Loss Function

Imbalanced learning is a critical challenge in machine learning, where underrepresented target values can bias models and degrade prediction performance on rare but important cases. Although extensively studied in classification, imbalanced regression remains relatively underexplored. Existing methods mainly focus on either data-level balancing, which may introduce noise and overfitting, or algorithm-level balancing, which often struggles with highly complex target distributions. To address these limitations, we propose a unified hybrid framework that integrates both data- and algorithm-level balancing strategies into a regressor-agnostic pipeline. The proposed framework consists of five stages: (1) adaptive bin partitioning to dynamically segment the target space based on local linear coherence; (2) target-conditioned representation learning using a Conditional Variational Autoencoder; (3) multistage data-level balancing through feature-space clustering and oversampling of minority clusters; (4) algorithm-level balancing using a novel Latent-Density Weighted Loss (LDWL) to emphasize rare samples in latent and target spaces; and (5) attention-based gated fusion for final regression. Experimental results on benchmark datasets demonstrate that the proposed framework consistently improves predictive performance compared to standalone regressors and existing imbalanced regression approaches.

Bounding-box regression is a fundamental component of object detection, playing a critical role in precise object localization. Existing Intersection-over-Union (IoU)-based loss functions extend the IoU objective by incorporating geometric penalties, such as center-distance and aspect-ratio mismatch, to improve bounding-box regression. However, these penalties typically remain fixed throughout training and do not account for the optimization dynamics in which predicted boxes initially exhibit large center-distance and shape errors, with later stages focusing on improving overlap with the ground truth. To address this limitation, we introduce MoEIoU, a mixture-of-experts based regression loss that jointly models overlap, center alignment, and aspect-ratio mismatch. MoEIoU aggregates these components using a log-sum-exp function, which emphasizes the dominant localization error while maintaining smooth contributions from other terms. Additionally, a curriculum-based weighting schedule is employed to prioritize correcting box position and shape in early training stages and improving overlap in later stages. We evaluated proposed MoEIoU on PASCAL VOC, HRIPCB, and MS COCO using multiple YOLO architectures, along with large-scale simulation experiments. It consistently outperforms standard and recent state-of-the-art losses, demonstrating faster convergence and improved localization accuracy. We further show that this adaptive aggregation improves existing IoU-based losses, yielding consistent gains and providing more effective optimization guidance for bounding-box regression in object detection frameworks.

Vision-language models (VLMs) deliver strong multimodal reasoning capabilities, but their large computational cost and high parameter counts make deployment challenging on resource-constrained devices. Low-rank decomposition has emerged as a promising compression technique, yet existing methods often optimize local matrix reconstruction error, rely on uniform or heuristic rank allocation, and focus mainly on attention projections while leaving feed-forward networks underexplored. In this paper, we propose~\textit{LASER} (\textbf{L}oss-\textbf{A}ware \textbf{S}ingular-value d\textbf{E}composition and \textbf{R}ank allocation), a low-rank compression framework for efficient low-precision VLM inference. LASER derives a curvature-weighted SVD objective from a second-order approximation of the model loss and uses Kronecker-factored Fisher information to guide decomposition toward downstream performance rather than reconstruction alone. We further introduce a loss-aware cross-layer rank allocation strategy based on calibration gradients, enabling more effective parameter budgeting across layers. Finally, we extend low-rank compression to FFN layers through a hybrid scheme that combines SVD with quantization. The evaluation results show that LASER achieves more than $2.3\times$ decoding speedup over previous work while preserving strong accuracy under low-precision inference.

Continual instruction tuning updates a language model through a sequence of new domains, yet each update can progressively erode previously learned capabilities and alignment behavior. Replay is the standard mitigation, but fixed replay ratios are inherently limited because the optimal mixture varies with the current domain, the training stage, and the evolving vulnerability of prior behaviors. We propose PROX-YMIX, a framework that learns a dynamic replay controller on a small proxy model and transfers the frozen controller to a larger target. The controller never observes future tasks and constructs its state from normalized validation losses and their temporal dynamics, producing a masked mixture over the current task and accessible replay buffers. Our core empirical hypothesis is forgetting mirroring: task vulnerability rankings remain largely consistent across model scales even when absolute loss magnitudes differ. We validate this assumption empirically before transferring controllers across scales. On LLaMA-3-8B across five continual instruction tuning sequences, PROXYMIX improves average accuracy by 3.4 points, reduces final forgetting by 3.5 points, and raises safety score by 5.8 points over the strongest non-oracle baseline, at roughly 50x lower policy learning cost than Oracle Target RL. The framework is leakage free and architecture independent at the interface level, and we also identify settings where the proxy assumption breaks down, highlighting limitations for robust deployment.

Masked diffusion models have seen great success in capturing data distributions over discrete sequences in domains such as text and proteins. These models generate data by iteratively unmasking tokens starting from a fully masked sequence, with the unmasking order typically chosen at random or using a heuristic based on denoiser probabilities. In this work, we propose a scheme for learning the unmasking order using an additional lightweight policy network on top of a diffusion model. Our proposed loss reweights terms in the masked diffusion loss according to policy probabilities, and results in a policy that prefers positions where the denoiser is more likely to be correct. We study this loss in two settings: (i) training solely the policy while using a frozen pre-trained denoiser, and (ii) training the policy and denoiser jointly with the weighted loss to allow for mutual adaptation. We demonstrate that our approach outperforms common heuristics on problems that are sensitive to token ordering, such as combinatorial tasks and proteins.

Fine-tuning often introduces spurious correlations alongside task knowledge, causing systematic failures on underrepresented groups. Existing mitigations require retraining, group labels, or curated counterfactual data. We show a simple post-hoc intervention reduces shortcut reliance without any of these: truncating the tail of the SVD of $ΔW = W_\mathrm{ft} - W_\mathrm{base}$ reduces the spurious-group gap while preserving task accuracy. Across three instruction-tuned models ($0.5$B--$7$B) and four classification benchmarks, top-$k$ truncation reduces the gap on every cell at $<2$ pp accuracy loss, by up to $5\times$ on CivilComments. We propose this works because the shortcut response sits in the tail of the singular ordering of $ΔW$, a claim about how truncation behaves rather than about the raw singular values, which are broadly distributed and look the same across all four datasets. A controlled boundary case in which fine-tuning has only a shortcut to learn shows the predicted FT-to-base collapse, and bottom-/random-$k$ and matched-rank LoRA controls rule out generic low-rank approximation and rank-constrained training as the explanation. We read this as preliminary evidence that the singular basis of $ΔW$ is a useful coordinate system for studying what fine-tuning has learned.

AI agents that persist across sessions need memory they can retrieve, audit, update, and erase. Existing memory systems often collapse source evidence, extracted facts, retrieved context, and answer policy into one opaque prompt path, making failures difficult to diagnose: a wrong answer may come from missing evidence, unsupported extraction, stale state, retrieval loss, or answer-model behavior. We present Eywa, a provenance-grounded memory architecture built around evidence before belief. Eywa stores immutable source evidence before deriving canonical facts, validates extracted memories against typed signals and source support, and retrieves bounded memory context through a deterministic multi-route read path with zero LLM calls inside retrieval. Retrieved context is returned separately from answer instructions, allowing the same memory substrate to be evaluated across frontier, budget, and local answer models. Under a frozen, artifact-recorded retrieval configuration, Eywa reaches 90.19% judge accuracy on the LoCoMo C1-C4 split with Claude Sonnet 4.6 write and QA roles. On LongMemEval-S, it reaches 88.2% retrieval-sufficiency accuracy. On BEAM, a 700-question technical-memory stress benchmark, it reaches 81.45% mean nugget score and 85.29% pass@score >= 0.5. Full per-question artifacts, including questions, gold answers, model answers, retrieved context, and labels, are published at https://eywa.to/research.

We introduce Score Broadcast and Decorrelation (SBD), a principled framework for broadcast-based credit assignment for general families of differentiable losses. Error broadcast is a biologically plausible alternative to backpropagation that sends output information to hidden layers without weight transport. The Error Broadcast and Decorrelation (EBD) framework, recently introduced for the mean-squared-error (MSE) setting, grounded this mechanism in the stochastic orthogonality of optimal estimators, under which the optimal residual is orthogonal to functions of the input. We generalize that foundation by introducing an orthogonality principle between the output score (the gradient of loss with respect to the final-layer output) and hidden-layer activations, which holds whenever the optimal score has conditional mean zero. This single principle unifies broadcast-based credit assignment across the standard differentiable-loss families, including cross-entropy, Bregman divergences, proper scoring rules, and exponential-family negative log-likelihoods. The framework supplies a theoretical grounding for the three-factor learning rule under general losses, with the neuromodulatory factor derived as the broadcast loss score. We derive the cross-entropy case explicitly, characterize the admissible loss class, and introduce a score vector expansion technique that enriches the broadcast signal while preserving the orthogonality framework. Experiments on CIFAR-10 and Tiny ImageNet show that SBD substantially improves over existing broadcast approaches, with score vector expansion delivering further gains. Overall, this work identifies the loss score as the signal to broadcast, supplies the orthogonality theory and theoretical grounding for the three-factor learning rule from neuroscience, and shows how score vector expansion enriches the decorrelation directions of the resulting objective.

The purpose of this article is to provide validation to my deep neural network alternative in the context of LLMs. Very recently, there has been a significant interest by Chinese researchers in a model called RBF network, as a substitute to standard DNNs, with increased explainability and higher accuracy. It turns out that my new model, discovered independently, is based on the exact same machinery. But with a major twist: it does not need DNN as it finds the global optimum of the loss function in closed form, in one iteration, thus eliminating the tedious training step. Here I provide a high-level overview of my technology, with case study and comparison to similar methods.

A crucial component of machine learning algorithms is minimizing loss functions with less computational cost and less oscillations. While adaptive learning rate-based optimizers have been widely used for real-world tasks, they do not guarantee convergence, which is why AMSGrad was later introduced to investigate the non-convergence behaviour of Adam. In this paper, popular adaptive optimization methods like Adam and AMSGrad are critically reviewed with an emphasis on their fundamental design concepts. To address limitations of the above mentioned optimizers, a new optimizer variant, C-Adam, is proposed based on the line of sight approach. A theoretical proof for convergence is also provided and the optimizer is validated through a number of real-life based numerical experiments.

While machine learning (ML) architectures have evolved rapidly to account for complex data, loss functions like cross-entropy remain mostly structure-agnostic in many real-world applications. However, the "class-symmetric" nature of these standard losses fundamentally limits the ability of ML models to exploit structural relationships between classes, particularly when facing structured noise. We propose Conveyance, a new classification approach and associated loss function tailored to structured class spaces. It allows users to encode graph-like relations between classes without having to define complex joint distributions or manually tune utility matrices. Technically, our loss function operates by maximizing two separate margins over distinct class partitions, while preserving formal properties such as monotonicity and partial convexity. We demonstrate the versatility and effectiveness of our method by applying it to hierarchical classification, ordinal regression, and multiple instance learning. Across these tasks, Conveyance either matches or exceeds the performance of specialized baselines, thereby offering a unified solution for structured class spaces.

Traditional network analysis focuses on single-layer networks, real-world systems often form multilayer networks with multiple relationship types. However, existing methods typically fail to capture complex inter-layer dependencies by treating layers independently or aggregating them. To address this, we propose T-GINEE (Tensor-Based Generalized Multilayer-graph Estimating Equation), a statistical regularization framework combining tensor-based generalized estimating equations with task-specific loss to model cross-network correlations explicitly. Key innovations include: (1) CP tensor decomposition capturing structural dependencies via shared latent factors; (2) a generalized estimating equation framework modeling inter-layer correlations through working covariance matrices; and (3) a flexible link function accommodating characteristics like sparsity. Our theoretical analysis establishes consistency and asymptotic normality under mild conditions. Extensive experiments on synthetic and real-world datasets validate T-GINEE's effectiveness for multilayer network analysis.

Scaling laws guide large language model training by relating compute to cross-entropy loss, and recent work further extends them to predict downstream benchmark performance. However, prior approaches face generalization limitations from two aspects: focusing on benchmark-level performance introduces scenario-specific artifacts, while relying on IID validation loss fails to track capability improvements when training distributions vary. In this work, we argue that downstream scaling should be studied at the capability level, which captures shared skill factors across related tasks while abstracting away benchmark-specific noise. We propose SuperValid, a framework that synthesizes OOD (out-of-distribution), capability-aligned validation data by distilling core concepts from benchmarks within a capability domain and expanding them into diverse, knowledge-rich texts. Extensive experiments spanning 16 benchmarks grouped into 6 capability domains show that SuperValid loss exhibits strong and stable correlation with downstream performance across models of different architectures, scales, and training data distributions. As a training-free metric computable during training without benchmark evaluation, SuperValid enables effective model selection, early stopping, and scaling decisions.

Driven by the wave of large language models, Video-Language Models (VLMs) have become a significant yet challenging technology to bridge the gap between videos and texts. Although previous VLM works have made significant progress, almost all of them implicitly assume that all the texts are predefined by the specific template. In real-world applications, such a strict assumption is impossible to satisfy since 1) predefining all the texts is extremely time-consuming and labor-intensive. 2) these predefined text inputs are too restrictive and user-unfriendly, limiting their applications. It is observed that given a video input, texts with similar semantics but different templates lead to various performances. To this end, in this paper, we propose a novel plug-and-play framework for various VLM-based methods to fully bridge videos and texts. Specifically, we first generate positive and negative texts from the original ones to target specific text components. Then, we propose an attribute-based text reasoning strategy to mine fine-grained textual semantics of generated texts. Finally, we utilize videos as guidance to conduct cross-modal bridging by designing a self-weighted loss. Extensive experiments show that the proposed method can serve as the plug-and-play module to effectively improve the performance of state-of-the-art VLMs.

We present the first theoretical convergence analysis of machine learning training under fully homomorphic encryption (FHE), combined with a differentially private (DP) training algorithm tailored to encrypted computation. Our approach improves computational efficiency over standard differentially private gradient descent (DP-GD) while achieving comparable utility. In particular, we prove convergence of approximate gradient descent using polynomial approximations of activation and loss functions, which are required for FHE compatibility. To preserve privacy in downstream tasks, we integrate differential privacy without relying on costly per-sample gradient clipping, enabling scalable encrypted learning. We also provide data-independent hyperparameter selection and theoretically grounded strategies for polynomial approximation which can be of independent interest. Together, these contributions advance the feasibility of efficient, private, and secure machine learning on sensitive data.

We study the adversarial kernel bandit problem, in which the loss at each round is induced by an arbitrary bounded element of a reproducing kernel Hilbert space (RKHS). We propose an exponential-weights algorithm built on a regularized importance-weighted loss estimator, together with an explicit correction term that cancels the bias introduced by the regularization. Our main result bounds the regret by $\widetilde{O}\big(\sqrt{T\, d_*(λ)\,\log|{X}|}\big)$, where $d_*(λ)$ is a widely-adopted notion of effective dimension that captures the complexity of the kernel. Up to logarithmic factors, this matches the known rate achieved in the related stochastic kernel bandit problem. A notable application is the Matérn$(ν,d)$ kernel with smoothness parameter $ν$ on $\mathbb{R}^d$, for which our bound specializes to $\widetilde{O}\big(T^{(ν+d)/(2ν+d)}\big)$, improving over the best-known prior rate of Chatterji et al. [2019] while simultaneously removing the rank-one adversary assumption required by their analysis. Moreover, this rate is the same as the known optimal rate for stochastic kernel bandits, and also matches a lower bound from concurrent work up to a $\log T$ factor.

Contextual dueling bandits form a cornerstone of preference-based decision-making, with critical applications in recommender systems and large language model alignment. However, standard algorithms rely on the idealized assumption of immediate feedback, a condition frequently violated in real-world scenarios such as prompt optimization. This setting introduces a unique theoretical challenge: unlike linear bandits, dueling bandit estimators lack closed-form solutions, rendering naive adaptations of standard weighting techniques biased. To address this, we formalize the problem of Contextual Dueling Bandits with Stochastic Delayed Feedback and propose two novel algorithms: Linear (LDB-DF) and Neural (NDB-DF) Dueling Bandits with Delayed Feedback. Central to our approach is a novel estimator that integrates an Inverse Probability Weighting (IPW) mechanism directly into the loss function, ensuring unbiased correction for delayed or missing feedback. We provide comprehensive theoretical analysis, establishing an O(d*sqrt(T)) regret bound for the linear setting and sub-linear guarantees for the neural setting. Extensive experiments on both simulated and real-world datasets demonstrate the effectiveness of our propose.

We introduce AdvantageFlow, a forward-process reinforcement learning algorithm for rectified flow models. Unlike Flow-GRPO, which optimizes the reverse process, we optimize an advantage-weighted forward-process prediction loss. This optimization problem is unstable when advantages are negative and the loss becomes non-convex. We stabilize it by rollout policy regularization, which reduces variance and arises from fitting a local reward-improving target distribution. We evaluate AdvantageFlow on image generation tasks with Stable Diffusion 3.5 Medium. It outperforms both Flow-GRPO and a state-of-the-art forward-process RL baseline based on negative-aware fine-tuning.

Policy loss estimation remains a fundamental and long-standing challenge in reinforcement learning (RL) for diffusion language models (DLMs). We introduce Reinforcement Learning from Denoising Feedback (RLDF), a novel training paradigm that leverages feedback obtained from rollout and training processes to facilitate accurate and efficient policy loss estimation. To balance the trade-off between computational efficiency and estimation effectiveness, RLDF optimizes the model toward the clipped clean state from intermediate noisy states, combined with weighted timestep sampling over denoising timesteps. Extensive experiments demonstrate that RLDF achieves consistent and substantial improvements in both performance and generalizability across two representative DLM architectures, LLaDA and Dream, on multiple reasoning benchmarks. Our work lays a principled foundation for scalable reinforcement learning in diffusion language models. We build Drift, a training framework for DLMs, available at https://github.com/ant-research/Drift.

Although deep neural networks (DNNs) achieve high predictive accuracy, their confidence estimates are often unreliable, potentially compromising user trust in their decisions. This has motivated research on calibrated models, where calibration measures how well a model's predicted confidence aligns with the empirical probability of correctness. However, calibration metrics can often be improved through post-processing techniques that merely mimic training-time uncertainty without genuinely improving the model's understanding. For this reason, statisticians recommend that models be not only calibrated but also refined. Intuitively, a model is considered more refined if it assigns significantly different confidence scores to correct and incorrect predictions, a property also referred to as sharpness. We observe that many existing calibration methods improve calibration at the cost of reduced refinement. To address this limitation, we propose: (1) a novel loss function that explicitly promotes refinement and can be optimized through supervised contrastive learning; and (2) a unified training framework, RefCal, that jointly optimizes calibration, refinement, and accuracy to improve DNN reliability. On the CIFAR-100-LT dataset with 10 percent class imbalance, RefCal achieves (accuracy, refinement, ECE) of (58.81, 95.67, 0.08), substantially outperforming the widely used Correctness Ranking Loss, which achieves (46.27, 93.7, 0.22).

Robustness, domain adaptation, photometric/occlusion invariance, sensor drift, and alignment style are treated as separate literatures with separate method families. Under label-preserving deployment shift they share one geometric object: the covariance Sigma_task = Cov_{Q_n}(n) of ways inputs can change without changing the label. CORAL, adversarial training, augmentation, metric learning, Jacobian penalties, and alignment constraints are not independent tricks--they are estimators of Sigma_task. Fix that object and the Jacobian penalty is pinned by a matrix Sigma' whose range must cover range(Sigma_task)--the matching principle. We prove optimality in a linear-Gaussian model (Thm. A), necessity of range coverage for any quadratic penalty that zeros deployment drift (Thm. G), and the same dichotomy at global minima (Thm. A_global). Wrong-direction/signal-aligned controls (Lemma C; Cor. E/E) and seven estimators (Lemmas D1--D7), plus label-free TDI, yield a falsifiable recipe when Sigma_task must be learned. Thirteen blocks (ML through Qwen2.5-7B) test matched vs isotropic vs wrong-direction penalties on geometry and deployment drift. Twelve match theory where identifiability holds; Office-31 is a named eigengap failure. Partial passes: geometry can improve without every headline task metric moving. A pilot 7B DPO run (one epoch, 240 pairs): matched style-PMH preserves Style TDI where standard DPO degrades it. We do not claim standard training reaches global minima (assumption (O) is open), that estimated Sigma_task is always identifiable, or dominance on every leaderboard. We claim a falsifiable design recipe: estimate Sigma_task, match Sigma', run the controls, report task and geometry separately.

Large language model post-training methods such as supervised fine-tuning (SFT), reinforcement learning (RL), and distillation are often analyzed through their loss functions: maximum likelihood, policy gradients, forward KL, reverse KL, or related objective-level variants. We study a complementary factor: the state distribution on which supervision is applied. For an autoregressive policy, a state is a prompt plus generated prefix. SFT trains on fixed dataset states, while RL and on-policy distillation (OPD) train on states induced by the current learner. We formalize post-training as state-distribution shaping and run a controlled smallscale study using Qwen3-0.6B-Base on GSM8K, with TruthfulQA and MMLU as retention evaluations. Our results show three phenomena. First, a mild SFT run improves GSM8K with little forgetting, while a stress SFT run causes substantial retention loss. Second, OPD from a degraded SFT teacher surpasses that teacher on GSM8K, TruthfulQA, and MMLU, despite using the teacher as its only supervision source. Third, a lightweight on-policy RL run improves GSM8K while preserving retention. These results support a state-centric view of post-training: the source and locality of training states can be as important as the form of the supervision signal.

Narang et al. (2021) evaluated 40+ Transformer modifications at T5-base scale and concluded that most did not transfer. Five years later, the typical working regime has moved to 1-3B parameters, downstream evaluation has replaced pretraining perplexity, and a substantially different catalogue of modifications has emerged. We revisit their question by testing 20 post-2021 Transformer modifications at 1.2B and 3B under strict iso-data, iso-compute, iso-recipe control, with a multi-seed baseline noise floor and CLIMB-12 downstream evaluation as the primary metric. The central finding reproduces theirs at this curated set: most modifications do not transfer. Of the 20 modifications, only two clear Bonferroni correction at 1.2B; one of those two further fails to train stably at 3B under the shared recipe. We also find that the loss-downstream gap reported by Tay et al. (2023) enlarges several-fold for attention-output modifications: two significant failures converge to within 2-3% of baseline validation loss yet drop 6-16 CLIMB-points. We conclude that noise-floor reporting, downstream evaluation, and cross-scale stability testing are now prerequisites for architecture comparisons at 1-3B.

Neural networks can be trained to rank the choices made by logical reasoners, resulting in more efficient searches for answers. A key step in this process is creating useful embeddings, i.e., numeric representations of logical statements. This paper introduces and evaluates several approaches to creating embeddings that result in better downstream results. We train embeddings using triplet loss, which requires examples consisting of an anchor, a positive example, and a negative example. We introduce three ideas: generating anchors that are more likely to have repeated terms, generating positive and negative examples in a way that ensures a good balance between easy, medium, and hard examples, and periodically emphasizing the hardest examples during training. We conduct several experiments to evaluate this approach, including a comparison of different embeddings across different knowledge bases, in an attempt to identify what characteristics make an embedding well-suited to a particular reasoning task.

Labeling a training set is often expensive and susceptible to errors, making the design of robust loss functions for label noise an important problem. The symmetry condition provides theoretical guarantees for robustness to such noise. In this work, we study a symmetrization method arising from the unique decomposition of any multi-class loss function into a symmetric component and a class-insensitive term. In particular, symmetrizing the cross-entropy loss leads to a linear multi-class extension of the unhinged loss. Unlike in the binary case, the multi-class version must have specific coefficients in order to satisfy the symmetry condition. Under suitable assumptions, we show that this multi-class unhinged loss is the unique convex multi-class symmetric loss. We also show that it has a fundamental local role: the linear approximation of any symmetric loss around score vectors with equal components is equivalent to the multi-class unhinged loss. We then introduce SGCE and alpha-MAE, two loss functions that interpolate between the multi-class unhinged loss and the Mean Absolute Error while allowing control of the beta-smoothness of the loss. Experiments on standard noisy-label benchmarks show competitive performance compared with existing robust loss functions.

Stochastic gradient methods are central to modern large-scale learning, but their use with incomplete covariates remains delicate since imputation schemes generally introduce systematic gradient biases, as shown for linear models. In this work, we prove that all parametric models exhibit similar gradient bias for various imputation procedures and characterize exactly the dependence on the missingness ratio vector $p$, with $O(\|p\|)$ as the leading term. We exploit this analysis to propose a simple debiasing procedure for stochastic gradient descent (SGD) with missing values based on Richardson extrapolation, which leverages the exact expression of the gradient bias. The key idea is to \emph{deliberately add missingness}: from an already incomplete observation, we generate a further-thinned version at a higher, controlled missingness level, and combine the two resulting stochastic gradients to cancel the leading bias term. We prove that one Richardson step reduces the gradient bias from $O(\|p\|)$ to $O(\|p\|^2)$ under several missingness scenarios. Our proposed method is computationally efficient, model-agnostic and applies to any parametric loss whose stochastic gradient can be computed after imputation. Furthermore, when missing indicators are independent, the population gradient bias is a multilinear polynomial in $p$ and depends only on population gradient errors induced by declaring a single coordinate missing. In this case, our method generalizes to a multi-step Richardson procedure which recursively cancels higher-order terms. Empirically, Richardson debiasing improves optimization and estimation across several generalized linear models and combines positively with widely used imputation procedures such as MICE. These results suggest that, somewhat counter-intuitively, adding controlled missingness on top of existing missing data can make stochastic learning from incomplete data more accurate.

Unsupervised fine-grained image hashing aims to learn compact binary codes that preserve subtle visual differences among highly similar instances without manual annotations. However, most existing methods neglect collision resistance, leading to identical hash codes for slightly semantically different samples. In this paper, we propose Collision-Resistant Single-Pass Self-Supervised Semantic Hashing (CS3H), a collision-resistant framework that directly optimizes Hamming-space similarity via a single-pass normalized Hamming distance loss to produce well-separated binary representations. We further introduce a collision-sensitive attention module to emphasize rare and discriminative local patterns, reducing hash collisions and improving fine-grained discrimination. Experiments on multiple benchmarks show that CS3H consistently outperforms state-of-the-art methods in retrieval accuracy while achieving superior collision resistance with minimal computational overhead.

Accurate simulation of fluid flow in porous media is challenging due to complex pore-space geometries and the computational cost of solving the Navier-Stokes equations. This difficulty is particularly important when repeated simulations are required, as standard numerical solvers may converge slowly in intricate porous domains. We present a neural-network-based framework for predicting pore-scale velocity fields directly from sample geometry. The method uses a convolutional encoder-decoder architecture with skip connections to preserve spatial detail while extracting multi-scale features. Physical consistency is encouraged through a custom loss function combining velocity reconstruction with incompressibility, no-flow conditions inside solids, periodicity constraints, and agreement with the global tortuosity index. We analyze the influence of the corresponding loss weights and quantify the contribution of individual loss components to prediction accuracy. Several CNN backbones are evaluated to identify architectures providing accurate and robust predictions. The generalization ability of the trained model is tested on samples outside the training distribution, including changes in obstacle geometry, boundary conditions, porosity, and realistic porous structures. Finally, we demonstrate a practical use of the predicted velocity fields as initial conditions for Lattice-Boltzmann simulations. This warm-start strategy accelerates solver convergence, reducing the number of iterations in over 90% of tested cases.

Many real-world combinatorial problems involve uncertain parameters, which can be predicted given contextual features and historical data. These predict-then-optimize' or contextual optimization' problems have gained significant attention: end-to-end training methods can now minimize the downstream task cost rather than the predictive error. However, despite their effectiveness, these decision-focused learning (DFL) approaches often rely on repeated solving of the underlying combinatorial optimization problem during training, making them computationally expensive and difficult to scale. We reframe the learning problem as a cost-sensitive multi-output regression problem: multi-output due to the combinatorial problem having multiple uncertain parameters, and cost-sensitive due to the downstream task cost being the real target. Our technical contribution is the formalization of multiple loss function components that follow from this reframing: cost-insensitive normalization, decision-aware asymmetric penalization of over- and underpredictions, and instance-based costs that mimic the true downstream task-based loss locally. These components require zero or one solve per training data instance, while requiring no further solves during training. Experiments show that the combination of loss components achieves comparable downstream task quality to the state of the art, while being significantly more efficient, enabling scaling to problem sizes that have not been tackled before with DFL.

Recent works have illustrated that modern NLP models trained for diverse tasks ranging from sentiment analysis to language generation succumb to universal adversarial attacks, a class of input-agnostic attacks where a common trigger sequence is used to attack the model. Although these attacks are successful, the triggers generated by such attacks are ungrammatical and unnatural. Our work proposes a novel technique combining parts-of-speech filtering and perplexity based loss function to generate sensible triggers that are closer to natural phrases. For the task of sentiment analysis on the SST dataset, the method produces sensible triggers that achieve accuracies as low as 0.04 and 0.12 for flipping positive to negative predictions and vice-versa. To build robust models, we also perform adversarial training using the generated triggers that increases the accuracy of the model from 0.12 to 0.48. We aim to illustrate that adversarial attacks can be made difficult to detect by generating sensible triggers, and to facilitate robust model development through relevant defenses.

Rearranging the rows or columns of a sparse matrix using an appropriate ordering can significantly reduce fill-ins, i.e., new nonzeros introduced during matrix factorization, decreasing memory usage and runtime. However, finding an ordering that minimizes fill-ins is NP-complete. Existing approaches, including graph-theoretic and deep learning methods, rely on surrogate objectives without theoretical guarantees. The Fill-Path Theorem reveals a direct and intrinsic relationship between fill-in generation and the sparse structure of the matrix as path triplet inequalities. Here we first employ a multigrid graph network to capture structural information for each vertex. We then derive a triplet sampling strategy based on inequalities. Finally, we introduce an end-max chain loss function to reduce the number of triplets whose predicted scores satisfy these inequalities. Experimental evaluations on the publicly available SuiteSparse matrix collection demonstrate the superiority of the proposed method in terms of both fill-in reduction and speedup in LU factorization time.

In recent years, Muon has emerged as the dominant method for training large language models, and transformers more broadly. The essential difference, when compared to standard gradient descent methods, is to replace the usual update matrix $M=UΣV^\top$ with its polar factor $UV^\top$. In this work, we consider a class of Muon-like updates, where we replace the update $M$ with $UΣ^p V^\top$ for some parameter $p$. We call this a "spectral-shaping" operation, and develop a theory of how to pick $p$ which depends on (a) local curvature of the loss function, (b) noise stemming from stochastic gradients and label noise, and (c) training stage. Our theory and experimentation reveal a previously overlooked behavior: positive $p$ helps early by emphasizing high-curvature directions and accelerating signal contraction, while mildly negative $p$ helps later by reallocating update strength toward low-curvature directions that still contain useful training signals. Building on the insight, we propose DynMuon, an efficient dynamic spectral shaping method that schedules $p$ from positive to mildly negative over training. Extensive experiments across model sizes, architectures, and training settings show that DynMuon consistently achieves lower validation loss than Muon, while requiring 10.6-26.5% fewer steps to reach the same target loss. Our code is available at https://github.com/fzwark/DynMuon.

We introduce a novel framework for uncertainty quantification of solution operators associated with stochastic partial differential equations (SPDEs). Although SPDEs play a central role in modeling complex physical systems under uncertainty, their practical use typically requires specifying the magnitude and structure of model uncertainties that are often unknown and difficult to infer from noisy measurements. To address this challenge, we develop a stochastic operator-learning framework that learns directly from noisy data and outputs both a mean solution field and a quantification of uncertainty. The proposed method, namely the Stochastic Operator Network (SON), is constructed by combining the structure of the Deep Operator Network (DeepONet) with Stochastic Neural Networks (SNNs) to model stochasticity and enable probabilistic prediction. The training procedure is carried out by minimizing a Hamiltonian-type loss and optimizing the resulting objective using the Stochastic Maximum Principle. Numerical experiments on benchmark SPDEs under multiple uncertainty sources demonstrate the accuracy and robustness of the proposed method in capturing solution structure and quantifying predictive uncertainty.

Clinical application of high-resolution diffusion MRI is hindered by hardware limitations and prohibitive scan times, motivating computational super-resolution. This study investigates the efficacy of a feature-based loss function in preserving diffusion signal consistency in deep learning super-resolution. Using 7T data from the human connectome project to generate pairs of low- and high-resolution diffusion weighted images (DWI), we trained UNets for 2D super-resolution. Ablation and isolation studies evaluated different VGG16-layers for feature-based losses against an image-based L1 baseline. Deeper layers and combinations thereof resulted in grid-like artifacts in super-resolution DWIs, which persisted in diffusion parameters like quantitative and fractional anisotropy. No such artifacts were present when using the shallowest layer. Downstream analysis for this layer showed great consistency with the ground truth, even for 9-fold super-resolution. Image SNR and used VGG16-layer depths modulated artifact appearance and severity, mandating careful selection of contributing layers for application in and beyond diffusion MRI.

Influence functions approximate how removing a training example changes a quantity of interest, called the target function, such as a held-out loss. To estimate the influence of a group of examples, the standard practice is to sum the individual influences of its members. However, this sum does not capture how examples jointly affect the target: a pair of examples may be redundant or complementary, but the sum cannot distinguish these cases. We propose an interaction-aware influence function that characterizes how interactions between examples influence the target. By expanding the target to second order around the trained parameters, we obtain an estimator that augments the standard sum with a pairwise interaction term that captures the alignment between two examples' effects on the target. We empirically evaluate our estimator in two settings. First, on six dataset-model pairs spanning logistic regression, MLPs, and ResNet-9, our estimator tracks leave-group-out retraining substantially better than first-order influence across all settings. Second, when used as a greedy selection rule for instruction-tuning data on Llama-3.1-8B, it beats prior influence-based and representation-similarity baselines on five of seven downstream tasks, in a regime where standard influence-based selection underperforms random selection.

The minima of modern neural network loss functions are typically not isolated, rather they form connected components of reparameterization invariant solutions on the training data. Analytically characterizing these solutions is a hard problem, but sampling approaches are feasible. By construction, existing methods either spread over low-loss regions, and thus do not sample reparameterization invariant solutions exactly, or are inherently local, which limits exploration of other minima valleys. We propose sampling such reparameterization invariant models using a dynamical system based on kinetic energy, subject to a gravitational pull and a friction term that dissipates energy from the system. Our proposed sampler, DiMS, is guaranteed to sample exactly from the minimum level sets and depends on physically motivated hyperparameters which allows control over the exploration capabilities of the sampler. We consider uncertainty quantification in Bayesian inference as the motivating problem and observe improved performance compared to previously proposed approaches.

For most languages of the world, language model pre-training operates in a data-constrained regime where models must repeat their training data many times, degrading generalization. Two remedies exist: aggressive hyperparameter tuning such as high weight decay, and mixing in data from a high-resource auxiliary language to directly aid the low-resource target. While hyperparameter tuning regularizes the model by shrinking weights to restrict network capacity, auxiliary data mixing uses a tunable mixing ratio to expand the training distribution and diversify the training signal with new knowledge. Both offer a principled way to improve training in a data-constrained domain. We compare these levers systematically across four model scales from 150M to 1.43B parameters, using Arabic as the low-resource target and English as the auxiliary, over approximately 1000 pre-training runs. Three findings emerge. First, mixing yields larger improvements than hyperparameter tuning on both validation loss and downstream task accuracy, and the gap grows with model size. Second, we quantify how much mixing helps: it boosts performance by an amount equivalent to 2--3$\times$ the unique target data on validation loss and 2--13$\times$ on downstream task accuracy, with the gain scaling steeply with model size. Third, this divergence reveals that target-language validation loss systematically underestimates mixing's value. Mixing regularizes by diversifying the training signal and contributes knowledge the repeated target corpus cannot supply; validation loss captures only the first effect. Our practical recommendations are: mix in a high-resource language, prioritize the mixing ratio over hyperparameter tuning, and transfer hyperparameters from a small proxy model via $μ$P.

Deep super-resolution networks for precipitation downscaling achieve strong bulk skill yet systematically under-predict the heavy-tail events that drive flood risk. We demonstrate that the primary obstacle is the loss function, not the data: under intensity-weighted MAE, real and synthetic labels at the same input are simply averaged, meaning data augmentation shifts the predicted mean rather than the conditional distribution. We resolve this with Q-SRDRN, a multi-quantile super-resolution network trained with pinball loss at tau in 0.50, 0.95, 0.99, 0.999. Two CNN-specific design choices make this practical: IncrementBound enforces monotonicity while preserving each quantile channel's gradient identity, and separate per-quantile output heads provide independent filter banks for bulk and tail detection. Under this design, data augmentation via cVAE becomes complementary: the median head absorbs synthetic patterns without contaminating upper quantiles. Empirically, on Florida (convective/tropical-cyclone dominated), the un-augmented Q-SRDRN P999 head detects 1,598 of 2,111 events at 200 mm/day versus 88 for the deterministic baseline--an 18x detection-rate gain (4.2% to 75.7%)--with 63% lower KL divergence and 3.9% lower RMSE. Adding cVAE-generated samples lifts the P50 channel from 14 to 1,038 hits at 200 mm/day. On California (atmospheric-river dominated), the architecture reaches near-perfect detection (P999 SEDI >= 0.996 through 300 mm/day). On Texas, the baseline catches only 2 of 10,720 events at 200 mm/day while the P999 head catches 8,776 (81.9%). While the cVAE does not transfer across regions, multi-quantile regression captures extremes wherever the large-scale signal is strong, while augmentation rescues the median where it is not.

For stochastic process models, parameter inference is often severely bottlenecked by computationally expensive likelihood functions. Simulation-based inference (SBI) bypasses this restriction by constructing amortized surrogate likelihoods, but most SBI methods assume a black-box data generating process. While these surrogates are exact in the limit of infinite training data, practical scenarios force a strict tradeoff between model quality and simulation cost. In this work, we loosen the black-box assumption of SBI to improve this tradeoff for structured stochastic process models. Specifically, for neural network likelihood surrogates trained via probabilistic classification, we propose to augment the standard binary cross-entropy loss with exact score information $\nabla_θ\log p(x \mid θ)$ and adaptive weighting based on loss gradients. We evaluate our approach on case studies involving network dynamics and spatial processes, demonstrating that our method improves surrogate quality at a drastically lower computational cost than generating more training data. Notably, in some cases, our approach achieves downstream inference performance equivalent to a 10x increase in training data with less than a 1.1x increase in training time.

Corruption studies, the standard tool for evaluating chain-of-thought (CoT) faithfulness, infer which steps are ``computationally important'' from accuracy loss when steps are corrupted. We show that when benchmark chains end with an explicit terminal answer line, as in GSM8K and MATH, these tests largely measure \emph{answer placement} rather than where intermediate computation is carried out. Using matched GSM8K examples, removing only the final answer statement while preserving all reasoning collapses suffix sensitivity by about $19\times$ for Qwen~2.5-3B ($N{=}300$, $p{=}0.022$). Conflicting-answer prompts, which contain correct reasoning but a wrong explicit final answer, drive accuracy to zero or near-zero at 7B across five open-weight model families; wrong-answer following is strong at 3B--7B and attenuates sharply at larger scales. Replications on MATH, within-stable comparisons at 7B, and suffix-free chains show the same pattern in different guises: corruption sensitivity tracks the location of explicit answer text, not a fixed computational depth in the reasoning. Generation-time probes indicate that final answers are rarely early-determined during generation (${<}5\%$ early commitment), yet consumption-time behavior systematically follows explicit answer text. The confound is therefore largely a readout effect when the chain is consumed. We propose a three-prerequisite protocol (question-only control, format characterization, and an all-position sweep) as a practical minimum for future corruption-based faithfulness studies.

Noisy labels are common in large-scale medical imaging datasets due to inter-observer variability and ambiguous cases. We propose a statistically grounded and task-agnostic framework, Standardized Loss Aggregation (SLA), for detecting noisy labels at the sample level. SLA quantifies label reliability by aggregating standardized fold-level validation losses across repeated cross-validation runs. This formulation generalizes discrete hard-counting schemes into a continuous estimator that captures both the frequency and magnitude of performance deviations, yielding interpretable and statistically stable noisiness scores. Experiments on a public fundus dataset demonstrate that SLA consistently outperforms the hard-counting baseline across all noise levels and converges substantially faster, especially under low noise ratios where subtle loss variations are informative. Samples with high SLA scores indicate potentially ambiguous or mislabeled cases, guiding efficient re-annotation and improving dataset reliability for any classification task.

Deep neural networks for medical image diagnosis often achieve high predictive accuracy while relying on spurious or clinically irrelevant visual cues, limiting their trustworthiness in practice. Post-hoc explanation methods are widely used to visualize model decisions in the form of saliency maps; however, these explanations do not influence how models learn during training, allowing non-causal or confounding features to persist. This motivates the incorporation of explanation supervision directly into the training objective to guide model attention toward clinically meaningful regions and promote clinically grounded decision-making. This paper presents a systematic approach to integrate explanation loss into model training and analyzes how different explanation loss designs and supervision strengths influence both predictive performance and spatial faithfulness of explanations. To quantitatively assess interpretability, two complementary explanation performance metrics-annotation coverage and saliency precision-are introduced, enabling rigorous evaluation beyond qualitative visualization. Our experimental results reveal a clear trade-off between explanation quality and explanation loss coefficients. Furthermore, quantitative statistical analysis yields consistently improved explanation alignment while maintaining comparable accuracy. Experiments were conducted on annotated chest X-ray datasets; however, the proposed framework is applicable to a broad range of annotated biomedical imaging modalities. Overall, these findings demonstrate that explanation supervision is not a monolithic design choice and provide practical guidance for incorporating explanation loss into training objectives under noisy clinical annotations.

Loss reweighting is a widely used strategy for long-tailed classification, but existing reweighting strategies often rely on heuristics and rarely define a well-specified target. Inspired by Neural Collapse (NC), the ideal simplex Equiangular Tight Frame (ETF) terminal geometry suggests equal per-class average loss as a reasonable target for reweighting. Based on the ideal equal loss objective, we consider loss reweighting as an inverse problem and propose an inverse-view reweighting strategy that infers class weights dynamically to match this ideal objective. Empirically, NC metrics suggest our method can effectively reduce the loss imbalance coefficient and closer alignment with NC geometry while consistently outperforming strong long-tailed baselines on different datasets.

We introduce a predictive model that estimates the pre-training loss of large models from model size (N), batch size (B) and number of weight updates (K). This is the first loss prediction model that can handle changing batch size. The model outperforms Chinchilla's loss model, a model of the test loss using the batch size and number of tokens, in terms of projecting the loss at extrapolated compute budgets (up to 1000 folds). A natural use of the model is to find optimal N, B, K configurations under explicit and compound resource constraints like time, memory and compute. In our experiments, the model-selected configurations are close to ground-truth optimal. Our work advocates for loss prediction as a better alternative to heuristic-based laws, which are growing in complexity. The implementation is available on https://github.com/chuningxdy/Noisy-Quadratic-System.

We present the Wristband Gaussian Loss, a deterministic batch loss for Gaussianizing point embeddings without sampling, KL terms, or iterative transport. Each $x \in \mathbb{R}^d$ is mapped to a direction $u = x/\|x\|$ and a CDF-transformed radius $t = F_{χ^2_d}(\|x\|^2)$ on the wristband $S^{d-1} \times [0,1]$. We prove (and machine-verify in Lean~4) that for $d \ge 2$ the pushforward wristband map equals $σ_{d-1} \otimes \mathrm{Unif}[0,1]$ iff the source is $\mathcal{N}(0, I_d)$, and that the Neumann-reflected wristband repulsion energy is uniquely minimized at the uniform target. We compute this reflected-kernel objective in two ways: a nearest three-image pairwise truncation at $O(N^2 d)$, and a spectral Neumann path joining angular and radial Mercer modes (spherical-harmonic and cosine) at $O(N d K)$, with empirically matched gradients. A 1D Wasserstein radial term and a moment penalty serve as finite-sample accelerators with the same optimum, and Monte-Carlo null calibration turns the components into a single standardized statistic. We evaluate direct point-cloud Gaussianization with a calibrated barycentric $W_2$ score: a deterministic Gaussian reference batch is built by recursive Hungarian averaging, with each method reported as a $z$-score against same-size Gaussian batches. On the axis-uniform X benchmark, Wristband is competitive in 2D and gives the best 10D score. On a harder radial--angular-copula impostor whose Gaussian radial and angular marginals are correct but dependent, Wristband gives the best 10D and 128D scores. Coupled with learnable-key Euclidean attention and exact invertible flows, the resulting Deterministic Gaussian Autoencoder delivers a Gaussian-latent interface for counterfactual sampling with independent factors and a context/residual construction for dependent factors.

Structured pruning and knowledge distillation (KD) are typical techniques for compressing large language models, but it remains unclear how they should be applied at pretraining scale, especially to recent mixture-of-experts (MoE) models. In this work, we systematically study MoE compression in large-scale pretraining, focusing on three key questions: whether pruning provides a better initialization than training from scratch, how expert compression choices affect the final model after continued training, and which training strategy is most effective. We have the following findings: First, across depth, width, and expert compression, pruning a pretrained MoE consistently outperforms training the target architecture from scratch under the same training budget. Second, different one-shot expert compression methods converge to similar final performance after large-scale continual pretraining. Motivated by this, we introduce a simple partial-preservation expert merging strategy that improves downstream performance across most benchmarks. Third, combining KD with the language modeling loss outperforms KD alone, particularly on knowledge-intensive tasks. We further propose multi-token prediction (MTP) distillation, which yields consistent gains. Finally, given the same training tokens, progressive pruning schedules outperform one-shot compression, suggesting that gradual architecture transitions lead to better optimization trajectories. Putting it all together, we compress Qwen3-Next-80A3B to a 23A2B model that retains competitive performance. These results offer practical guidance for efficient MoE compression at scale.

Neural scaling laws approximate a language model's loss as a power-law function of parameter count $N$ and token count $D$. Following Chinchilla-style compute-optimal training, many studies fit scaling laws from runs performed under a fixed tokens-per-parameter (TPP) ratio $k$ and set $D = kN$. We show that this collinear design, combined with the empirically common near-equality of the exponents governing $N$ and $D$, induces an inherent ill-conditioning in the Gauss-Newton least-squares problem: the condition number of the design grows as the inverse square of the gap between the $N$ and $D$-exponents. The scale coefficients become practically unidentifiable, with confidence intervals inflating by an order of magnitude or more, yielding a ``sloppy'' model whose extrapolations degrade sharply off the training ray. We prove this for four scaling-law formalisms and derive a closed-form TPP-diversity threshold that is necessary and sufficient for well-conditioned estimation. Empirically, non-collinear designs outperform collinear ones on held-out splits with a 97.3% win rate across four laws, five corpora, multiple floating point precision modes. We further show the degeneracy is rooted in Jacobian geometry and is not an artifact of the loss function: any smooth estimation objective whose curvature involves the Jacobian inherits the same ill-conditioning.

A key strategy for balancing performance and cost in modern machine learning systems is to dynamically route queries to either a low-cost model or a more expensive oracle (such as a large pretrained model or human expert), an approach known as model routing. In this work we present a new uncertainty-aware router that (1) avoids unnecessary oracle calls on inherently ambiguous queries, and (2) adapts dynamically to different loss functions and cost parameters through simple hyperparameter changes, without retraining. Our method, applicable to any classification setting where multiple independent annotations per input are available, is based on decomposing total uncertainty into irreducible and reducible components using higher-order predictors [Ahdritz et al., 2025]. This enables a unified approach to both routing and abstention: predict with the weak model when uncertainty is low, route to the oracle when reducible uncertainty is high, and abstain when irreducible uncertainty is high. Our router comes with strong theoretical guarantees bounding regret relative to optimal task-specific routers. We conduct experiments on both synthetic and real-world datasets that demonstrate the benefits of our approach in suitable regimes -- in particular, whenever reducible and irreducible uncertainty are not too correlated.

Modern deep models are often pretrained on large-scale data with missing labels using composite objectives, where the relative weights of multiple loss terms act as hyperparameters. Tuning these weights with random search or Bayesian optimization is computationally expensive, as it requires many independent training runs. To address this, we propose a gradient-based bilevel method that learns pretraining loss weights online by aligning the composite pretraining gradient with a downstream objective. By exploiting the structure of the loss, the method avoids the multiple backward passes typically required by truncated backpropagation through the full model, reducing the overhead of hyperparameter tuning to approximately 30% above a single training run. We evaluate the approach on event-sequence modeling and self-supervised computer vision, where it matches or improves upon carefully tuned baselines while substantially reducing the cost of hyperparameter tuning compared to random or Bayesian search.

Mixture-of-Experts (MoE) language models route each token to a small subset of experts, but whether the routes selected by a trained top-$k$ router are good ones is rarely evaluated directly. Holding the model fixed, we compare each standard route against sampled equal-compute alternatives for the same token and score each by the next-token probability it assigns to the realized token in a verified reasoning trajectory. The result is sharply token-conditional: the standard router is well-aligned with route utility on confident tokens but uninformative on the fragile tokens that drive hard reasoning, where lower-loss equal-compute routes consistently exist inside the frozen model but are not selected. The same pattern holds across Qwen3-30B-A3B, GPT-OSS-20B, DeepSeek-V2-Lite, and OLMoE-1B-7B, and follows structurally from how standard top-$k$ training evaluates routing decisions: the language modeling loss scores only the executed route, and load balancing depends only on aggregate routing statistics. A minimal router-only update to the final-layer router, leaving every expert and every other router frozen, is sufficient to shift pass@K on AIME 2024+2025 and HMMT 2025 for both Qwen3-30B-A3B and GPT-OSS-20B, suggesting that at least part of the failure reflects router-reachable misallocation rather than expert capacity alone.

While many approaches to improve VQ-VAE performance focus on codebook size and utilization, the effect of dimensional collapse, where trained VQ-VAE representations live in an extremely low-dimensional subspace (1-2% of full rank), remains unaddressed. We show theoretically and empirically that dimension collapse causes a hard loss lower bound that various codebook improvement techniques fail to surpass. Our analytic framework extends the sequential learning effect of Saxe et al. [2014] by introducing ideas from rate-distortion theory and explains how the latent collapse is caused by the VQ suppressing lower-variance directions. Our theory justifies a simple solution: a "warm-up phase" that trains the model as an (unquantized) autoencoder before introducing VQ. On both synthetic experiments and large-scale image (VQGAN) and audio (WavTokenizer) VQ-VAEs, we show that AE Warm-Up successfully restores representation dimension, leading to lower reconstruction and perceptual loss at the same training budget. Across codebook sizes $K \in$ {$2^{10}, 2^{14}, 2^{16}$}, AE warm-up raises VQGAN codebook effective dimension from 3-5 to 17-19 and reduces rFID by 17-35%; on WavTokenizer at $K \in$ {$2^{13}, 2^{14}$}, it raises codebook dimension from 4 to 17-19 and improves PESQ by 11-14%. We empirically characterize how warm-up duration governs the achievable final loss. In agreement with experiment, our theoretical analysis predicts downstream performance as a function of warm-up length, enabling an adaptive criterion for switching from AE Warm-up to VQ-VAE training.

Pre-training of Large Language Models is often prohibitively expensive and inefficient at scale, requiring complex and invasive modifications in order to achieve high data throughput. In this work, we present Token-Superposition Training (TST), a simple drop-in method that significantly improves the data throughput per FLOPs during pre-training without modifying the parallelism, optimizer, tokenizer, data, or model architecture. TST is done in two phases: (i) A highly efficient superposition phase where we combine many contiguous tokens into one bag and train using a multi-hot cross-entropy (MCE) objective, and (ii) a recovery phase where we revert back to standard training. We extensively evaluate TST on the scale of 270M and 600M parameters and validate on 3B and a 10B A1B mixture of experts model, demonstrating that it is highly robust in different settings. Ultimately, TST consistently outperforms baseline loss and downstream evaluations, and under equal-loss settings, TST yields up to a 2.5x reduction in total pre-training time at the 10B A1B scale.

Standard cross-entropy is the default classification loss across virtually all of machine learning, yet it treats all misclassifications equally, ignoring the semantic distances that a class hierarchy encodes. We propose Hierarchy-Aware Cross-Entropy (HACE), a drop-in replacement for standard cross-entropy that incorporates a known class hierarchy directly into the loss. HACE combines two components: prediction aggregation, which propagates the model's probability mass upward through the class hierarchy to ensure that parent nodes accumulate the confidence of their children; and ancestral label smoothing, which distributes the ground-truth signal along the path from the true class to the root. We evaluate HACE on CIFAR-100, FGVC Aircraft, and NABirds in two regimes: end-to-end training across six architectures spanning convolutional and attention-based designs, and linear probing on frozen DINOv2-Large features. In end-to-end training, HACE improves accuracy over standard cross-entropy in 15 out of 18 architecture--dataset pairs, with a mean gain of 4.66%. In linear probing on frozen DINOv2-Large features, HACE outperforms all competing methods on all three datasets, with a mean improvement of 2.18% over the next best baseline.

Backdoor attacks can implant malicious behaviours into deep models while preserving performance on clean data, posing a serious threat to safety-critical vision systems. Although backdoor mitigation has been studied extensively for image classification, defenses for object detection remain comparatively underdeveloped. Adversarial fine-tuning is a common backdoor mitigation approach in classification, but adapting it to detection is nontrivial as classification-oriented adversarial generation does not match the detection attack space, where attacks may cause object misclassification or disappearance, and standard detection losses can dilute the repair signal across many predictions. We address these challenges through a detection-aware adversarial fine-tuning framework for mitigating object-detection backdoors when the defender has access only to a compromised detector and a small clean dataset, without knowing the attack objective. For adversarial generation that does not require knowledge of the attack objective, we introduce soft-branch minimisation, which uses a soft gate to combine objectives aligned with misclassification and disappearance attacks, together with a detection-aware classification-loss maximisation. For targeted repair, we introduce a dual-objective fine-tuning loss applied to target-matched predictions, concentrating the defensive update on predictions most relevant to the backdoor behaviour. Experiments across CNN- and Transformer-based detectors show that our approach more effectively reduces attack success while preserving true detections, compared with classification-oriented baselines, and maintains competitive clean detection performance.

Federated learning (FL) systems typically employ stateless client selection, treating each communication round independently and ignoring accumulated evidence of client contribution quality. Under non-IID data, this leads to slow convergence and unstable training, particularly when selection relies on local proxies (e.g., training loss) that are misaligned with the global optimization objective. These challenges are especially pronounced in Internet of Things (IoT) and Industrial IoT (IIoT) environments, where data is highly heterogeneous and distributed across devices observing different traffic patterns. In this paper, we propose VARS-FL (Validation-Aligned Reputation Scoring for Federated Learning), a client selection framework that quantifies each client's contribution using the reduction in server-side validation loss induced by its update. These per-round signals are aggregated into a Reputation score that combines a sliding-window average of recent contributions with a logarithmically scaled participation term, enabling robust exploration-exploitation selection. VARS-FL requires no changes to local training or aggregation and remains fully compatible with standard FedAvg. We evaluate VARS-FL on a 15-class non-IID IoT intrusion detection task using the Edge-IIoTset dataset, with 100 clients across multiple seeds, and compare it against FedAvg, Oort, and Power-of-Choice. VARS-FL consistently improves accuracy, F1-Macro, and loss, while accelerating convergence (up to 36% fewer rounds to reach 80% accuracy). These results demonstrate that validation-aligned, history-aware client selection provides a more reliable and efficient training process for federated learning in heterogeneous IoT environments.

Algorithms in machine learning and AI do critically depend on at least three key components: (i) the risk function, which is the expectation of the loss function, (ii) the function space, which is often called the hypothesis space, and (iii) the set of probability measures, which are allowed for the specified algorithm. This paper gives a survey of a certain class of loss functions, which we call ratio-based. In supervised learning, margin-based loss functions for classification tasks depending on the product of the output values $y_i$ and the predictions $f(x_i)$ as well as distance-based loss functions depending on the difference of $y_i$ and $f(x_i)$ for regression are common. Distance-based loss functions are in particular useful, if an additive model assumption seems plausible, i.e. the common signal plus noise assumption. However, in the literature, several loss functions proposed for regression purposes have a multiplicative error structure in mind and pay attention to relative errors, i.e. to the ratio of $y_i$ and $f(x_i)$. In this survey article, we systematically investigate such ratio-based loss functions and propose a few new losses, which may be interesting for future research. We concentrate on investigating general properties of ratio-based loss functions like continuity, Lipschitz-continuity, convexity, and differentiability, because these properties play a central role in most machine learning algorithms. Therefore, we do not focus on some specific machine learning algorithm to derive universal consistency, learning rates, or stability results. Instead, we want to enable future research in this direction.

Reducing power consumption in AI accelerators is increasingly important. Approximate computing can reduce power consumption while keeping the accuracy loss small. Since multipliers are power-hungry components in AI models, this paper focuses on synthesizing low-power approximate multipliers (AxMs). Unlike prior works that design AxMs separately from AI model training, we present TRAM, which jointly optimizes the AxM structure and AI model parameters to lower power with small accuracy loss. Experiments show that compared to state-of-the-art AxMs, TRAM achieves up to 25.05% AxM power reduction on CNNs with CIFAR-10, and reduces power by up to 27.09% on vision transformers with ImageNet.

A brain tumor is a medical disorder faced by individuals of all demographics. Medically, it is described as the spread of non-essential cells close to or throughout the brain. Symptoms of this ailment include headaches, seizures, and sensory changes. This research explores two main categories of brain tumors: benign and malignant. Benign spreads steadily, and malignant expresses growth, making it dangerous. Early identification of brain tumors is a crucial factor for the survival of patients. This research provides a state-of-the-art approach to the early identification of tumors within the brain. We implemented the SegResNet architecture, a widely adopted architecture for three-dimensional segmentation, and trained it using the automatic multi-precision method. We incorporated the dice loss function and dice metric for evaluating the model. We got a dice score of 0.84. For the tumor core, we got a dice score of 0.84; for the whole tumor, 0.90; and for the enhanced tumor, we got a score of 0.79.

We study strong universal Bayes-consistency in the realizable setting for learning with general metric losses, extending classical characterizations beyond $0$-$1$ classification (Bousquet et al., 2020; Hanneke et al., 2021) and real-valued regression (Attias et al., 2024). Given an instance space $(X,ρ)$, a label space $(Y,\ell)$ with possibly unbounded loss, and a hypothesis class $H \subseteq Y^{X}$, we resolve the realizable case of an open problem presented in Tsir Cohen and Kontorovich (2022). Specifically, we find the necessary and sufficient conditions on the hypothesis class $H$ under which there exists a distribution-free learning rule whose risk converges almost surely to the best-in-class risk (which is zero) for every realizable data-generating distribution. Our main contribution is this sharp characterization in terms of a combinatorial obstruction: Similarly to Attias et al. (2024), we introduce the notion of an infinite non-decreasing $(γ_k)$-Littlestone tree, where $γ_k \to \infty$. This extends the Littlestone tree structure used in Bousquet et al. (2020) to the metric loss setting.

We propose Evolutionary Dynamic Loss (EDL), a framework that learns a transferable classification loss in the probability space using unlimited synthetic prediction-label pairs, without accessing real samples during the main loss pretraining stage. EDL parameterizes the loss as a lightweight network and is trained with a semantics-free ranking-consistency objective that assigns larger penalties for more erroneous predictions. To robustly explore the space of loss functions, we optimize EDL via an evolutionary strategy and introduce chaotic mutation to improve exploration under noisy fitness evaluations. Experiments on CIFAR-10 with ResNet backbones show that EDL can serve as a drop-in replacement for cross-entropy and achieves competitive or improved accuracy, while ablation studies confirm that chaotic mutation yields faster convergence and better synthetic pretraining metrics than standard Gaussian mutation.