Loss Function

Medical image segmentation is a crucial task in the field of clinical analysis and applications. Though deep learning techniques recently play a crucial role in several scenarios, the training at the individual pixel level leads to a lack of geometric prior information. Scholars proposed to integrate the Chan-Vese model into the loss function for training which can take into account the region and length of the region inside and outside the segmentation process and then improve the performance in medical image segmentation. However, these methods still lack an effective characterization of the segmented region. To overcome this problem, we introduce the mean curvature as a geometric natural constraint and propose a Deep Active Contour and Mean Curvature (DACMC) loss function where the convolution kernel is used to approximate the mean curvature to save computational cost. We have validated the performance of our method on the liver and spleen dataset. Our proposed method demonstrates new state-of-the-art performance on several segmentation datasets.

Multi-task model merging combines separately trained expert models into a single model that handles all tasks without co-training. Standard practice merges experts at their optimal validation loss. We challenge this convention by systematically studying how training duration of domain experts affects the quality of the merged model. We fine-tune experts on five domains (Math, Code, Instruction Following, Multilingual, and Safety) across three model sizes (Qwen 3.5 0.8B, 2B, and 4B), saving checkpoints from 25% to 500% of the optimal training steps and evaluating five merging methods at each duration. Our findings reveal a striking method-dependent pattern: simple averaging degrades sharply with overfitting, while sparsification-based methods achieve their best performance well past the validation optimum. We formalize this through bias-variance decomposition analysis, drawing a parallel to random forests where averaging benefits from high-variance individual learners. These results suggest that training duration and merging method should be chosen jointly rather than independently.

Federated learning distributes data among $n$ clients, making it vulnerable to malicious attacks and data heterogeneity, which together pose challenges for robust learning. To tackle this issue, centered clipping and Huber aggregators have been exploited for Byzantine robustness. In this paper, we first demonstrate their equivalence via convex conjugate theory, and show that they can yield biased solutions in the presence of outliers, leading to failure under high data heterogeneity and a substantial fraction of outliers. Next, we propose a new robust aggregation rule that utilizes the truncated-quadratic (TQ) loss, effectively mitigating the biases of existing methods, such as centered clipping and Huber aggregators. We show that our aggregator achieves order-optimal Byzantine-robust learning under nonconvex loss functions and heterogeneous data, ultimately enhancing the reliability of federated learning systems. Additionally, we provide a robust deviation estimation strategy for TQ, demonstrating its effectiveness. Furthermore, we show that TQ maintains robustness even when only an estimate of the number of Byzantine clients is available. Finally, experimental results on MNIST, Fashion-MNIST, and CIFAR-10, indicate that our aggregator provides better robustness performance than the competing techniques.

Vietnam's ethnic minority languages are almost absent from the field of Natural Language Processing (NLP), and the challenge goes beyond data scarcity: Cham, Khmer, and Tay-Nung differ sharply in script, Vietnamese contact, and standardization, conditions under which standard multilingual adaptation can learn the wrong signals. We introduce CKTN, the first corpus and benchmark for these languages (44,367 documents, 24M subword tokens), spanning continued pretraining, category classification, and summary-document retrieval. We show that existing multilingual encoders severely fragment these languages, and that common adaptation metrics can mislead: models may lower language-modeling loss or excel at lexical-overlap retrieval while still failing at semantic generalization across documents. We address this with a script-aware adaptation recipe - vocabulary augmentation combined with calibrated replaced-token pretraining - that prevents the discriminator from exploiting trivial script mismatches. The result is an encoder with substantially less fragmentation and the strongest classification performance among evaluated models, exposing the limits of lexical-overlap retrieval as an evaluation signal.

The stationary distribution of reflected Brownian motion (RBM) plays an important role in the analysis of high-dimensional stochastic systems, yet closed-form solutions are known only for a few special cases. Computing important performance metrics, such as tail probabilities, is even more intractable, despite their practical relevance. In this paper, we develop a deep learning approach that accurately and efficiently learns the Laplace transform of high-dimensional RBMs based on the basic adjoint relationship (BAR). Our framework combines a careful design of the loss function, training data sampling procedure, and neural network architecture. We evaluate the proposed method on RBM instances with known ground-truth tail probabilities and demonstrate near-perfect prediction in high-dimensional settings, highlighting its potential as a general tool for analyzing stochastic systems beyond analytically tractable regimes. Our code can be found at https://github.com/zhangz73/NN4MGF.

In this paper we first study the problem of generalized linear bandit (GLB) under heavy-tailed noise. The characteristics of heavy-tailed distributions are widely observed in real-world applications such as personalized recommendation, financial markets, and medical treatments. Based on the online mirror descent (OMD) method, we propose an algorithm EHM that extends the adaptive Huber loss method (Wang et al., 2025) with one-pass update ($\mathcal{O}(1)$ computational complexity with respect to current round $t$ and the time horizon $T$), which simultaneously achieves an almost optimal regret of $\widetilde{\mathcal{O}}(T^{\frac{1}{1+ε}})$ where $T$ is the time horizon. In addition, by utilizing a special property of some link function (Sawarni et al., 2025), our algorithm eliminates the need to know a commonly used parameter. Next, we study the GLB problem under the case when contextual characteristic becomes piecewise constant, and we slightly revised former algorithm to obtain the PGLB-EHM algorithm. After theoretical analysis, we prove that the regret upper bound order stays the same. Furthermore, we look deeper into a special case of nonlinear bandit (NB) and present the NB-EHM algorithm with bisection method and special restriction. Eventually we utilize the affine lifting approach and show that the general NB problem can be applied with NB-EHM to achieve a sublinear regret bound.

Self-paced learning (SPL) is an effective learning paradigm that simulates the human learning process by progressing from easy to difficult samples based on the value of the loss function during the learning process. It has shown great potential in improving model performance and training efficiency. However, the prediction results of samples with smaller loss values are not necessarily reliable, indicating that such samples are not always simple samples for the model. Hence, this article proposes an uncertainty-aware self-paced learning based on evidential neural networks, termed UASPL, which integrates predictive reliability into sample selection through a general loss function within the Subjective Logic framework. This loss function incorporates uncertainty estimation and can be extended to different variants of SPL. Moreover, this loss function couples a sample selection preference, thereby ensuring the interpretability of the sample selection process. Finally, the experimental results on multiple datasets show that UASPL outperforms other SPL methods in terms of classification performance, interpretability, and generality. The source code is available at: https://github.com/treelife979/UASPL.

Echocardiography is the first imaging modality used for assessing cardiac function, and accurate segmentation of cardiac structures is essential for deriving biomarkers. However, the development of effective automated segmentation models for multiple cardiac structures is challenged by the difficulty of training on datasets from different sources that are often partially-labelled. This study aims to address this challenge by evaluating the performance of three loss functions - adaptive categorical cross entropy (aCCE) loss, marginal loss, and the adaptive binary cross entropy (aBCE) loss - in handling partially-labelled data. We conduct a comprehensive comparison of these loss functions across multiple scenarios and network architectures: intra-domain and inter-domain tasks, with both single and multiple partial-labels, and varying proportions of fully-labelled to partially-labelled data. Our experiments reveal that all three loss functions exhibit strong performance in intra-domain segmentation tasks, effectively handling label variations within the same domain. For inter-domain tasks, where models are trained on datasets with a domain shift, the aBCE and marginal losses show superior performance when dealing with the case of one label being missing from some training examples. In scenarios involving more than one label being missing, marginal loss outperforms the other methods, demonstrating its robustness in such complex conditions. These results highlight the strengths of each loss function depending on the labelling scenario, emphasizing the importance of selecting the appropriate loss function to optimize model performance. This study represents the first investigation of techniques for handling partially-labelled data from multiple different domains in echocardiography segmentation and provides a comprehensive comparison of loss-based solutions.

The Gaussian Error Linear Unit is usually motivated as the expected output of an input-dependent Bernoulli gate. This work gives an alternative interpretation: GELU is the expected output of a hard linear gate with a Gaussian random threshold. This view provides a generative interpretation for the Bernoulli gate: the gate opens once the input clears a latent Gaussian threshold. This interpretation stems from a decomposition based on well-known results in stochastic inventory theory and leads to a threshold-transmission family that includes ReLU, GELU, SiLU/Swish, and hard swish as special cases. By considering a latent uniform threshold, we recover a hard-swish-like piecewise-polynomial gate whose nonlinear transition is confined to a finite interval, yielding fixed- and learned-width variants. Controlled experiments on compact vision and language models show that calibrated or learned uniform-threshold gates are consistently competitive with GELU, ReLU, and SiLU/Swish, improve over them in most tested settings, and use the finite transition region nontrivially.

Image encoders trained with LeJEPA can deliver strong features for downstream tasks, but, like other image-level self-supervised methods, typically require large training datasets. Aligning representations at the level of objects rather than whole scenes promises greater data efficiency, but doing this in a completely self-supervised way, effectively jointly partitioning a scene and representing its objects, is unstable: the two are locked in a cyclic dependency, partitioning requires meaningful representations, while meaningful representations require consistent partitioning. We sidestep this instability by taking object masks as given during training, using cheap, off-the-shelf SAM proposals. We extend LeJEPA - whose distributional anti-collapse objective ports naturally from whole images to variable-sized sets of objects - to align object-centric representations rather than whole images. An additional instance-separating loss, which treats other objects in the same scene as negatives, further boosts downstream performance. Across two model scales and 10-100% of COCO, object-level LeJEPA outperforms image-level LeJEPA on tracking (DAVIS), classification (ImageNet-1k), segmentation (ADE20k), and re-identification (NAVI).

Most existing multitask learning approaches are limited by their reliance on task-specific loss functions tailored to the scale and type of each outcome. When outcomes differ across tasks, these losses are generally not directly comparable, which makes it difficult to formulate a unified objective and may limit information sharing across tasks. We propose a multitask transformation framework in which task-specific responses may differ through unknown monotone transformations. Motivated by high-dimensional biological applications in which the predictor dimension may diverge with the sample size while only a common subset of predictors is informative, we consider shared sparsity across tasks. Under this framework, we estimate the target functions and identify important predictors by optimizing a smoothed rank-based criterion with a group-Lasso penalty, implemented through a multitask deep neural network with a shared first layer. We establish the nonasymptotic excess-risk bounds, and variable-selection consistency for the proposed estimator. Simulation studies show that the proposed method achieves competitive prediction and variable-selection performance compared with competing approaches. Analyses of gene-expression studies with continuous, binary, and mixed outcomes further illustrate that the proposed method improves prediction and identifies biologically meaningful shared predictors.

Deep learning is widely applied in medical image analysis, but up to 10% of manually labelled images may be incorrect, degrading model performance. This paper proposes an automated method to identify incorrectly labelled medical images by analyzing sequences of loss functions from deep learning classification networks over multiple training epochs. Identified images can be reviewed and relabelled by experts, improving dataset quality and model performance. Two experiments validate the method on a fundus image dataset for referable diabetic retinopathy screening. In the first, 6% (648) of 10,788 gold-standard labels were intentionally flipped. The method identified 75.31% (488) of the flipped samples, with only 4.85% (492) false positives among correctly labelled samples. In the second, reviewing and correcting the 980 identified samples (9.1% of the dataset) and retraining the model improved best accuracy on an independent test set from 95.93% (with 6% label noise) to 96.50% (with 1.5% noise), approaching the ideal 96.57% (with 0% noise). The results demonstrate the method's effectiveness in improving model performance through automated label quality control.

Single image super-resolution aims to reconstruct high-resolution (HR) images from low-resolution (LR) inputs. Training SR models typically requires paired HR-LR data, which is difficult to obtain in reality. As a result, most methods synthesize LR images by artificially degrading HR images with handcrafted kernels or camera ISP adjustments. However, these synthetic degradations fail to capture the complexity of real LR images, leading to poor generalization in practice. To address this, we observe that even within a single high-quality image, regions at different depths exhibit varying resolutions, where distant regions act as LR patches and closer ones as HR patches. This allows the extraction of real, degradation-induced LR patches from real images. Since these LR patches lack paired HR counterparts, we propose LA-SR (Language Assistant for SR), a novel framework for unpaired SR. The key idea of LA-SR is to redefine unpaired SR in the language space, using vision-language models to bridge the LR-HR gap. LA-SR projects images into a semantically rich space representing both content and quality, and applies two language-guided losses: linguistic content loss to preserve semantic fidelity, and linguistic quality loss to enhance perceptual realism. With this alignment, LA-SR effectively super-resolves real LR inputs, producing realistic outputs that overcome the limitations of synthetic-data-trained methods.

We study binary classification problems whose decision sets are given by definable sets in o-minimal expansions of the real field. Motivated by cell decomposition of definable sets, we introduce traceable sets as a classical proxy for definable decision regions and analyze their approximation by ReLU neural networks. Under uniform bounds on the number of connected components and suitable $C^m$ extensions for the boundary functions, we prove that characteristic functions of traceable subsets of $[-1/2,1/2]^n$ can be approximated in $L^p$ to accuracy $\varepsilon>0$ by ReLU neural networks of size $\mathcal{O}(\varepsilon^{-p(n-1)/m})$, with depth independent of $\varepsilon$ and polynomially bounded weights. This establishes quantitative approximation rates for certain definable collections in o-minimal structures using ReLU neural networks. The same approach also yields the stated approximation rates for a subclass of definable maps $[-1/2,1/2]^n \to \mathbb{R}$. We then combine the approximation capabilities with entropy estimates for ReLU neural network classes to obtain statistical learning rates for empirical risk minimization with hinge loss. For $N$ uniformly distributed samples, the resulting classifiers achieve expected misclassification error of order $N^{-m/(m+pn-p)}$ up to an arbitrarily small polynomial loss.

Source-free domain adaptive object detection adapts a source-trained detector to an unlabeled target domain, typically through teacher-student self-training with pseudo-labels. We revisit this setting when a small, uniformly sampled subset of target images is labeled. We introduce Random-Target Supervised Mixing (RTSM), a simple anchor that incorporates these annotations through a supervised detection loss while leaving the original unlabeled adaptation branch unchanged. Across evaluations spanning four SFDA-OD methods, two object detectors, multiple adaptation tasks, and target-label budgets from 1% to 10%, RTSM consistently improves pure SFDA by 1.7 to 18.3 AP50. We then examine whether the same annotations can provide further gains by steering unlabeled self-training. To this end, we evaluate ten sparse-label feedback plugins covering pseudo-label selection, object completion, and optimization control, which yield limited and method-dependent gains over RTSM. These results reveal a bitter lesson for sparse-label SFDA-OD: simple supervision is hard to beat. RTSM therefore provides a simple yet effective anchor for sparse-label SFDA-OD.

Contrastive embedding models trained with scale-invariant losses are typically paired with distance metrics like cosine similarity, effectively ignoring embedding magnitudes. However, surprisingly, empirical studies reveal that despite this, these "discarded" norms seem to correlate with semantic properties such as concept specificity, token frequency, and human uncertainty. In this work, we provide a formal theoretical framework explaining this phenomenon. By analyzing the optimization dynamics, we derive an analytic formula demonstrating that embedding length naturally encodes this information as a byproduct of the training process. We also show how this gives rise to signals that can serve as "free" calibration tools in specific models and retrieval tasks, providing a grounded explanation for a previously heuristic observation.

Real-world evaluation is the gold standard for robot policies because it tests them against the physical conditions and deployment challenges they are ultimately designed to handle. However, real-world evaluation is also the bottleneck for iterating on robot policies: it is costly, difficult to reproduce, and often too sparse to reliably compare nearby model variants. A straightforward proxy for performance is validation loss on expert demonstrations, but this proxy is often poorly correlated with real-world performance. In this paper, we introduce Critical Interval MSE (CI-MSE), an intuitively simple yet effective offline validation metric. CI-MSE restricts error computation to task-critical segments and pairs it with simple action-alignment procedures that better match rollout-time behavior. Across simulation and real-world experiments, CI-MSE yields a stronger correlation between validation error and rollout performance than raw MSE. Across a wide range of policy checkpoints, CI-MSE achieves a Spearman's rank correlation of $-0.87$, much closer to the ideal value of $-1$ than raw MSE's $-0.61$, demonstrating a significant improvement. We show through sensitivity analysis that our metric is robust to a wide range of hyperparameters. We further study the effectiveness of CI-MSE under evaluation distribution shifts and suggest design boundaries when using this metric. In summary, this paper provides a simple and reliable offline validation tool for accelerating policy iteration. Project webpage: https://ci-mse.github.io/

Language model loss follows remarkably regular scaling laws over model and data size, yet it remains unclear why the aggregate loss should exhibit a power-law form. Existing explanations often attribute this regularity to a heavy-tailed spectrum of pattern difficulty in natural language, but this view has not been directly validated at token-level granularity in large-scale real-data training. We present a token-level framework that decomposes scaling laws into localized learning events of individual contextualized tokens. By fitting token loss trajectories with sigmoids, we show that token learning is concentrated in localized transitions, giving rise to a learning-time spectrum that dominates the scaling-law shape. Across more than one hundred pre-training runs on large and diverse real-language corpora with modern LLM architectures, scaling up to 6B parameters and 300B training tokens, the measured learning-time spectrum quantitatively reconstructs the validation loss derivative along the training-step $T$, data-scale $D$, and model-scale $M$ axes. We further show that the same signal is actionable: by reshaping the training distribution according to when tokens become learnable, we alter the optimization trajectory and achieve 11% faster validation-loss reduction. These results provide direct empirical evidence that scaling laws are governed primarily by the distribution of token-level learning times, and that this distribution can be used not only to explain scaling behavior but also to improve training performance.

Machine learning for underwater acoustics is constrained by the scarcity of publicly available labeled datasets. In contrast to air-acoustic domains, where large benchmarks enable rapid model development, underwater datasets are typically small and limited in acoustic diversity, restricting robust model training and cross-domain generalization. To help address this gap, we introduce a curated underwater audio dataset derived from an open-source maritime sound archive. The dataset contains over one thousand labeled audio segments across eight biologically and mechanically relevant acoustic classes, providing an additional resource for training models in data-limited underwater environments. Additionally, we establish a lightweight Convolutional Neural Network (CNN) baseline and propose a margin-enhanced loss with feature alignment to mitigate class confusion arising from data imbalance, acoustic similarity, and cross-domain mismatch. While the baseline achieves 96.35% in-domain accuracy, evaluation on ShipsEar reveals substantial domain shift; the proposed feature alignment improve zero-shot ship detection by 42.60%, demonstrating stronger robustness under distribution mismatch. We further release a transparent curation pipeline and reproducible benchmark to support future research on imbalance mitigation, domain adaptation, and data-efficient underwater acoustic classification.

Automated classification of marine species from underwater imagery is essential for scalable ocean biodiversity monitoring and conservation policy. Existing approaches struggle with severe domain shift across collection platforms, fine-grained visual similarity between closely related species, and uneven annotation granularity, where many specimens can only be identified to genus or a coarser taxonomic rank. We present a taxonomy-aware deep learning framework that aligns both the training loss and the inference rule with the hierarchical structure of biological classification, combining a taxonomy-weighted loss, minimum-risk Bayesian inference, multi-scale feature encoding, and independent per-rank classification heads. Evaluated on the FathomNet 2025 dataset1 (79 marine classes across seven taxonomic ranks), the system achieves a mean taxonomic distance of 1.581, within 3% of the 1st-place solution (1.535), with the largest gains from metric-aligned inference and simple, decoupled components that generalize better than learned dependencies under distribution shift.

Deep learning approaches to biometric verification are commonly trained by optimizing indirect objectives, creating a misalignment between the optimization process and the primary evaluation metric, typically the Equal Error Rate (EER). This paper introduces EERLoss: a subdifferentiable, arbitrarily accurate approximation to EER for training deep biometric models. Furthermore, this framework has the potential to be adapted to optimize any specific operating point on the DET curve, enhancing its generalizability. To validate this approach, EERLoss is evaluated on a particularly demanding behavioral biometric modality: keystroke dynamics verification. This task is characterized by its high intra-class and low inter-class variability. Experiments are conducted on the large-scale KVC-onGoing benchmark, incorporating data from over 185,000 subjects across different scenarios. A comprehensive ablation study initially demonstrates the superiority of EERLoss in comparison to existing state-of-the-art loss functions. It also converges substantially faster compared to other losses, reducing the overall training cost. Additionally, a comparison is made between the proposed loss and the KVC-winning architecture by re-training it with EERLoss, demonstrating that the proposed approach significantly outperforms the original SoTA, achieving a relative EER reduction of up to approx. 30%. This improvement on a challenging, large-scale benchmark validates the effectiveness of EERLoss as a task-aligned training objective specifically suited for high-variance biometric traits.

Accurate particulate matter (PM) prediction is crucial for mitigating air pollution. Graph Neural Networks (GNNs) effectively model spatiotemporal dependencies, but predefined graphs limit adaptability, and some datasets complicate learning. This study introduces a graph construction method based on a confusion matrix from a supervised learning process to dynamically capture inter-class relationships. Additionally, a hybrid loss function that combines energy distance and Huber loss is applied to address the vanishing gradient problem and improve learning stability. The approach is evaluated using air pollution data from the University of Utah AirU Pollution Monitoring Network in Salt Lake City, UT, with five GNN models: Graph Convolutional Networks (GCNs), Simple Graph Convolutional Networks (SGConv), Graph Isomorphism Networks (GINs), Graph Attention Networks (GATs), and GraphSage. The experimental results of single- and multistep predictions confirm that GraphSage achieves the highest accuracy in predicting the concentrations of PM${1}$, PM${10}$, and PM$_{2.5}$ over different time horizons. Furthermore, {\color{black} GNNExplainer (Graph Neural Network Explainer) and PGExplainer (Probabilistic Graph Explainer)} are applied to interpret feature importance and graph structure, ensuring model transparency. Results show improved prediction accuracy, with GNN models outperforming traditional machine learning \textcolor{black}{and deep learning models (i.e., Prophet, Long short-term memory, Gated recurrent units} in air pollution forecasting.

Pruning Large Language Models (LLMs) reduces memory and inference costs by removing parts of the network, producing smaller models that retain most of their accuracy. As attention layers are the most resource-intensive parts of LLMs, pruning them is a promising compression strategy. Prior work shows that up to 33% of attention layers can be pruned with minimal accuracy loss. Nevertheless, the impact of attention pruning on model interpretability, specifically faithfulness and confidence calibration, remains unstudied. To address this gap, we study how pruning attention layers affects explanation faithfulness and confidence calibration across five LLMs and eight datasets. While the pruned models often maintain high accuracy, we find that their faithfulness and calibration often degrade. Notably, faithfulness and calibration can fluctuate significantly, even when accuracy remains stable, highlighting a misalignment between model confidence, interpretability, and accuracy. Our findings suggest that layer pruning can affect LLMs' interpretability and reliability in ways not captured by accuracy and efficiency measures alone. We recommend including explainability and calibration metrics when evaluating pruned models.

Bayesian experimental design (BED) has traditionally been based on maximising expected uncertainty reductions from prior to posterior. A major shortfall of this approach is that it leads to doubly intractable objectives that are difficult to optimise, while customising them to particular downstream tasks of interest can also be difficult. Following first principles decision theory, we demonstrate that BED can alternatively be formulated in terms of an expected future loss (EFL) on downstream actions, providing a simple and naturally task-driven framework. Critically, we then show that all such EFLs can be rearranged into singly intractable objectives that can be jointly optimised with respect to both the design policy and a downstream action policy using stochastic gradients, an approach we refer to as ACTION-BED. This formulation further sidesteps the need for any explicit posterior or marginal likelihood estimation and is naturally implicit, requiring only the ability to sample from the joint model over model parameters and data, and evaluate the downstream loss function. It thus allows design policies to be learned more effectively, efficiently, and simply than existing methods, while providing easy customisation to different downstream tasks and losses.

Medical image segmentation is a fundamental task for medical image processing and computer-assisted intervention, yet data imbalance and small lesion detection pose significant challenges. Dice Loss, which measures the overlap between predicted and ground truth regions, is widely used to mitigate these issues. To further emphasize its properties, we propose Polynomial Dice Loss, a polynomial extension of Dice Loss. Specifically, by leveraging the geometric characteristics of Dice Loss and formulating the loss function as a polynomial representation via Taylor expansion, we enable the adjustment of the contribution of higher-order components to the loss function. In our experiments, we evaluate the proposed method against loss functions derived from conventional Dice and Tversky coefficients. Experimental results and further analysis show that the polynomial formulation provides a simple way to control the loss shape and achieves competitive performance across multiple segmentation settings.

Sample reweighting is a major approach to addressing distribution shifts, such as label noise and class imbalance. Meta-Weight-Net (MW-Net) is a promising sample reweighting network that computes weights based on classification loss. Although MW-Net improves prediction performance under a single type of distribution shift using a simple neural network, its performance degrades when facing both label noise and class imbalance, where it is hard to determine appropriate weights solely from classification loss and using a simple network. In this study, we introduce neural architecture search to MW-Net to mitigate such performance degradation. Using the tree-structured Parzen estimator, we explore the optimal number of hidden layers and nodes and select the most suitable intermediate layer in the classification model to serve as the input for MW-Net. Experimental results on the CIFAR-10 and CIFAR-100 datasets that were modified to include both label noise and class imbalance demonstrate the effectiveness of neural architecture search for MW-Net.

On-policy distillation (OPD) trains an LLM on states induced by the current or recent student policy: the student generates complete or partial rollouts, a teacher or self-teacher scores the resulting tokens under their generated contexts, and dense log-probability, logit, or distributional signals are converted into post-training updates. This survey studies OPD as a feedback-to-update problem rather than a single loss family. We develop a formula-driven taxonomy from two routes -- direct distributional losses and policy-gradient-style log-ratio updates -- and use it to organize core methods, verifier- or outcome-guided hybrids, industrial reports, framework implementations, failure modes, and stabilization recipes under explicit evidence boundaries. The taxonomy shows that OPD effectiveness depends not only on KL direction or teacher access, but also on state compatibility, support construction, temporal credit, vocabulary-level probability routing, gates and weights, and regularization. We further separate two mechanisms often conflated in sampled-token OPD stability discussions. Temporal credit asks how teacher-student log-ratio returns should weight sampled actions across a rollout; vocabulary routing asks where probability mass should move when negative feedback suppresses a sampled token. This distinction yields bias boundaries for immediate, return-to-go, discounted, and baseline-corrected estimators, motivates GAE-OPD as a value-based hypothesis for log-ratio returns, and motivates Counterfactual Routed OPD (CR-OPD) for routing probability mass toward teacher-supported, student-reachable alternatives. We close by mapping actionability diagnostics, failure mechanisms, case studies, open problems, and a reporting checklist onto the same feedback-to-update variables.

Distribution shift between training and deployment is a pervasive challenge for modern AI systems. In many cases, the target marginals of covariates and response are known or specified through population-level observations, boundary conditions, properties of simulator configurations, or alignment-time distributional constraints. Such knowledge may provide valuable side information for regression estimation. We study this problem in the multivariate linear regression setting with a stable conditional mean $E[Y\mid X]$ across source and target, and identify the hybrid-loss estimator, which jointly incorporates both target marginals, as a benchmark target-aware estimator. Its direct computation, however, requires solving a coupled nonlinear optimization that is expensive at scale. Our main contribution is to develop and evaluate two computationally tractable alternatives: a constrained moment-matching estimator and a two-stage estimator that augments ordinary least squares with a calibration step. For all three estimators, we derive and compare closed-form asymptotic mean squared errors, yielding conditions under which the tractable alternatives match or closely approximate the hybrid benchmark, and regimes in which they do not. Monte Carlo experiments across three controlled shift regimes validate the theoretical results, investigate the accuracy-runtime tradeoffs among the three estimators, and translate into guidance on estimator choice. In particular, the two-stage estimator nearly matches the hybrid benchmark in the high signal-to-noise regime at essentially no additional cost, providing theoretical grounding for empirical observations in nonlinear settings.

Adaptive stochastic convex optimization (SCO) methods face a fundamental ``price of adaptivity'' barrier: under the standard set of assumptions, they cannot efficiently adapt to large uncertainty in both the initial distance to optimality and the Lipschitz constant. We circumvent this barrier by requiring a small amount of additional structure common to many learning problems. Specifically, we assume that the objective decomposes into a model and a loss function, enabling us to intervene by modifying the model's output before it passes to the loss function. Under this assumption, we design a method that clips the learned model output in tail events where it deviates too much from the output of a fixed reference model. Our method matches the optimal bounds for known-parameter SCO up to logarithmic factors in the uncertainty in the distance and Lipschitz parameters, thus efficiently adapting to large uncertainty in both.

Identity-Preserving Text-to-Video Generation (IPT2V) seeks to synthesize a temporally coherent video from a reference image and a textual description, while simultaneously preserving the subject's identity and allowing fine-grained control over facial dynamics. Although recent methods such as ID-Animator and ConsisID inject identity features only at inference time, they ignored the ID-irrelevant information contained in Facial embedding, leading to monotonous or inaccurate facial movements that poorly follow the prompt. We introduce Identity-Action Decoupling (IaD) framework as well as two loss function Identity Decoupling Loss and Text Alignment Loss to solve this problem. Without any subject-specific fine-tuning, IaD yields videos that (1) maintain cross-temporal identity consistency and (2) exhibit rich, controllable expressions and scene variations that closely match the input text.

Most real-world datasets used for training supervised learning models are contaminated with noisy data and outliers leading to large prediction errors. This paper proposes a new approach for achieving robustness where the learning rate is modulated by a factor that is sensitive to outliers. In this approach a reduction of the learning rate is shown to be achieved by using alternate loss functions that are infinitely differentiable, strictly convex or quasiconvex and more closely approximate the absolute error than Huber and log-cosh losses. A comparison of the performance of regression models trained with different loss functions on a wide variety of benchmarks and datasets is presented to demonstrate the superior performance of the Square Root Loss (SRL) and Smooth Mean Absolute Error (SMAE) losses proposed in this paper. Two new robust linear regression models are presented. Highly vectorized robust parameter update formulae that take advantage of modern GPUs for both stochastic and batch gradient descent are presented.

Conventional training losses for speech enhancement based on the signal-to-distortion ratio (SDR) treat all time-frequency (TF) regions uniformly, overlooking the fine-grained spectral cues that are relevant to specific phoneme intelligibility. We propose a TF weighting framework that modulates the SDR objective based on local speech presence, speech-to-interference ratio (SIR), and spectral flux. By integrating these factors into a differentiable objective, the framework emphasizes TF bins with high speech-noise competition while also accounting for transient cues such as consonant bursts. Experimental results show that our approach improves objective frequency-weighted enhancement metrics, as well as phoneme recognition accuracy, particularly for consonants. Spectral analysis shows better reconstruction of mid-frequency structures at less adverse SIR.

Despite the success of deep learning, training deep networks in biologically plausible and hardware-efficient ways remains an open challenge. Feedback alignment (FA) methods address this by replacing backpropagation's symmetric backward weights with fixed random matrices, but their effectiveness depends critically on whether they can be accurately evaluated. The standard evaluation relies on two quantities: task accuracy and cosine similarity between the method's credit signal and the backpropagation gradient. We show that this reporting pair is insufficient by identifying two independent failure modes, both silent under current reporting: (1) measurement degeneracy, where the BP reference gradient collapses to the numerical floor in terminal-LayerNorm residual architectures, rendering cosine uninterpretable; and (2) aggregation collapse, where the aggregate cosine masks layerwise heterogeneity that concentrates credit at one end of the network. To address these limitations, we propose a diagnostic evaluation protocol based on three checks -- scale stability, reference validity, and depth utility -- together with per-layer rather than aggregate cosine reporting. Across multiple architectures and methods, the standard reporting pair gives no signal of failure in any audited case, while our protocol identifies all failures with wide calibration margins. The two failure modes are causally independent: a per-block scale penalty alleviates Mode 1 (residual scale explosion driving reference collapse) without affecting Mode 2 (cosine ranking that contradicts every functional metric we measured). Identifying these silent failures prevents researchers from building on non-functional credit assignment and provides actionable guidance for developing FA methods that genuinely train deep layers.

In multi-task learning, handling an increasing number of objectives can quickly become challenging, both in terms of the computational resources and the decision maker's capacity to choose appropriate trade-offs. A widely used approach is thus to aggregate the individual losses in a single loss function by a weighted sum. This often fails to capture either the decision maker's preferences as a result of the shape of the Pareto front, or requires multiple adjustments and computations which becomes prohibitively expensive in deep learning applications. To address these issues, we introduce a novel framework, Preference Pareto Exploration (PPE), which enforces the decision maker's preferences while accounting for the geometry of the Pareto set in an interactive exploration process. PPE is based on a predictor-corrector method that performs predictor steps tangential to the manifold of Pareto-optimal solutions, following the decision maker's preference. The subsequent corrector step results in a new trade-off reflecting this preference. To avoid explicit Hessian computations when characterizing the tangent space of the manifold, we employ a Krylov subspace method that relies solely on matrix-vector products. These products can be efficiently obtained via automatic differentiation, ensuring both efficiency and robustness throughout the optimization process. The method's functionality and performance are demonstrated using both toy problems and examples from deep learning.

We study PAC-Bayes derandomization for smooth loss functions. Our goal is to obtain generalization bounds that hold with high probability for deterministic predictors by exploiting smoothness properties of both the loss and the predictor class. We show that passing from the Gibbs predictor to the deterministic predictor at the posterior mean has a precise cost, given by the generalization gap of the Jensen gap class. We control this class through its Rademacher complexity, leading to bounds for deterministic predictors that involve flatness quantities expressed in terms of parameter Jacobians and Hessians of the score map. The framework applies to both bounded and unbounded smooth loss functions, and we specialize the results to linear predictors and smooth neural networks. Finally, the Jacobian and Hessian quantities appearing in the theory motivate a practical regularizer. For BatchNorm networks, we compute this regularizer with respect to effective BatchNorm weights obtained by folding the BatchNorm transformation into the adjacent affine weights. Experiments on CIFAR-10 illustrate the behavior of this regularizer under different batch sizes.

An experimental investigation of neural image classification on the CIFAR-10 benchmark is presented through fully connected and convolutional network formulations. The analysis emphasizes the complete learning pipeline: image vectorization, normalization, one-hot class encoding, supervised loss minimization, learning-rate selection, mini-batch training, convolutional feature extraction, max-pooling, and validation-based generalization assessment. A convolutional architecture with six convolutional layers and three max-pooling stages is evaluated for ten training epochs using a batch size of 128 and an Adam optimizer with a learning rate of 0.001. The validation accuracy reaches approximately 74.77%, while the validation loss begins to increase after the middle of training despite continued reduction in training loss. The resulting behavior illustrates the practical difference between representation learning and memorization, and it provides a compact experimental baseline for future studies on regularization, data augmentation, deeper architectures, and reproducible image-classification education.

We develop a mathematically explicit link between shock-wave theory and the symmetry-quotiented learning dynamics of stochastic gradient descent, drawing on differential geometry, Lie group theory, and fluid mechanics. Specifically, after quotienting parameter symmetries and applying local-entropy coarse-graining, the effective dynamics satisfy a viscous Hamilton--Jacobi equation on the quotient manifold. Moreover, under the assumption that the raw parameter dynamics can be summarized by a gradient field on the quotiented space, the gradient of the coarse-grained loss function obeys a Burgers-type equation, and shock formation can be established rigorously. We apply our theory to multilayer perceptrons, convolutional neural networks, Transformers, and mean-field networks, and show that they obey the Hamilton--Jacobi or Burgers-type equations. We conjecture that this framework also yields practical diagnostics for deep learning. In architectures such as Transformers, raw parameter norms are often distorted by symmetry redundancy and may therefore be misleading, whereas symmetry-corrected quotient observables provide a principled basis for monitoring, forecasting, and controlling training-phase transitions.

Engineered robust losses such as Huber, Student-$t$, and generalised cross-entropy make supervised models tolerant of contamination but cannot answer which observations are corrupted. We introduce Neural Bayesian Anomaly Mitigation (NBAM), a general-purpose drop-in loss derived from a Bayesian latent-switch mixture model: the marginal likelihood defines a robust supervised loss, and the associated posterior defines an unsupervised contamination classifier. Like Huber or Student-$t$, NBAM can replace the standard training loss in any supervised pipeline; unlike them, it additionally learns a structured contamination model and returns a calibrated per-sample contamination posterior. A learned input-dependent prior $π_φ(x)$ captures the spatial locality of contamination, so that samples near known corruptions are more likely to be flagged, while an Occam penalty emerges automatically and regularises against over-flagging. On CIFAR-10 with asymmetric label contamination, NBAM recovers the structure of the corruption process without supervision: the contamination posterior separates clean from corrupted samples, and the learned anomaly head identifies the direction of every label-flip pair. Alongside these capabilities, NBAM outperforms the four robust-loss baselines considered here at contamination rates 0.2-0.6.

Robust deep learning under heavy-tailed and impulsive noise remains challenging because conventional losses such as mean squared error (MSE) exhibit unbounded sensitivity to outliers. Although correntropy-based objectives improve robustness, existing formulations rely on fixed kernel parameters that must be empirically tuned and remain static during training. To address these limitations, we propose an Adaptive Log-Correntropy Loss (ALCL), a heavy-tailed loss formulation that adaptively learns its robustness geometry during optimization. ALCL introduces a logarithmic residual model whose shape and scale parameters are learned jointly with network weights through differentiable reparameterization. This yields a principled maximum likelihood formulation whose influence function is formally bounded and redescending, allowing the loss geometry to adapt dynamically to evolving residual statistics while suppressing extreme outliers. Comparative experiments on four widely used benchmark datasets spanning grayscale and red-green-blue (RGB) image data under mixed heavy-tailed and impulsive noise demonstrate that ALCL consistently outperforms MSE and optimally tuned generalized correntropy losses in both reconstruction fidelity and downstream classification accuracy. While performance differences remain small under low-noise conditions, under high-noise regimes ALCL improves median accuracy by up to 4.75% on grayscale benchmarks and 4.51% on RGB datasets, with reduced variance across runs. These results demonstrate that adaptive robustness through joint learning of loss parameters provides a computationally efficient alternative to static correntropy-based losses for deep learning in non-Gaussian environments.

The Edge of Stability (EoS) phenomenon, where gradient descent operates with sharpness exceeding the classical convergence threshold yet the loss decreases over long timescales, is ubiquitous in modern deep learning but remains poorly understood in realistic settings. Prior rigorous analyses have been largely confined to scalar or low-dimensional losses with specific structural forms. In this work, we develop a bifurcation theory framework for gradient descent on the edge of stability that applies directly to overparameterized neural networks. By decomposing the training dynamics into components normal and tangent to the manifold of minimizers, we show that stable EoS training arises from a flip bifurcation in the normal direction, governed by the sign of the first Lyapunov coefficient, while the tangent dynamics drift toward regions of decreasing sharpness. Under mild spectral and geometric assumptions on the loss landscape, we prove convergence to the minimizing manifold when training at the EoS threshold. As a corollary, we recover and unify prior results: we show that the product-stability condition of Gan (2026) is an instance of our framework.

Deep learning models achieve state-of-the-art image classification but face deployment challenges due to computational costs and energy demands. We propose a lightweight training strategy that adapts normalization layers of the model to the new domain and decouples feature extraction from classifier optimization, reducing overhead by precomputing features only once. A redesigned classifier head with margin-based weighted loss further minimizes ambiguity without end-to-end backpropagation. Evaluated across four CNN architectures (ResNet18, ResNet50, MobileNet, DenseNet121), three Transformer models (ViT, Swin and DeiT) and three medical datasets (Brain Cancer MRI, BreakHis and PatchCamelyon), our approach significantly reduces the required training time with only a marginal accuracy trade-off, often matching or surpassing baseline performance. This efficiency translates to reducing CO2 by orders of magnitude, offering a practical and environmentally sustainable solution for resource-constrained clinical or prototyping environments.

This paper provides identification results to characterize a fairness-accuracy (FA) frontier, and statistical inference tools to test hypotheses and build a confidence set for the FA-frontier, when outcomes are observed only for selected individuals. When the selection process is unrestricted but loss is measured in specific ways, we provide a characterization of the sharp identification region of the FA-frontier. Under an assumption of unconfoundedness conditional on observables (and unrestricted loss functions), we obtain point identification and propose a debiased machine learning estimator, derive its asymptotic distribution, and show how this can be used to carry out inference for the FA-frontier. In work in progress, we extend the partial identification results to a broader class of loss functions.

While large and diverse datasets have driven recent advances in large models, identifying the optimal data mixture for pre-training and post-training remains a significant open problem. We address this challenge with FASTMIX, a novel framework that automates data mixture discovery while training only a single proxy model. Instead of relying on predefined heuristics or resource-intensive simulations, FASTMIX jointly optimizes mixture coefficients and model parameters, substantially improving efficiency and scalability over prior approaches. At the core of FASTMIX is a reformulation of mixture selection as a bilevel optimization problem. Under this reformulation, we show that optimizing mixture ratios is mathematically equivalent to assigning per-source loss weights under uniform source sampling. This embeds the mixture coefficients directly into the differentiable iterative optimization objective, enabling efficient, gradient-based optimization of both mixture and model. To solve the optimization problem, FASTMIX implements an approximate iterative optimization procedure, alternating between (i) updating model parameters on data sampled according to current mixture ratios (inner loop) and (ii) updating mixture ratios based on validation feedback (outer loop). Across pre- and post-training, FASTMIX outperforms baselines while drastically reducing search cost. Code (https://github.com/hrtan/fastmix)

This paper proposes a novel loss concept for supervised classification tasks. Rather than enforcing a direct mapping from each input sample to a single assigned label, we define an optimization objective over all classifier outputs as a bimodal Gaussian distribution. This softer target formulation implicitly captures class ambiguity, mitigates overfitting, and encourages the learning of more robust decision boundaries, all without requiring additional label information. Experimental results demonstrate consistent improvements in robustness, with particularly pronounced gains in low-data regimes, while requiring only minimal modifications to standard training pipelines.

Transfer learning is usually studied as a consequence of distribution shift. This paper identifies an orthogonal failure mode in which the data distribution is fixed and the loss changes. This setting is called \emph{loss shift}. A loss determines which information in $X$ is Bayes-relevant, and two losses may therefore require different representations even under the same joint law $P(X,Y)$. The idea is formalized using Bayes quotients, which allow losses to be ordered by refinement. In the Bayes-quotient formulation, strict refinement gives an immediate qualitative obstruction. A source-minimal representation for a coarser loss is insufficient for a strictly finer target loss. For finite-output log loss, this obstruction becomes an exact quantitative identity. The excess risk is the conditional information about $Y$ discarded by the representation. Experiments in controlled, learned, synthetic-image, and real-image settings show the predicted effect, i.e., classification-equivalent representations can have different optimal log-loss performance under a fixed data distribution.

As large language models (LLMs) are increasingly deployed across heterogeneous hardware with varying resource constraints, the ability to adaptively manage the trade-off between performance and efficiency without retraining is critical. We propose Drop-by-Drop, a novel multi-bitwidth post-training quantization framework that enables inference-time precision control over LLM weights from a single trained model. Our method is theoretically grounded in information theory and successive refinement. We establish that LLM weights, which commonly follow a Gaussian distribution, can be optimally reconstructed with increasing fidelity as additional bits are incorporated, under a weighted mean squared error distortion motivated by LLM loss functions. To realize this in practice, Drop-by-Drop incorporates Matryoshka-style supervision into the loss function, exploiting the structure of additive codebooks. Drop-by-Drop produces a single model where ordered subsets of codebooks yield accurate partial reconstructions at each precision level. This approach significantly reduces storage and memory overhead by allowing a single checkpoint to serve multiple bitwidths, while maintaining competitive perplexity and accuracy across major architectures, such as Qwen, LLaMA, Gemma, and Mistral.

Machine-learning drug-discovery pipelines increasingly rely on generative models that propose molecules far from the data used to train downstream synthesizability filters. Existing filters (SAScore, SCScore, RAscore, DeepSA) are purely statistical and degrade in exactly this out-of-distribution (OOD) regime. We ask whether cheap, closed-form physical priors, used as auxiliary supervision on a graph neural network (GNN), improve OOD generalization. We add two auxiliary losses to a GINE backbone: a topological complexity regression supervised by the Bertz index, and a strain-energy soft penalty supervised by MMFF94 force-field energy. On a 65,177-molecule corpus (HIV, Tox21, COCONUT) labeled by SAScore thresholds we reproduce a strong in-distribution baseline, then evaluate a 4-way ablation (baseline / +complexity / +strain / +both) on a single-source OOD split (train on drug-like HIV+Tox21, test on COCONUT natural products), repeated over 5 seeds with paired bootstrap confidence intervals. All three physics-aware variants give a small but statistically significant OOD improvement over the baseline (mean OOD AUC 0.9774): +complexity Delta = +0.0060 (95% CI [+0.0023, +0.0102]), +strain Delta = +0.0032 ([+0.0008, +0.0052]), +both Delta = +0.0066 ([+0.0038, +0.0093]); every interval excludes zero, and the combination is best. The variants are indistinguishable in-distribution, so the effect is visible only under OOD evaluation. We are explicit that the effects are modest, and we report a cautionary methodological finding: a single-seed version of this experiment produced a qualitatively different (non-monotone) story that did not survive multi-seed evaluation.

We explore whether intrinsic symmetries of the training data lead to conserved quantities during gradient-flow training of neural networks. Under the assumption that the loss function is analytic and non-polynomial, we prove that data symmetries generically do not induce any additional integrals of motion. For mean squared error (MSE) loss, on the other hand, there are situations in which data augmentation yields extra conserved quantities. We build a framework, utilizing \emph{tensorizable networks} to describe this phenomenon. Tensorizable networks are a family of architectures whose dependence on parameters and inputs can be separated using an intermediate representation. They include linear and polynomial networks, as well as Lightning Attention.

The Fokker-Planck equation (FPE) plays a pivotal role in describing the time evolution of probability density functions (PDFs) for systems governed by stochastic dynamics. In this work, we propose a conditional normalizing flow-based physics-informed neural network (PINN) framework for efficiently approximating the solution operator of the FPE for a whole range of initial conditions. Leveraging the Chapman-Kolmogorov equation for Markovian stochastic processes, the problem is reformulated into approximating a transition PDF starting at initial time from a Dirac mass centered at an arbitrary point. The PDF of an associated linearized stochastic differential equation (SDE) is employed as the base distribution for the normalizing flow, providing a good approximation of the target PDF, especially for small times, and thereby avoiding the singularity of the map associated with the Dirac delta initial distribution. Furthermore, a time-weighted loss function is introduced to mitigate numerical instabilities arising at small times, achieving a balance between causality and training difficulty as time progresses. A variety of numerical experiments are presented to illustrate the effectiveness and robustness of the proposed method.

The vascular network in the human body is characterized by blood vessels exhibiting drastic structural variations in radius, length, topological properties, and branching patterns. This heterogeneity, together with location-specific anatomical background variations, poses a significant challenge for robust, large-scale analysis of the entire cardiovascular system. As a result, most research has focused on narrow, isolated segments of the vascular network. While such targeted studies provide valuable insights, they inherently limit the ability to assess the systemic health and functional integrity of the vascular network as a whole. In this work, we aim to bridge this gap to advance both clinical diagnostics and our fundamental understanding of vascular physiology. We propose the task of segmenting all vessels in CT images, ranging from the largest components of the cardiovascular system to even minuscule mesenteric vessels. To this end, we introduce vesselFM-CT, the first model capable of robustly segmenting all blood vessels in 3D CT images. VesselFM-CT is trained via an iterative, multi-step process and optimizes our proposed TubeLoss loss function, effectively addressing the inherent heterogeneity of the cardiovascular system. We demonstrate that vesselFM-CT outperforms all baselines and enables automated, precise extraction of the cardiovascular system from CT images, thereby unlocking a wide range of clinical and technical perspectives, including automated disease classification and synthetic CT image generation.

Statistical post-processing has proven to be an effective tool in improving ensemble forecast of different weather variables. Case studies show that post-processing can remedy the typically underdispersive and potentially biased behaviour of the ensemble while optimizing a proper scoring rule expressing the forecast skill. The price of these positive effects is generally a deterioration in sharpness; the width of the central prediction intervals and the uncertainty of the predictions are increasing, especially for shorter lead times. This work aims to reduce the extent of the latter phenomenon for neural network-based parametric post-processing methods by extending the network's loss function with a penalty term. We demonstrate the effect of the proposed technique for 2m temperature ensemble forecasts of the European Centre for Medium-Range Weather Forecasts downloaded from the EUPPBench benchmark dataset and verified against synoptic observations. Here, the predictive distribution is Gaussian, and we use the continuous ranked probability score (CRPS) as loss function. The case studies confirm a substantial relative decrease ($8.2\%-12.5\%$) in the width of the nominal central prediction interval compared to the width of the predictive distribution computed without the penalty term, while there is no deterioration in the mean CRPS of probabilistic forecasts and in the RMSE of the predictive mean.

Recent research has established empirical scaling laws to predict model performance on multi-domain data mixtures. However, a theoretical understanding of these model loss behaviors remains absent. In this work, we propose a unified framework to explain the underlying mechanics of data mixing. Our approach extends theoretical perspectives originally developed for standard neural scaling laws (e.g., Kaplan and Chinchilla) to the multi-domain setting. Based on the distributional assumption that domains overlap on fundamental skills while diverging on specialized skills, we identify two key factors that govern the domain losses of models trained on different data mixtures: \textit{Capacity Competition}, where the allocation of finite model capacity couples domain losses globally, and \textit{Noise Reduction}, where optimal weights shift toward harder-to-learn domains to minimize overall noise. Empirical evaluations show that our framework outperforms existing baselines by fitting the loss landscape with a lower Mean Relative Error and identifying higher-performing training mixtures. Most importantly, our model successfully extrapolates across scales, predicting highly effective mixtures for large, unseen scales using parameters fitted on smaller ones. In addition, our model achieves these results using significantly fewer parameters compared to previous empirical laws. Our code is available at https://github.com/meiqwq/Explaining-Data-Mixing-Scaling-Laws.

3D Gaussian Splatting (3DGS) has become an efficient explicit representation for radiance field reconstruction and real-time novel view synthesis. However, its standard photometric loss treats flat and structure-rich regions similarly, which may limit the recovery of sharp contours and fine details. Edge-Guided Gaussian Splatting (EGGS) improves structure awareness through edge-guided weighting, but mainly relies on first-order gradient responses and linear weighting. In this paper, we propose LEGS, a Laplacian-Enhanced Gaussian Splatting method with a nonlinearly weighted loss. LEGS replaces first-order gradient guidance with second-order Laplacian structural guidance and maps the normalized Laplacian response into pixel-wise weights through nonlinear response-to-weight functions. The proposed loss improves structure-aware Gaussian optimization while keeping the original 3DGS rendering pipeline unchanged. Experiments on the full Tanks&Temples and Mip-NeRF360 datasets show that LEGS improves peak signal-to-noise ratio (PSNR) by up to 1.68 dB over 3DGS and up to 0.52 dB over EGGS. Incorporating the proposed second-order nonlinear weighting strategy into FastGS and FasterGS further improves PSNR by up to 1.69 dB, demonstrating its effectiveness as a general loss-level extension for Gaussian Splatting pipelines with potential applications in AR/VR, immersive visualization, and real-time 3D content generation.

In our previous work, a deep learning-based framework for 3D intraoral reconstruction was proposed. The model directly predicts explicit 3D point cloud coordinates from ten fixed-angle intraoral images, employing MobileNetV2 and Multi-head Attention for multi-view feature fusion, with a combined L1 Loss and Chamfer Distance as the loss function. Although the model achieved an accuracy of 77.49%, predicted vertices tended to concentrate in high-density regions of the ground truth, leaving other regions largely uncovered. In this paper, an improved loss function is proposed to address this limitation. Hungarian matching with filtering and Repulsion Loss are introduced to enforce more uniform vertex distribution across the reconstructed model. The proposed model achieves an accuracy of 68.02%, which is numerically lower than the previous model. However, the vertex clustering issue observed in the prior work is substantially alleviated, with predicted vertices distributed more evenly across the entire reconstructed surface.

Confidence-based loss weighting is usually avoided in generative models because it accelerates errors when the model is confidently wrong, but this intuition breaks down in supervised diffusion training. We introduce the Eisbach log-barrier, a parameter-free weight derived from the entropy of the DiT output's spatial energy distribution: high entropy damps the gradient, while low entropy preserves it. Applied to LoRA fine-tuning of Stable Audio 3 Medium on MusicCaps, it unexpectedly yields stronger thematic development, clearer acoustic differentiation, and higher textural diversity than unweighted training, the opposite of mode collapse. This works because in supervised diffusion the gradient direction is locked to ground truth, so confidence only scales the step size, and because temporal entropy downweights flat samples while preserving high-contrast ones. The result is an online, self-referential data curriculum that emerges purely from the forward pass, with analyzed noise-level dynamics and testable predictions.

Many modern applications of deep learning involve training a neural network via a one-step prediction loss (e.g., $L^2$ regression, cross-entropy), but deploy the network by rolling out along its own predictions. Key examples include autoregressive language modeling, flow-based generative modeling, and robot policy learning. It is well-documented that these settings induce a phenomenon we call test-time feedback (TTF): the mismatch between the training/validation loss and downstream metrics of interest, such as task success rate and generation quality, which grows with task length. While data curation, architecture, and objective design have been proposed to combat train-test shift in TTF settings, this paper proposes optimization as a new design axis to mitigate error accumulation. Specifically, we introduce a new optimization paradigm called double-preconditioning (DoPr) uniquely tailored to the challenges of TTF. DoPr combines gradient-wise preconditioning, as in Adam and Muon, with activation-wise preconditioning (AP), such as in KFAC. We show that the addition of AP yields a drop-in intervention for increasing downstream model performance across a range of TTF settings. Interestingly, these gains in test-time performance do not consistently accompany improvements in validation loss, opening new questions about how to properly evaluate models trained with one-step supervised objectives.

The support vector machine (SVM) is a widely used classifier, but choosing an appropriate loss function remains difficult. Convex losses such as the hinge loss and least-squares loss are sensitive to outliers, while bounded non-convex losses often lead to high computational cost. To address this, we propose a hybrid truncated loss function ($L_{\mathrm{ht}}$) that is both sparse and bounded, and build the $L_{\mathrm{ht}}$-SVM model for single-view classification. We introduce the P-stationary point and use it to establish the first-order necessary and sufficient optimality conditions. Based on these conditions, we design an alternating direction method of multipliers with a working-set strategy that reduces computational cost and achieves global convergence. We further extend $L_{\mathrm{ht}}$-SVM to multi-view learning by adding structural information and view weights, resulting in Mv$L_{\mathrm{ht}}$-SVM, which follows both the consensus and complementarity principles. Experiments on synthetic, real-world, and image datasets show that $L_{\mathrm{ht}}$-SVM achieves higher accuracy with fewer support vectors and better noise robustness than five single-view methods, while Mv$L_{\mathrm{ht}}$-SVM outperforms six multi-view methods in accuracy, precision, recall, and F1-score.

Gradient boosted decision trees require a stopping rule to avoid overfitting. The standard rule monitors a validation loss and stops if the loss fails to improve for a fixed patience period. However, the patience parameter has no interpretable scale and validation losses can be noisy or implicitly defined by a user-specified gradient. We propose ScoreStop, a gradient-based early-stopping rule that casts the stopping decision at each iteration as a test of the null hypothesis that the current predictor is the population risk minimizer. We use a functional score test, computed on validation data, with a statistic that is scale-invariant in the update direction, with a known asymptotic distribution under the null. Because our test uses gradients rather than loss values, the same construction applies to implicit losses such as LambdaRank, and data-dependent losses such as Cox regression via influence functions. In synthetic experiments and real-data benchmarks, we show that ScoreStop is competitive with loss-based methods.

Many machine learning problems, including similarity learning, ranking, and clustering, rely on empirical pairwise loss functions whose quadratic computational cost quickly becomes prohibitive at scale. We demonstrate how a frugal approach that retains only a fraction of the available information on pairs can achieve estimation or optimization performance comparable to that obtained by using all pairs, by leveraging survey sampling techniques. A central finding, supported by both theory and experiments, is that such sampling plans must target pairs directly rather than individual observations. In particular, for pairwise losses between high-dimensional vectors such as embeddings in vision or graph learning, assigning higher inclusion probabilities to informative pairs using suitable auxiliary information yields performance close to full pairwise evaluation, providing a principled and theoretically grounded trade-off between accuracy and computational cost.

We propose DENSER, a Depth-guided ENSemble with Staged EFA-GS Reconstruction for soccer novel view synthesis. DENSER extends EFA-GS with three key contributions: (1) camera-height-based loss weighting that prioritises ground-level broadcast views, (2) monocular depth supervision from Depth-Anything-V2 to regularise geometry in textureless regions, and (3) a three-model pixel-average ensemble whose members diverge from a shared base checkpoint by varying training length and Gaussian scale clamping. On five held-out challenge scenes we achieve a mean PSNR of 29.89 dB, SSIM of 0.791, and LPIPS of 0.366.