sample performance of the proposed estimator in terms of both estimation and computational efficiency.

We consider two data driven approaches, Reinforcement Learning (RL) and Deep Trajectory-based Stochastic Optimal Control (DTSOC) for hedging a European call option without and with transaction cost according to a quadratic hedging P&L objective at maturity ("variance-optimal hedging" or "final quadratic hedging"). We study the performance of the two approaches under various market environments (modeled via the Black-Scholes and/or the log-normal SABR model) to understand their advantages and limitations. Without transaction costs and in the Black-Scholes model, both approaches match the performance of the variance-optimal Delta hedge. In the log-normal SABR model without transaction costs, they match the performance of the variance-optimal Barlett's Delta hedge. Agents trained on Black-Scholes trajectories with matching initial volatility but used on SABR trajectories match the performance of Bartlett's Delta hedge in average cost, but show substantially wider variance. To apply RL approaches to these problems, P&L at maturity is written as sum of step-wise contributions and variants of RL algorithms are implemented and used that minimize expectation of second moments of such sums.

This paper discusses the weight parametrization of two standard 1-Lipschitz network architectures, the Almost-Orthogonal-Layers (AOL) and the SDP-based Lipschitz Layers (SLL). It examines their impact on initialization for deep 1-Lipschitz feedforward networks, and discusses underlying issues surrounding this initialization. These networks are mainly used in certifiably robust classification applications to combat adversarial attacks by limiting the impact of perturbations on the classification output. Exact and upper bounds for the parameterized weight variance were calculated assuming a standard Normal distribution initialization; additionally, an upper bound was computed assuming a Generalized Normal Distribution, generalizing the proof for Uniform, Laplace, and Normal distribution weight initializations. It is demonstrated that the weight variance holds no bearing on the output variance distribution and that only the dimension of the weight matrices matters. Additionally, this paper demonstrates that the weight initialization always causes deep 1-Lipschitz networks to decay to zero.

In recent years, performance on existing anomaly detection benchmarks like MVTec AD and VisA has started to saturate in terms of segmentation AU-PRO, with state-of-the-art models often competing in the range of less than one percentage point. This lack of discriminatory power prevents a meaningful comparison of models and thus hinders progress of the field, especially when considering the inherent stochastic nature of machine learning results. We present MVTec AD 2, a collection of eight anomaly detection scenarios with more than 8000 high-resolution images. It comprises challenging and highly relevant industrial inspection use cases that have not been considered in previous datasets, including transparent and overlapping objects, dark-field and back light illumination, objects with high variance in the normal data, and extremely small defects. We provide comprehensive evaluations of state-of-the-art methods and show that their performance remains below 60% average AU-PRO. Additionally, our dataset provides test scenarios with lighting condition changes to assess the robustness of methods under real-world distribution shifts. We host a publicly accessible evaluation server that holds the pixel-precise ground truth of the test set (https://benchmark.mvtec.com/). All image data is available at https://www.mvtec.com/company/research/datasets/mvtec-ad-2.

Static word embeddings are ubiquitous in computational social science applications and contribute to practical decision-making in a variety of fields including law and healthcare. However, assessing the statistical uncertainty in downstream conclusions drawn from word embedding statistics has remained challenging. When using only point estimates for embeddings, researchers have no streamlined way of assessing the degree to which their model selection criteria or scientific conclusions are subject to noise due to sparsity in the underlying data used to generate the embeddings. We introduce a method to obtain approximate, easy-to-use, and scalable reconstruction error variance estimates for GloVe (Pennington et al., 2014), one of the most widely used word embedding models, using an analytical approximation to a multivariate normal model. To demonstrate the value of embeddings with variance (GloVe-V), we illustrate how our approach enables principled hypothesis testing in core word embedding tasks, such as comparing the similarity between different word pairs in vector space, assessing the performance of different models, and analyzing the relative degree of ethnic or gender bias in a corpus using different word lists.

Typical neural network trainings have substantial variance in test-set performance between repeated runs, impeding hyperparameter comparison and training reproducibility. We present the following results towards understanding this variation. (1) Despite having significant variance on their test-sets, we demonstrate that standard CIFAR-10 and ImageNet trainings have very little variance in their performance on the test-distributions from which those test-sets are sampled, suggesting that variance is less of a practical issue than previously thought. (2) We present a simplifying statistical assumption which closely approximates the structure of the test-set accuracy distribution. (3) We argue that test-set variance is inevitable in the following two senses. First, we show that variance is largely caused by high sensitivity of the training process to initial conditions, rather than by specific sources of randomness like the data order and augmentations. Second, we prove that variance is unavoidable given the observation that ensembles of trained networks are well-calibrated. (4) We conduct preliminary studies of distribution-shift, fine-tuning, data augmentation and learning rate through the lens of variance between runs.

This article studies the change in the prediction accuracy of a response variable when the number of predictors increases, and all variables follow a multivariate normal distribution. Assuming that the correlations between variables are independently drawn, I show that adding variables leads to globally increasing returns to scale when the mean of the correlation distribution is zero. The speed of learning depends positively on the variance of the correlation distribution. I use simulations to study the more complex case of correlation distributions with a non-zero mean and find a pattern of decreasing returns followed by increasing returns to scale - as long as the variance of correlations is not degenerate, in which case globally decreasing returns emerge. I train a collaborative filtering algorithm using the MovieLens 1M dataset to analyze returns from adding variables in a more realistic setting and find globally increasing returns to scale across 2,000 variables. The results suggest significant scale advantages from additional variables in prediction tasks.

A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some scenarios where stronger results are needed in order to establish an asymptotic normal approximation uniformly over a family of probability measures. In this note we collect some results in this direction. We restrict ourselves to weak convergence in mathbb R^d with continuous limit measures.

Most bandit algorithms assume that the reward variances or their upper bounds are known, and that they are the same for all arms. This naturally leads to suboptimal performance and higher regret due to variance overestimation. On the other hand, underestimated reward variances may lead to linear regret due to committing early to a suboptimal arm. This motivated prior works on variance-adaptive frequentist algorithms, which have strong instance-dependent regret bounds but cannot incorporate prior knowledge on reward variances. We lay foundations for the Bayesian setting, which incorporates prior knowledge. This results in lower regret in practice, due to using the prior in the algorithm design, and also improved regret guarantees. Specifically, we study Gaussian bandits with {unknown heterogeneous reward variances}, and develop a Thompson sampling algorithm with prior-dependent Bayes regret bounds. We achieve lower regret with lower reward variances and more informative priors on them, which is precisely why we pay only for what is uncertain. This is the first result of its kind. Finally, we corroborate our theory with extensive experiments, which show the superiority of our variance-adaptive Bayesian algorithm over prior frequentist approaches. We also show that our approach is robust to model misspecification and can be applied with estimated priors.

Evaluation benchmarks are the cornerstone of measuring capabilities of large language models (LLMs), as well as driving progress in said capabilities. Originally designed to make claims about capabilities (or lack thereof) in fully pretrained models, evaluation benchmarks are now also extensively used to decide between various training choices. Despite this widespread usage, we rarely quantify the variance in our evaluation benchmarks, which dictates whether differences in performance are meaningful. Here, we define and measure a range of metrics geared towards measuring variance in evaluation benchmarks, including seed variance across initialisations, and monotonicity during training. By studying a large number of models -- both openly available and pretrained from scratch -- we provide empirical estimates for a variety of variance metrics, with considerations and recommendations for practitioners. We also evaluate the utility and tradeoffs of continuous versus discrete performance measures and explore options for better understanding and reducing this variance. We find that simple changes, such as framing choice tasks (like MMLU) as completion tasks, can often reduce variance for smaller scale (sim7B) models, while more involved methods inspired from human testing literature (such as item analysis and item response theory) struggle to meaningfully reduce variance. Overall, our work provides insights into variance in evaluation benchmarks, suggests LM-specific techniques to reduce variance, and more generally encourages practitioners to carefully factor in variance when comparing models.

Portfolio risk assessment ordinarily relies on reliable estimates of cross-asset return covariances, which are difficult to obtain in short, high-dimensional panels. We show that firm-level distribution-valued characteristics can instead provide one-sided certificates of portfolio risk. Under maintained links from characteristics to systematic exposures and from exposures to returns, multi-firm Wasserstein-2 dispersion yields a sharp upper bound on systematic portfolio variance and a corresponding bound for standardized returns. A weighted pairwise relaxation produces an objective that is convex under a checkable condition and requires marginal volatility scales but no cross-asset return covariances. With zero firm-specific slack, the common-map scale changes the certified variance reduction but not the normalized allocation, which depends only on observed information geometry. In a 52-firm panel from 2018-2022, an allocation constructed from Qwen3-Embedding-8B news representations lies between the 0.69th and 1.33rd in-sample variance percentiles across four prespecified capped portfolio populations; equal risk weighting lies between the 21.1st and 28.6th percentiles. The lower in-sample variance ranking relative to equal risk also appears across the reported frozen language-model representations. The framework therefore distribution-valued firm information into a coherent risk bound and an implementable allocation rule constructed without cross-asset return covariances.

Recent innovations on hardware (e.g. Nvidia A100) have motivated learning N:M structured sparsity masks from scratch for fast model inference. However, state-of-the-art learning recipes in this regime (e.g. SR-STE) are proposed for non-adaptive optimizers like momentum SGD, while incurring non-trivial accuracy drop for Adam-trained models like attention-based LLMs. In this paper, we first demonstrate such gap origins from poorly estimated second moment (i.e. variance) in Adam states given by the masked weights. We conjecture that learning N:M masks with Adam should take the critical regime of variance estimation into account. In light of this, we propose STEP, an Adam-aware recipe that learns N:M masks with two phases: first, STEP calculates a reliable variance estimate (precondition phase) and subsequently, the variance remains fixed and is used as a precondition to learn N:M masks (mask-learning phase). STEP automatically identifies the switching point of two phases by dynamically sampling variance changes over the training trajectory and testing the sample concentration. Empirically, we evaluate STEP and other baselines such as ASP and SR-STE on multiple tasks including CIFAR classification, machine translation and LLM fine-tuning (BERT-Base, GPT-2). We show STEP mitigates the accuracy drop of baseline recipes and is robust to aggressive structured sparsity ratios.

Evaluation budgets in agentic retrieval-augmented generation span questions, search trajectories, and repeated answers. We measure allocation precision, reading efficiency, and cost boundaries using a retrieval-feedback comparison on HotpotQA and MuSiQue. At 34.14--34.39M model tokens, broader question coverage lowers standard error by 33\% versus five reads and 12.6\% versus three trajectories. Archived nested and Q-only forecasts predict these allocations within 4.0\% and 3.5\%, respectively. Depth subsets establish no clear forecasting advantage beyond the two-trajectory audit. One-read variance penalties relative to the fitted optimum at the same token budget are 0--9.9\%, with substantial Pro uncertainty. Under recorded model fees, more questions beat more trajectories at search prices of \$0--1 per 1,000 requests; question-versus-read fee rankings remain unresolved. Temperature zero cuts answer disagreement from 14.3\% to 3.4\% while comparison precision stays similar. \par\medskip\noindentKeywords: Agentic RAG; Evaluation budget; Generalizability theory; Repeated sampling.

Many applications involve estimating the mean of multiple binomial outcomes as a common problem -- assessing intergenerational mobility of census tracts, estimating prevalence of infectious diseases across countries, and measuring click-through rates for different demographic groups. The most standard approach is to report the plain average of each outcome. Despite simplicity, the estimates are noisy when the sample sizes or mean parameters are small. In contrast, the Empirical Bayes (EB) methods are able to boost the average accuracy by borrowing information across tasks. Nevertheless, the EB methods require a Bayesian model where the parameters are sampled from a prior distribution which, unlike the commonly-studied Gaussian case, is unidentified due to discreteness of binomial measurements. Even if the prior distribution is known, the computation is difficult when the sample sizes are heterogeneous as there is no simple joint conjugate prior for the sample size and mean parameter. In this paper, we consider the compound decision framework which treats the sample size and mean parameters as fixed quantities. We develop an approximate Stein's Unbiased Risk Estimator (SURE) for the average mean squared error given any class of estimators. For a class of machine learning-assisted linear shrinkage estimators, we establish asymptotic optimality, regret bounds, and valid inference. Unlike existing work, we work with the binomials directly without resorting to Gaussian approximations. This allows us to work with small sample sizes and/or mean parameters in both one-sample and two-sample settings. We demonstrate our approach using three datasets on firm discrimination, education outcomes, and innovation rates.

Deep Learning has revolutionized vision via convolutional neural networks (CNNs) and natural language processing via recurrent neural networks (RNNs). However, success stories of Deep Learning with standard feed-forward neural networks (FNNs) are rare. FNNs that perform well are typically shallow and, therefore cannot exploit many levels of abstract representations. We introduce self-normalizing neural networks (SNNs) to enable high-level abstract representations. While batch normalization requires explicit normalization, neuron activations of SNNs automatically converge towards zero mean and unit variance. The activation function of SNNs are "scaled exponential linear units" (SELUs), which induce self-normalizing properties. Using the Banach fixed-point theorem, we prove that activations close to zero mean and unit variance that are propagated through many network layers will converge towards zero mean and unit variance -- even under the presence of noise and perturbations. This convergence property of SNNs allows to (1) train deep networks with many layers, (2) employ strong regularization, and (3) to make learning highly robust. Furthermore, for activations not close to unit variance, we prove an upper and lower bound on the variance, thus, vanishing and exploding gradients are impossible. We compared SNNs on (a) 121 tasks from the UCI machine learning repository, on (b) drug discovery benchmarks, and on (c) astronomy tasks with standard FNNs and other machine learning methods such as random forests and support vector machines. SNNs significantly outperformed all competing FNN methods at 121 UCI tasks, outperformed all competing methods at the Tox21 dataset, and set a new record at an astronomy data set. The winning SNN architectures are often very deep. Implementations are available at: github.com/bioinf-jku/SNNs.

Designing an optimum portfolio that allocates weights to its constituent stocks in a way that achieves the best trade-off between the return and the risk is a challenging research problem. The classical mean-variance theory of portfolio proposed by Markowitz is found to perform sub-optimally on the real-world stock market data since the error in estimation for the expected returns adversely affects the performance of the portfolio. This paper presents three approaches to portfolio design, viz, the minimum risk portfolio, the optimum risk portfolio, and the Eigen portfolio, for seven important sectors of the Indian stock market. The daily historical prices of the stocks are scraped from Yahoo Finance website from January 1, 2016, to December 31, 2020. Three portfolios are built for each of the seven sectors chosen for this study, and the portfolios are analyzed on the training data based on several metrics such as annualized return and risk, weights assigned to the constituent stocks, the correlation heatmaps, and the principal components of the Eigen portfolios. Finally, the optimum risk portfolios and the Eigen portfolios for all sectors are tested on their return over a period of a six-month period. The performances of the portfolios are compared and the portfolio yielding the higher return for each sector is identified.

Agentic systems are evaluated on benchmarks where agents interact with environments to solve tasks. Most papers report a pass@1 score computed from a single run per task, assuming this gives a reliable performance estimate. We test this assumption by collecting 60,000 agentic trajectories on SWE-Bench-Verified, spanning three models and two scaffolds. We find substantial variance: single-run pass@1 estimates vary by 2.2 to 6.0 percentage points depending on which run is selected, with standard deviations exceeding 1.5 percentage points even at temperature 0. This variance has critical implications: reported improvements of 2--3 percentage points may reflect evaluation noise rather than genuine algorithmic progress. Through token-level analysis, we show that trajectories diverge early, often within the first few percent of tokens, and that these small differences cascade into different solution strategies. To enable reliable evaluation of agentic systems, we recommend three concrete practices: (1) estimate pass@1 from multiple independent runs per task, especially when measuring small improvements, (2) use statistical power analysis to determine the number of runs needed to detect expected effect sizes, and (3) consider metrics like pass@k (optimistic bound) and pass^k (pessimistic bound) with k>1 to better characterize the full performance envelope. While these practices increase evaluation cost, they are essential for distinguishing genuine scientific progress from statistical noise.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

Deep learning methods for unsupervised registration often rely on objectives that assume a uniform noise level across the spatial domain (e.g. mean-squared error loss), but noise distributions are often heteroscedastic and input-dependent in real-world medical images. Thus, this assumption often leads to degradation in registration performance, mainly due to the undesired influence of noise-induced outliers. To mitigate this, we propose a framework for heteroscedastic image uncertainty estimation that can adaptively reduce the influence of regions with high uncertainty during unsupervised registration. The framework consists of a collaborative training strategy for the displacement and variance estimators, and a novel image fidelity weighting scheme utilizing signal-to-noise ratios. Our approach prevents the model from being driven away by spurious gradients caused by the simplified homoscedastic assumption, leading to more accurate displacement estimation. To illustrate its versatility and effectiveness, we tested our framework on two representative registration architectures across three medical image datasets. Our method consistently outperforms baselines and produces sensible uncertainty estimates. The code is publicly available at https://voldemort108x.github.io/hetero_uncertainty/.

Mean Field Variational Inference (MFVI) is widely understood to underestimate posterior variance. By analysing conjugate Bayesian Linear Regression (BLR), we show that this characterization is incomplete: while MFVI underestimates the variance in parameter space, it can overestimate the predictive variance compared to the exact posterior. We show that if the MFVI posterior underestimates predictive variances in some directions, it necessarily overestimates them in others. Crucially, this overestimation occurs in directions where the training data concentrates. This leads to the surprising result that, for a test point drawn from the training distribution, MFVI's expected predictive variance exceeds that of the exact posterior. We demonstrate a pathological case of this effect, where the MFVI posterior fails to reduce predictive variance compared to the prior on in distribution data. We connect these results to the Cold Posterior Effect, arguing that varying the temperature can correct this overestimation, yielding predictions closer to those of the exact posterior. We validate our theory on synthetic and real-world regression tasks.

This paper first answers the question "why do the two most powerful techniques Dropout and Batch Normalization (BN) often lead to a worse performance when they are combined together?" in both theoretical and statistical aspects. Theoretically, we find that Dropout would shift the variance of a specific neural unit when we transfer the state of that network from train to test. However, BN would maintain its statistical variance, which is accumulated from the entire learning procedure, in the test phase. The inconsistency of that variance (we name this scheme as "variance shift") causes the unstable numerical behavior in inference that leads to more erroneous predictions finally, when applying Dropout before BN. Thorough experiments on DenseNet, ResNet, ResNeXt and Wide ResNet confirm our findings. According to the uncovered mechanism, we next explore several strategies that modifies Dropout and try to overcome the limitations of their combination by avoiding the variance shift risks.

Feature Normalization (FN) is an important technique to help neural network training, which typically normalizes features across spatial dimensions. Most previous image inpainting methods apply FN in their networks without considering the impact of the corrupted regions of the input image on normalization, e.g. mean and variance shifts. In this work, we show that the mean and variance shifts caused by full-spatial FN limit the image inpainting network training and we propose a spatial region-wise normalization named Region Normalization (RN) to overcome the limitation. RN divides spatial pixels into different regions according to the input mask, and computes the mean and variance in each region for normalization. We develop two kinds of RN for our image inpainting network: (1) Basic RN (RN-B), which normalizes pixels from the corrupted and uncorrupted regions separately based on the original inpainting mask to solve the mean and variance shift problem; (2) Learnable RN (RN-L), which automatically detects potentially corrupted and uncorrupted regions for separate normalization, and performs global affine transformation to enhance their fusion. We apply RN-B in the early layers and RN-L in the latter layers of the network respectively. Experiments show that our method outperforms current state-of-the-art methods quantitatively and qualitatively. We further generalize RN to other inpainting networks and achieve consistent performance improvements. Our code is available at https://github.com/geekyutao/RN.

Run the same LLM agent on the same task twice: do you get the same behavior? We find the answer is often no. In a study of 3,000 agent runs across three models (Llama 3.1 70B, GPT-4o, and Claude Sonnet 4.5) on HotpotQA, we observe that ReAct-style agents produce 2.0--4.2 distinct action sequences per 10 runs on average, even with identical inputs. More importantly, this variance predicts failure: tasks with consistent behavior (leq2 unique paths) achieve 80--92% accuracy, while highly inconsistent tasks (geq6 unique paths) achieve only 25--60%, a 32--55 percentage point gap depending on model. We trace variance to early decisions: 69% of divergence occurs at step 2, the first search query. Our results suggest that monitoring behavioral consistency during execution could enable early error detection and improve agent reliability.

Deep learning weather models now match numerical weather prediction accuracy while running orders of magnitude faster, but produce deterministic forecasts without uncertainty estimates, a critical gap for high-stakes decisions during extreme weather events. This paper proposes Neural Tangent Kernel-based uncertainty quantification (NTK-UQ) using last-layer empirical features. Theoretical analysis predicts that UQ quality is architecture-dependent through two mechanisms. First, a variance collapse mechanism explains when UQ fails: when the eigenvalue truncation rank approaches the effective rank of the feature space, the GP correction term consumes nearly all prior variance, destroying discrimination between tropical cyclones and routine conditions; architectures with concentrated spectra (spectral operators) require aggressive truncation (k leq 10), while attention-based models tolerate full-rank computation. Second, decomposition performance depends on the non-Gaussian, heavy-tailed structure of extreme weather: Independent Component Analysis exploits higher-order statistics (kurtosis, negentropy) to isolate heavy-tailed extreme-event features, achieving higher discrimination than singular value decomposition, which captures only second-order variance. A data-driven selection rule chooses ICA or SVD from the feature eigenspectrum concentration ratio, correctly prescribing the superior decomposition for all four evaluated architectures. Compared to split conformal prediction (the natural post-hoc baseline), NTK-UQ achieves 31--37\% sharper prediction intervals at 90\% coverage, and uniquely produces adaptive intervals that scale with extreme event severity, which conformal prediction cannot achieve by construction. The framework requires no retraining; inference-time uncertainty requires only a single matrix-vector product per sample.

Strong empirical evidence that one machine-learning algorithm A outperforms another one B ideally calls for multiple trials optimizing the learning pipeline over sources of variation such as data sampling, data augmentation, parameter initialization, and hyperparameters choices. This is prohibitively expensive, and corners are cut to reach conclusions. We model the whole benchmarking process, revealing that variance due to data sampling, parameter initialization and hyperparameter choice impact markedly the results. We analyze the predominant comparison methods used today in the light of this variance. We show a counter-intuitive result that adding more sources of variation to an imperfect estimator approaches better the ideal estimator at a 51 times reduction in compute cost. Building on these results, we study the error rate of detecting improvements, on five different deep-learning tasks/architectures. This study leads us to propose recommendations for performance comparisons.

Based on the weight-sharing mechanism, one-shot NAS methods train a supernet and then inherit the pre-trained weights to evaluate sub-models, largely reducing the search cost. However, several works have pointed out that the shared weights suffer from different gradient descent directions during training. And we further find that large gradient variance occurs during supernet training, which degrades the supernet ranking consistency. To mitigate this issue, we propose to explicitly minimize the gradient variance of the supernet training by jointly optimizing the sampling distributions of PAth and DAta (PA&DA). We theoretically derive the relationship between the gradient variance and the sampling distributions, and reveal that the optimal sampling probability is proportional to the normalized gradient norm of path and training data. Hence, we use the normalized gradient norm as the importance indicator for path and training data, and adopt an importance sampling strategy for the supernet training. Our method only requires negligible computation cost for optimizing the sampling distributions of path and data, but achieves lower gradient variance during supernet training and better generalization performance for the supernet, resulting in a more consistent NAS. We conduct comprehensive comparisons with other improved approaches in various search spaces. Results show that our method surpasses others with more reliable ranking performance and higher accuracy of searched architectures, showing the effectiveness of our method. Code is available at https://github.com/ShunLu91/PA-DA.

Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across splits already predict much of the generated images. To formalize this, we develop a random matrix theory (RMT) framework that quantifies how finite datasets shape the expectation and variance of the learned denoiser and sampling map in the linear setting. For expectations, sampling variability acts as a renormalization of the noise level through a self-consistent relation σ^2 mapsto κ(σ^2), explaining why limited data overshrink low-variance directions and pull samples toward the dataset mean. For fluctuations, our variance formulas reveal three key factors behind cross-split disagreement: anisotropy across eigenmodes, inhomogeneity across inputs, and overall scaling with dataset size. Extending deterministic-equivalence tools to fractional matrix powers further allows us to analyze entire sampling trajectories. The theory sharply predicts the behavior of linear diffusion models, and we validate its predictions on UNet and DiT architectures in their non-memorization regime, identifying where and how samples deviates across training data split. This provides a principled baseline for reproducibility in diffusion training, linking spectral properties of data to the stability of generative outputs.

Understanding the gradient variance of black-box variational inference (BBVI) is a crucial step for establishing its convergence and developing algorithmic improvements. However, existing studies have yet to show that the gradient variance of BBVI satisfies the conditions used to study the convergence of stochastic gradient descent (SGD), the workhorse of BBVI. In this work, we show that BBVI satisfies a matching bound corresponding to the ABC condition used in the SGD literature when applied to smooth and quadratically-growing log-likelihoods. Our results generalize to nonlinear covariance parameterizations widely used in the practice of BBVI. Furthermore, we show that the variance of the mean-field parameterization has provably superior dimensional dependence.

Sequential trial emulation (STE) estimates the effect of a sustained treatment by stacking nested emulated trials with inverse-probability weighting. Additive-hazards STE estimators of the marginal risk difference recommend the nonparametric bootstrap without evaluating its coverage. Using a correctly-specifiable mechanism (up to a small, disclosed residual), we compare analytic and bootstrap standard errors for both estimands. Exploiting the closed-form linearity of the additive-hazards estimating equation, we derive the influence functions and prove the default row-level robust variance inconsistent for the marginal risk-difference curve, and show the same failure empirically for the constant hazard difference: the row-level variance omits a within-subject cross-trial covariance that is positive under a sign condition we verify across our mechanisms, and is anticonservative at every horizon except the first - only there, where the covariance is zero, is the row-level standard error unimpaired. The subject-clustered variance and multiplier bootstrap are consistent for the fixed-weight linearisation and support simultaneous confidence bands, whose measured coverage is 0.88. Across our simulations the model-based and row-level robust intervals are anticonservative and worsen with sample size, coverage falling to 0.71 at n=5000; clustering leaves the constant-hazard-difference coverage near 0.86 at n=5000, and the multiplier bootstrap leaves the risk-difference-curve coverage near 0.90 (0.86 at the longest horizon). The STE constant hazard difference is a design-weighted summary of a time-varying effect, dependent on the trial structure. We illustrate on the Stanford heart transplant data and provide them in the steCI R package.

Hypertension, defined as blood pressure (BP) that is above normal, holds paramount significance in the realm of public health, as it serves as a critical precursor to various cardiovascular diseases (CVDs) and significantly contributes to elevated mortality rates worldwide. However, many existing BP measurement technologies and standards might be biased because they do not consider clinical outcomes, comorbidities, or demographic factors, making them inconclusive for diagnostic purposes. There is limited data-driven research focused on studying the variance in BP measurements across these variables. In this work, we employed GPT-35-turbo, a large language model (LLM), to automatically extract the mean and standard deviation values of BP for both males and females from a dataset comprising 25 million abstracts sourced from PubMed. 993 article abstracts met our predefined inclusion criteria (i.e., presence of references to blood pressure, units of blood pressure such as mmHg, and mention of biological sex). Based on the automatically-extracted information from these articles, we conducted an analysis of the variations of BP values across biological sex. Our results showed the viability of utilizing LLMs to study the BP variations across different demographic factors.

Few-shot industrial anomaly detection requires modeling category-specific normality from only a handful of defect-free images. Common approaches tie inference to stored exemplars, impose rigid linear structure, or risk reproducing anomalous content. Flownomaly instead casts the problem as normal-counterpart recovery in frozen DINOv2 feature space. Given normal supports, a velocity field is learned through conditional flow matching over frozen patch tokens to transport Gaussian noise toward normal features. Along straight paths, a single recovery step using one evaluation of the optimal field yields the posterior mean of the clean normal token without trajectory integration. The operating time governs how strongly recovery modifies a query token. With no anomalous validation samples available for tuning, a normal-only Jacobian gain-to-noise criterion selects this time from the supports alone. Squared residuals between query tokens and their recovered counterparts yield anomaly signals for both dense localization and image-level detection. Across 1-, 2-, and 4-shot benchmarks on MVTec-AD and VisA, together with sample-shot evaluations on Real-IAD, Flownomaly achieves state-of-the-art performance against recent category-specific methods. In the 1-shot setting, image- and pixel-level AUROC reach 97.8% and 98.0% on MVTec-AD and 95.3% and 98.7% on VisA, with a 2.1-point image-level AUROC improvement over the strongest baseline on VisA. Code is available at https://github.com/b-rbmp/Flownomaly.

Recent advances in machine learning have significantly improved prediction accuracy in various applications. However, ensuring the calibration of probabilistic predictions remains a significant challenge. Despite efforts to enhance model calibration, the rigorous statistical evaluation of model calibration remains less explored. In this work, we develop confidence intervals the ell_2 Expected Calibration Error (ECE). We consider top-1-to-k calibration, which includes both the popular notion of confidence calibration as well as full calibration. For a debiased estimator of the ECE, we show asymptotic normality, but with different convergence rates and asymptotic variances for calibrated and miscalibrated models. We develop methods to construct asymptotically valid confidence intervals for the ECE, accounting for this behavior as well as non-negativity. Our theoretical findings are supported through extensive experiments, showing that our methods produce valid confidence intervals with shorter lengths compared to those obtained by resampling-based methods.

We consider in this paper the problem of optimal experiment design where a decision maker can choose which points to sample to obtain an estimate hatβ of the hidden parameter β^{star} of an underlying linear model. The key challenge of this work lies in the heteroscedasticity assumption that we make, meaning that each covariate has a different and unknown variance. The goal of the decision maker is then to figure out on the fly the optimal way to allocate the total budget of T samples between covariates, as sampling several times a specific one will reduce the variance of the estimated model around it (but at the cost of a possible higher variance elsewhere). By trying to minimize the ell^2-loss E [lVerthatβ-β^{star}rVert^2] the decision maker is actually minimizing the trace of the covariance matrix of the problem, which corresponds then to online A-optimal design. Combining techniques from bandit and convex optimization we propose a new active sampling algorithm and we compare it with existing ones. We provide theoretical guarantees of this algorithm in different settings, including a O(T^{-2}) regret bound in the case where the covariates form a basis of the feature space, generalizing and improving existing results. Numerical experiments validate our theoretical findings.

This paper investigates an important problem of an appropriate variance-covariance matrix estimation in the Modern Portfolio Theory. We propose a novel framework for variancecovariance matrix estimation for purposes of the portfolio optimization, which is based on deep learning models. We employ the long short-term memory (LSTM) recurrent neural networks (RNN) along with two probabilistic deep learning models: DeepVAR and GPVAR to the task of one-day ahead multivariate forecasting. We then use these forecasts to optimize portfolios of stocks and cryptocurrencies. Our analysis presents results across different combinations of observation windows and rebalancing periods to compare performances of classical and deep learning variance-covariance estimation methods. The conclusions of the study are that although the strategies (portfolios) performance differed significantly between different combinations of parameters, generally the best results in terms of the information ratio and annualized returns are obtained using the LSTM-RNN models. Moreover, longer observation windows translate into better performance of the deep learning models indicating that these methods require longer windows to be able to efficiently capture the long-term dependencies of the variance-covariance matrix structure. Strategies with less frequent rebalancing typically perform better than these with the shortest rebalancing windows across all considered methods.

Variance reduction (VR) techniques have contributed significantly to accelerating learning with massive datasets in the smooth and strongly convex setting (Schmidt et al., 2017; Johnson & Zhang, 2013; Roux et al., 2012). However, such techniques have not yet met the same success in the realm of large-scale deep learning due to various factors such as the use of data augmentation or regularization methods like dropout (Defazio & Bottou, 2019). This challenge has recently motivated the design of novel variance reduction techniques tailored explicitly for deep learning (Arnold et al., 2019; Ma & Yarats, 2018). This work is an additional step in this direction. In particular, we exploit the ubiquitous clustering structure of rich datasets used in deep learning to design a family of scalable variance reduced optimization procedures by combining existing optimizers (e.g., SGD+Momentum, Quasi Hyperbolic Momentum, Implicit Gradient Transport) with a multi-momentum strategy (Yuan et al., 2019). Our proposal leads to faster convergence than vanilla methods on standard benchmark datasets (e.g., CIFAR and ImageNet). It is robust to label noise and amenable to distributed optimization. We provide a parallel implementation in JAX.

Objective estimators of multimedia quality are often judged by comparing estimates with subjective "truth data," most often via Pearson correlation coefficient (PCC) or mean-squared error (MSE). But subjective test results contain noise, so striving for a PCC of 1.0 or an MSE of 0.0 is neither realistic nor repeatable. Numerous efforts have been made to acknowledge and appropriately accommodate subjective test noise in objective-subjective comparisons, typically resulting in new analysis frameworks and figures-of-merit. We take a different approach. By making only basic assumptions, we derive bounds on PCC and MSE that can be expected for a subjective test. Consistent with intuition, these bounds are functions of subjective vote variance. When a subjective test includes vote variance information, the calculation of the bounds is easy, and in this case we say the resulting bounds are "fully data-driven." We provide two options for calculating bounds in cases where vote variance information is not available. One option is to use vote variance information from other subjective tests that do provide such information, and the second option is to use a model for subjective votes. Thus we introduce a binomial-based model for subjective votes (BinoVotes) that naturally leads to a mean opinion score (MOS) model, named BinoMOS, with multiple unique desirable properties. BinoMOS reproduces the discrete nature of MOS values and its dependence on the number of votes per file. This modeling provides vote variance information required by the PCC and MSE bounds and we compare this modeling with data from 18 subjective tests. The modeling yields PCC and MSE bounds that agree very well with those found from the data directly. These results allow one to set expectations for the PCC and MSE that might be achieved for any subjective test, even those where vote variance information is not available.

Monocular normal estimation for transparent objects is critical for laboratory automation, yet it remains challenging due to complex light refraction and reflection. These optical properties often lead to catastrophic failures in conventional depth and normal sensors, hindering the deployment of embodied AI in scientific environments. We propose TransNormal, a novel framework that adapts pre-trained diffusion priors for single-step normal regression. To handle the lack of texture in transparent surfaces, TransNormal integrates dense visual semantics from DINOv3 via a cross-attention mechanism, providing strong geometric cues. Furthermore, we employ a multi-task learning objective and wavelet-based regularization to ensure the preservation of fine-grained structural details. To support this task, we introduce TransNormal-Synthetic, a physics-based dataset with high-fidelity normal maps for transparent labware. Extensive experiments demonstrate that TransNormal significantly outperforms state-of-the-art methods: on the ClearGrasp benchmark, it reduces mean error by 24.4% and improves 11.25° accuracy by 22.8%; on ClearPose, it achieves a 15.2% reduction in mean error. The code and dataset will be made publicly available at https://longxiang-ai.github.io/TransNormal.

Generalist Anomaly Detection (GAD) aims to train a unified model on an original domain that can detect anomalies in new target domains. Previous GAD methods primarily use only normal samples as references, overlooking the valuable information contained in anomalous samples that are often available in real-world scenarios. To address this limitation, we propose a more practical approach: normal-abnormal-guided generalist anomaly detection, which leverages both normal and anomalous samples as references to guide anomaly detection across diverse domains. We introduce the Normal-Abnormal Generalist Learning (NAGL) framework, consisting of two key components: Residual Mining (RM) and Anomaly Feature Learning (AFL). RM extracts abnormal patterns from normal-abnormal reference residuals to establish transferable anomaly representations, while AFL adaptively learns anomaly features in query images through residual mapping to identify instance-aware anomalies. Our approach effectively utilizes both normal and anomalous references for more accurate and efficient cross-domain anomaly detection. Extensive experiments across multiple benchmarks demonstrate that our method significantly outperforms existing GAD approaches. This work represents the first to adopt a mixture of normal and abnormal samples as references in generalist anomaly detection. The code and datasets are available at https://github.com/JasonKyng/NAGL.

In this paper I investigate the effect of random seed selection on the accuracy when using popular deep learning architectures for computer vision. I scan a large amount of seeds (up to 10^4) on CIFAR 10 and I also scan fewer seeds on Imagenet using pre-trained models to investigate large scale datasets. The conclusions are that even if the variance is not very large, it is surprisingly easy to find an outlier that performs much better or much worse than the average.

Normalizing Flows (NFs) learn invertible mappings between the data and a Gaussian distribution. Prior works usually suffer from two limitations. First, they add random noise to training samples or VAE latents as data augmentation, introducing complex pipelines including extra noising and denoising steps. Second, they use a pretrained and frozen VAE encoder, resulting in suboptimal reconstruction and generation quality. In this paper, we find that the two issues can be solved in a very simple way: just fixing the variance (which would otherwise be predicted by the VAE encoder) to a constant (e.g., 0.5). On the one hand, this method allows the encoder to output a broader distribution of tokens and the decoder to learn to reconstruct clean images from the augmented token distribution, avoiding additional noise or denoising design. On the other hand, fixed variance simplifies the VAE evidence lower bound, making it stable to train an NF with a VAE jointly. On the ImageNet 256 times 256 generation task, our model SimFlow obtains a gFID score of 2.15, outperforming the state-of-the-art method STARFlow (gFID 2.40). Moreover, SimFlow can be seamlessly integrated with the end-to-end representation alignment (REPA-E) method and achieves an improved gFID of 1.91, setting a new state of the art among NFs.

Benchmarks measure whether a model is correct. They do not measure whether a model is reliable. This distinction is largely academic for single-shot inference, but becomes critical for agentic AI systems, where a single rephrased prompt can trigger cascading failures in multi-step execution. Yet this form of instability is not captured by existing evaluations. Hallucinations live in variance: they arise when semantically equivalent prompts activate inconsistent internal pathways, producing divergent outputs. Consistent but incorrect outputs reflect bias or missing knowledge; confident guessing reflects calibration failure. Neither constitutes hallucination under this definition. When error is variance-dominated, reducing redundant pathways improves reliability without adding knowledge. We formalize this through Semantic Stability (SS), measured via Paraphrase Consistency (PC@k): generate k paraphrases, greedy decode each, compute mode agreement. SS is a diagnostic for variance-driven unreliability, not a method for improving correctness. We show that a dense Qwen3-0.6B agrees with itself only 23.8% of the time; at 32% sparsity, agreement jumps to 55.9%. A phase diagram reveals the sweet spot where variance reduction outpaces bias accumulation, and regimes where stability collapses onto wrong answers.

Benchmark contamination is diagnosed with n-gram overlap, likelihood-based membership inference, or canary strings, and each needs something usually unavailable: the training corpus, a well-chosen test statistic, or foresight at release. A recent alternative reads it off a linear probe on internal activations. We show the natural way to do this does not work, specify one that survives measurement, then find that the correction making it work carries more variance than the null it is tested against. The protocol reports a zero-sum contrast on the depth profile of probe accuracy, recentred on a level-matched placebo baseline, tested against a label-permutation null, with the reference set twice the size of the suspect set. Each choice replaces a simpler alternative we rejected on measurement. Reporting the level of excess separability rather than its shape makes the false positive rate track the size of the analyst's own control set, 0.03 to 0.99 under a true null. Contrasting against a flat depth profile rejects a true null 0.72 of the time when surface decodability rises with depth, and loses all power when it falls. On real transformers the protocol fails a test the simulations did not pose. The recentring subtracts an estimate, and the permutation null holds it fixed. Re-estimated across split seeds on four audits of contaminated checkpoints, its standard deviation is 1.30 to 1.56 times the null's own in every arm: what is subtracted to remove a bias is more variable than what it corrects. The one nominally significant result, p = 0.0075, becomes 0.0745 once that variance is propagated, and no verdict is issued. The simulations missed this because their surface key is the covariate driving item variation; on real text it is a proxy, and degrading key quality in simulation reproduces it. We add a companion measurement and a widened null. No arm shows contamination.

High-dimensional mean testing is challenging under strong dependence and heavy tails, since classical Hotelling statistics are ill posed and regularized versions based on sample moments remain sensitive to outliers. This paper develops a robust regularized Hotelling framework for one-sample mean inference under elliptical distributions. The proposed HRST statistic combines a Hettmansperger-Randles spatial location estimator with the inverse of a trace-normalized shrinkage Tyler scatter matrix, and calibrates the resulting quadratic form through ridge-resolvent random-matrix theory rather than sparse covariance or precision-matrix assumptions. In the regime p/nto yin(0,infty), allowing a vanishing lower bulk edge and finite-rank diverging spikes, we establish feasible asymptotic normality for each shrinkage level, derive local-alternative distributions with explicit noncentrality parameters, and prove joint Gaussian limits over finite shrinkage grids. These results justify an adaptive Cauchy combination test across shrinkage levels. Simulations and a paired tumor-normal gene-expression study show that HRST maintains size and improves robustness under heavy-tailed distributions while retaining power under strong correlation.

We investigate stochastic combinatorial semi-bandits, where the entire joint distribution of outcomes impacts the complexity of the problem instance (unlike in the standard bandits). Typical distributions considered depend on specific parameter values, whose prior knowledge is required in theory but quite difficult to estimate in practice; an example is the commonly assumed sub-Gaussian family. We alleviate this issue by instead considering a new general family of sub-exponential distributions, which contains bounded and Gaussian ones. We prove a new lower bound on the expected regret on this family, that is parameterized by the unknown covariance matrix of outcomes, a tighter quantity than the sub-Gaussian matrix. We then construct an algorithm that uses covariance estimates, and provide a tight asymptotic analysis of the regret. Finally, we apply and extend our results to the family of sparse outcomes, which has applications in many recommender systems.

Machine learning for time-series forecasting remains a key area of research. Despite successful application of many machine learning techniques, relating computational efficiency to forecast error remains an under-explored domain. This paper addresses this topic through a series of real-time experiments to quantify the relationship between computational cost and forecast error using meteorological nowcasting as an example use-case. We employ a variety of popular regression techniques (XGBoost, FC-MLP, Transformer, and LSTM) for multi-horizon, short-term forecasting of three variables (temperature, wind speed, and cloud cover) for multiple locations. During a 5-day live experiment, 4000 data sources were streamed for training and inferencing 144 models per hour. These models were parameterized to explore forecast error for two computational cost minimization methods: a novel auto-adaptive data reduction technique (Variance Horizon) and a performance-based concept drift-detection mechanism. Forecast error of all model variations were benchmarked in real-time against a state-of-the-art numerical weather prediction model. Performance was assessed using classical and novel evaluation metrics. Results indicate that using the Variance Horizon reduced computational usage by more than 50\%, while increasing between 0-15\% in error. Meanwhile, performance-based retraining reduced computational usage by up to 90\% while also improving forecast error by up to 10\%. Finally, the combination of both the Variance Horizon and performance-based retraining outperformed other model configurations by up to 99.7\% when considering error normalized to computational usage.

Upcoming deep galaxy surveys with JWST will probe galaxy evolution during the epoch of reionisation (EoR, 5leq zleq10) over relatively compact areas (e.g. sim 300\,arcmin^2 for the JADES GTO survey). It is therefore imperative that we understand the degree of survey variance, to evaluate how representative the galaxy populations in these studies will be. We use the First Light And Reionisation Epoch Simulations (FLARES) to measure the galaxy bias of various tracers over an unprecedentedly large range in overdensity for a hydrodynamic simulation, and use these relations to assess the impact of bias and clustering on survey variance in the EoR. Star formation is highly biased relative to the underlying dark matter distribution, with the mean ratio of the stellar to dark matter density varying by a factor of 100 between regions of low and high matter overdensity (smoothed on a scale of 14,h^{-1}cMpc). This is reflected in the galaxy distribution --the most massive galaxies are found solely in regions of high overdensity. As a consequence of the above, galaxies in the EoR are highly clustered, which can lead to large variance in survey number counts. For mean number counts Nlesssim 100 (1000), in a unit redshift slice of angular area 300\,arcmin^2 (1.4\,deg^2), the 2-sigma range in N is roughly a factor of four (two). We present relations between the expected variance and survey area for different survey geometries; these relations will be of use to observers wishing to understand the impact of survey variance on their results.

Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of the distribution. In this paper, we focus on improving the ability of normalizing flows to correctly capture the tail behavior and, thus, form more accurate models. We prove that the marginal tailedness of an autoregressive flow can be controlled via the tailedness of the marginals of its base distribution. This theoretical insight leads us to a novel type of flows based on flexible base distributions and data-driven linear layers. An empirical analysis shows that the proposed method improves on the accuracy -- especially on the tails of the distribution -- and is able to generate heavy-tailed data. We demonstrate its application on a weather and climate example, in which capturing the tail behavior is essential.

We bound the excess risk of interpolating deep linear networks trained using gradient flow. In a setting previously used to establish risk bounds for the minimum ell_2-norm interpolant, we show that randomly initialized deep linear networks can closely approximate or even match known bounds for the minimum ell_2-norm interpolant. Our analysis also reveals that interpolating deep linear models have exactly the same conditional variance as the minimum ell_2-norm solution. Since the noise affects the excess risk only through the conditional variance, this implies that depth does not improve the algorithm's ability to "hide the noise". Our simulations verify that aspects of our bounds reflect typical behavior for simple data distributions. We also find that similar phenomena are seen in simulations with ReLU networks, although the situation there is more nuanced.

Layer-sequential unit-variance (LSUV) initialization - a simple method for weight initialization for deep net learning - is proposed. The method consists of the two steps. First, pre-initialize weights of each convolution or inner-product layer with orthonormal matrices. Second, proceed from the first to the final layer, normalizing the variance of the output of each layer to be equal to one. Experiment with different activation functions (maxout, ReLU-family, tanh) show that the proposed initialization leads to learning of very deep nets that (i) produces networks with test accuracy better or equal to standard methods and (ii) is at least as fast as the complex schemes proposed specifically for very deep nets such as FitNets (Romero et al. (2015)) and Highway (Srivastava et al. (2015)). Performance is evaluated on GoogLeNet, CaffeNet, FitNets and Residual nets and the state-of-the-art, or very close to it, is achieved on the MNIST, CIFAR-10/100 and ImageNet datasets.

We study the problem of mapping parameter-space variance of a 3D Morphable Model (3DMM) to per-vertex variance. Traditionally, per-vertex variance has been used to visually interpret the learnt parameter uncertainty. However, mapping parameter-space variance to per-vertex using sampling or error propagation is computationally expensive. We address this limitation with Closed-form Local Uncertainty Estimation (CLUE), which transforms the parameter-space distribution of 3DMMs to per-vertex through a closed-form approximation. CLUE emerges from applying the law of total variance to the 3DMM formulation and is modular, computationally inexpensive, and accurate. Subsequently, we study integrating CLUE for in-the-wild human mesh recovery training and inference. We note that CLUE uses the geometry of the mesh as an inductive bias when predicting the variance, leading to improved accuracy. Through extensive qualitative and quantitative experiments, we show that when used in training, CLUE (1) outpeforms probabilistic and deterministic baselines on metrics evaluating joints, mesh and uncertainty, and (2) has the highest uncertainty-to-error spearman correlation, with applications including data mining and interpretable uncertainty. Finally, we share SAM 3D Body (CLUE) which augments the regressor with high resolution uncertainty maps. We make our code available at https://github.com/vita-epfl/CLUE

In this paper, we propose a dimensionless anomaly detection method for multivariate streams. Our method is independent of the unit of measurement for the different stream channels, therefore dimensionless. We first propose the variance norm, a generalisation of Mahalanobis distance to handle infinite-dimensional feature space and singular empirical covariance matrix rigorously. We then combine the variance norm with the path signature, an infinite collection of iterated integrals that provide global features of streams, to propose SigMahaKNN, a method for anomaly detection on (multivariate) streams. We show that SigMahaKNN is invariant to stream reparametrisation, stream concatenation and has a graded discrimination power depending on the truncation level of the path signature. We implement SigMahaKNN as an open-source software, and perform extensive numerical experiments, showing significantly improved anomaly detection on streams compared to isolation forest and local outlier factors in applications ranging from language analysis, hand-writing analysis, ship movement paths analysis and univariate time-series analysis.

We propose Delta L Normalization, a simple yet effective loss aggregation method tailored to the characteristic of dynamic generation lengths in Reinforcement Learning with Verifiable Rewards (RLVR). Recently, RLVR has demonstrated strong potential in improving the reasoning capabilities of large language models (LLMs), but a major challenge lies in the large variability of response lengths during training, which leads to high gradient variance and unstable optimization. Although previous methods such as GRPO, DAPO, and Dr. GRPO introduce different loss normalization terms to address this issue, they either produce biased estimates or still suffer from high gradient variance. By analyzing the effect of varying lengths on policy loss both theoretically and empirically, we reformulate the problem as finding a minimum-variance unbiased estimator. Our proposed Delta L Normalization not only provides an unbiased estimate of the true policy loss but also minimizes gradient variance in theory. Extensive experiments show that it consistently achieves superior results across different model sizes, maximum lengths, and tasks. Our code will be made public at https://github.com/zerolllin/Delta-L-Normalization.

We consider the convergence of the ESD for non-Hermitian random band matrices with independent entries to the circular law, which is the uniform measure on the unit disk in the center of the complex plane. We assume that the bandwidth of the matrix scales like n^γ for some γin(0,1], where n is the matrix size, and the variance profile of the matrix is only assumed to be doubly stochastic with no additional assumption on its specific mixing properties. We prove that the circular law limit holds either (1) when γ>5{6} and the entries are independent Gaussians, (2) or when γ>8{9} and the entries are independent subgaussian random variables. This new threshold improves the previous threshold γ>32{33} which was only proven for block band matrices and periodic band matrices. After the initial version of this paper, the author further extended the range of circular law for much smaller values of γ in 2508.18143 and 2511.01744 when the variance profile has specific mixing properties, but not for an arbitrary doubly stochastic variance profile. Thus the main contribution of this paper is the circular law for a genuine power law bandwidth for any doubly stochastic variance profile. We also prove an extended form of product circular law with a growing number of matrices. Weak delocalization estimates on eigenvectors are also derived. The new technical input is new polynomial lower bounds on some intermediate small singular values, and this estimate does not depend on the specific structure of the variance profile beyond the fact that it is doubly stochastic.

Normalised citation counts are routinely used to assess the average impact of research groups or nations. There is controversy over whether confidence intervals for them are theoretically valid or practically useful. In response, this article introduces the concept of a group's underlying research capability to produce impactful research. It then investigates whether confidence intervals could delimit the underlying capability of a group in practice. From 123120 confidence interval comparisons for the average citation impact of the national outputs of ten countries within 36 individual large monodisciplinary journals, moderately fewer than 95% of subsequent indicator values fall within 95% confidence intervals from prior years, with the percentage declining over time. This is consistent with confidence intervals effectively delimiting the research capability of a group, although it does not prove that this is the cause of the results. The results are unaffected by whether internationally collaborative articles are included.