Cross-Entropy Losses

While Large Language Models excel in natural language processing, efficiently extending their capabilities to spoken input remains a significant challenge. Existing methods for building SpeechLLMs often rely on computationally expensive full-model fine-tuning, or employ parameter-efficient projectors that suffer from inefficient token sequence lengths and costly full-model supervision. In this paper, we introduce Aligned Continuous Integrate-and-Fire, a highly efficient framework for zero-shot speech processing. Our method dynamically compresses continuous acoustic frames into the exact discrete token length of the target text utilizing explicit Dynamic Time Warping alignments. This allows our initial training stage to establish a robust acoustic-to-semantic bridge using lightweight distance metrics, entirely bypassing the computationally expensive LLM forward pass. For subsequent fine-tuning, we propose a memory-efficient knowledge distillation objective that targets a single LLM layer, performing competitively with full-model cross-entropy training at a fraction of the computational cost. Through extensive evaluations on Automatic Speech Recognition and Speech Translation, we demonstrate that our method achieves superior performance compared to prior parameter-efficient baselines.

In sign language recognition, the isolated (ISLR) classification loss treats a single label as ground truth, as does the frame-level auxiliary classifier over pseudo-labels we add to continuous (CSLR) methods, which lack one. Stylistic variation blurs ISLR annotation and the lack of temporal boundaries in CSLR forces pseudo-labels; both are noisy. We therefore apply symmetric and generalized cross entropy (SCE, GCE), robust alternatives to cross entropy (CE) from image classification, not to connectionist temporal classification but to the preceding single-label classifier. On ASL Citizen with injected symmetric noise on three backbones (three seeds for ST-GCN), robust losses cost at most 2.5 pt when labels are clean and beat CE by 2.9-10.0 pt in all six conditions at noise rate 0.2, one of which only after q was re-selected on dev. GCE gains more, but its optimal q does not transfer across backbones, whereas one SCE setting works in all nine conditions; both vary 2-11 times more than CE across runs, so a favorable point estimate does not establish stability. For CSLR (PHOENIX-2014) we report no gain; our frame-level targets carry a systematic assignment bias, making that study a diagnosis of a single configuration. At lambda_aux = 25 the pseudo-label CE auxiliary raises word error rate above the no-auxiliary baseline on VAC, CorrNet and SlowFastSign, and GCE/SCE improve on CE by 1.7-3.2 pt (three of six conditions return below that baseline). However, the three losses differ by more than an order of magnitude in effective gradient at a common lambda_aux: matching the initial gradient shrinks the gap to 0.4-0.9 pt, and lowering the CE weight alone already beats that baseline, so neither the degradation nor the improvement can be separated from the effect of the weight. We use only symmetric noise; multi-seed evaluation covers only ST-GCN and VAC isolated.

Standard cross-entropy loss causes neural networks trained on ordinal classification tasks to hedge predictions toward center classes, a failure mode we term \emph{center-class hedging}. This occurs because predicting the middle class minimizes expected symmetric loss, making it the path of least resistance regardless of the true label. Existing ordinal losses address related problems such as large-error penalization and rank consistency, but none directly suppresses center-class hedging as a function of where the true label lies relative to the ordinal center. We propose the Adaptive Margin Ordinal Loss (AMOL), a multiplicative weight applied to per-class loss terms of the form $m(k,y) = 1 + \alpha \cdot (1 - |k-c|/c) \cdot (|y-c|/c)$, where $c$ is the center class, $k$ is the candidate class, and $y$ is the true label. The weight encodes a joint condition: it is large only when the candidate class is near center and the true label is far from center, collapsing to standard behavior otherwise. We further introduce the Center-Hedging Rate (CHR) as a diagnostic metric that directly quantifies this failure mode. Across four ordinal classification benchmarks and five random seeds, AMOL achieves the best or tied-best Quadratic Weighted Kappa (QWK) on all four datasets compared to cross-entropy, OLL, and SORD baselines. An asymmetric variant (AMOL-asym) eliminates center-class hedging entirely on the Abalone dataset ($\text{CHR} = 0.000 \pm 0.000$ across all five seeds, $n \approx 266$ extreme-class test samples per run), compared to $0.074 \pm 0.005$ for standard cross-entropy.

Large language models are typically trained under uniform token weighting, which allows frequent and low-information tokens to dominate learning and can increase the tendency to memorize surface-level text spans. To address this, we present an information-weighted cross-entropy loss that rescales token-level contributions using TF-IDF statistics, emphasizing semantically informative tokens while down-weighting ubiquitous ones. Experiments on five decoder-only LLMs ranging from 1.1B to 13B parameters show consistent reductions in memorized substring length while preserving perplexity and downstream task performance. Under LoRA fine-tuning, TF-IDF reduces average substring memorization length by 14% across all five models. Under full-weight fine-tuning on TinyLLaMA 1.1B, the reduction reaches 58%. Our approach is architecture-agnostic and can be incorporated into existing training pipelines with less than 3% computational overhead, offering a lightweight and principled way to mitigate memorization without disrupting standard training dynamics.

Supervised fine-tuning (SFT) applies a uniform cross-entropy loss to all target tokens, even though different tokens provide unequal learning signals for mathematical reasoning. This uniform treatment can over-sharpen already mastered tokens while amplifying learning pressure on uncertain, low-confidence tokens, leading to suboptimal training dynamics. We propose Trimmed Logit-Gap SFT (TrimSFT), a simple token-level reweighting method that scales the SFT loss according to the logit gap between the gold token and its strongest competitor. TrimSFT trims supervision away from both extremes: tokens already mastered (large logit gap) and tokens weakly supported by the current model (small or negative logit gap), concentrating learning within an intermediate logit-gap region between them. We instantiate this principle with a Gaussian weight centered at margin m with bandwidth τ, requiring no reference model or additional forward pass. We evaluate TrimSFT on six base models from the Llama, Qwen, and DeepMath families across five mathematical reasoning benchmarks. TrimSFT consistently improves over standard SFT, achieving the best average performance on five out of six models, with gains of up to +26.9 points over SFT on MATH500. Further analyses show that the bandwidth τ matters more than the exact margin location, and that half-trim variants that remove supervision pressure from only one side yield inferior trade-offs. A token-level logit-gap distribution analysis suggests that TrimSFT reshapes model confidence in a more balanced way than uniform SFT or monotonic reweighting methods. These results suggest that reasoning SFT can benefit from trimming both extremes rather than treating all tokens uniformly.

We study the training dynamics of multiclass logistic regression on high-dimensional Gaussian mixture models with a large number of classes and establish precise scaling laws governing the cross-entropy risk under gradient-based optimization. We show that learning proceeds sequentially across classes, from most to least frequent. When the class priors follow a power law distribution, the risk dynamics decompose into three phases: an initial plateau until the first class is learned, a power-law decay regime during which sequential learning occurs, and a final convergence regime. We then analyze how model capacity interacts with optimization under a fixed compute budget. When the effective dimension is restricted via projection onto leading principal components, the risk decomposes into a capacity term (a power law in the retained dimension) and an optimization term (a power law in training time). Optimizing this tradeoff yields a compute-optimal scaling law for logistic regression, with explicit prescriptions for model size and training time as functions of compute. These results extend theoretical scaling laws from linear regression to multiclass classification, while connecting to empirical scaling laws observed in large-scale neural networks.

Vision-Language Pretrained Models (VLPMs) offer a scalable path to open-vocabulary chest radiology understanding, yet two aspects remain underexplored: how structured clinical semantics extracted from medical reports can reduce in-batch noise during contrastive learning, and how cross-modal fusion can be designed to produce more faithful spatial grounding without added complexity. We introduce AlphaRAD, addressing these opportunities through two contributions. First, we construct a large-scale structured medical concept space from medical reports parsed by a Large Language Model for training, thereby mitigating in-batch learning noise and removing heuristic pair matching in contrastive learning, and thus naturally positioning AlphaRAD as a medical concept discriminator trained via $α$-Corrected Binary Cross-Entropy. Second, we propose FLaS (Factorized Latent Supervision), an extremely simple yet effective cross-modal feature fusion module that factorizes VLPM representations into independent subspaces, using dedicated alignment supervision to enhance the expressiveness of spatial grounding without introducing additional model parameters. Through extensive empirical validation, AlphaRAD shows strong zero-shot generalization across diverse chest radiology tasks. Notably, it establishes state-of-the-art average performance across 16 classification benchmarks, while achieving individual state-of-the-art results via distinct gains on 7 grounding/phrase grounding and 3 segmentation datasets.

Virtual try-on (VTON) requires not only realistic generation but also faithful preservation of garment characteristics. However, existing evaluation metrics such as PSNR, SSIM, KID and FID struggle to measure the consistency between the generated and reference garments, particularly in capturing the multi-dimensional characteristics of garment fidelity. To address this, we propose DAT: a Dimension-wise Assessment framework for virtual Try-on, which decomposes garment consistency into seven interpretable dimensions: silhouette, color, neckline and sleeve shape, major decoration and structure, material texture, fine-detail fidelity, and logo preservation, each formulated as a discrete attribute-level prediction task. To train this specialized assessment model, we adopt a two-stage learning paradigm comprising large-scale weak supervision on 50K samples, followed by refinement on 10K higher-quality annotations obtained via multi-model voting. Furthermore, we employ weighted cross-entropy loss to mitigate the severe label imbalance inherent across evaluation dimensions. Beyond its role as an evaluation framework, the assessment model can be integrated into reinforcement learning optimization of Qwen-Image-Edit for VTON, where dimension-wise rewards are adaptively aggregated to emphasize under-optimized aspects during training. Experimental results show that our method (8B parameters) achieves state-of-the-art performance in terms of balanced accuracy, SROCC, and PLCC, outperforming strong proprietary models such as Gemini-3.1, Qwen3.7-plus, and GPT-5.5, while also serving as an effective optimization signal for reward-guided VTON generation

Latent world models are judged by how well they predict, so when planning fails at long horizons the natural reading is that the predictor degrades. On a reproduction of LeWorldModel on TwoRoom we show the binding constraint is the planner's objective instead. The predictor is not the limit: its imagined state seventy-five environment steps ahead is still only 0.189 as wrong as assuming the world froze, while the planner never imagines beyond twenty-five. The objective is. Cross-entropy-method planning minimises squared latent distance, which tracks true distance at r = 0.426, saturates by about eighty arena units and decreases beyond a hundred and twenty, so moving away from the goal can lower the cost. The information is present throughout: a ridge probe recovers position from the frozen embedding at R^2 0.9922. The pathology is the method's, not one reimplementation's. It is present in the authors' released weights, and across four checkpoints long-horizon success rank-orders exactly with metric quality and inversely with prediction accuracy. Replacing only the objective, with nothing retrained and no GPU, lifts goals reached at offset 100 from 26.0% to 98.0%, equals the 98.0% at offset 25, and reaches 92.0% under a third of the budget: planning stops depending on the horizon. The best cost is not the most accurate. A head learned from frame separation alone predicts spatial distance worse than a position probe (r = 0.819 against 0.9897) yet plans better, charging 24% more to cross the environment's dividing wall where squared latent distance charges 4% less. It has learned reachability, not proximity.

Reinforcement learning with verifiable rewards yields no group-relative signal when rollout groups are uniformly correct or uniformly wrong, which account for 63.0-68.0% of groups in our experiments. We propose SKALD (Skill-Anchored Latent Distillation), an on-policy self-distillation framework that uses two context views of the same Qwen3-Base model: a question-only student and a teacher conditioned on an abstract, explicit-answer-filtered skill card. The student is trained on its own prefixes, transferring the skill-induced advantage into shared parameters without privileged input at test time. To stabilize context-induced distribution mismatch, SKALD employs an annealed exponentially tilted objective that downweights teacher-preferred tokens with very low student likelihood; as the tilt vanishes, it converges to teacher cross-entropy and recovers the forward-KL student gradient. An empirical gate activates distillation only when verified rollouts estimate a positive teacher advantage. Across five held-out mathematics benchmarks, SKALD improves overall avg@8 over GRPO by +2.46, +4.85, and +12.01 at 0.6B, 1.7B, and 4B, respectively. At 1.7B, zero-variance-only distillation recovers 84.7% of the full gain, while SKALD remains +4.06 above FLOP-matched GRPO and exceeds contextual skill exposure by +3.77. These results show that abstract skills provide dense supervision where group-relative rewards become uninformative.

Muon's polar update is exact for an unweighted spectral geometry. We introduce GO-MUON, which uses a matched data-dependent geometry and reuses it across several optimization steps. Conditioned on any positive-definite left and right maps, its raw update exactly solves the corresponding weighted spectral oracle; this statement is independent of how the maps are estimated or how recently they were refreshed. For softmax cross-entropy, we quantify when the observed-label backward factor approaches the model Fisher and generalized Gauss--Newton factor. We also show that four-step refresh nearly preserves the tracking delay of slowly changing geometry while increasing stationary factor noise, making lazy geometry a compute--statistics tradeoff rather than a denoising mechanism.

Neural network classifiers trained by cross-entropy minimization are highly sensitive to label noise and adversarial contamination. While robust alternatives offer bounded influence and resistance to corruption, their statistical foundations in the deep learning setting are insufficient due to a fundamental difficulty: neural parameterizations are non-identifiable, so the population loss minimizer is an equivalence class of parameters, not a unique point. We develop a consistency theory for robust neural classifiers based on the S-divergence family that requires no identifiability assumption. Casting training as stochastic optimization over a non-identifiable parameter space, we prove that empirical S-divergence minimizers converge to the population-optimal equivalence class under mild regularity conditions, and verify these conditions for three architecture choices. We further establish that limit points of the robust training algorithm are stationary points of the empirical objective. Experiments on vision and language benchmark datasets confirm that S-divergence training maintains clean-data accuracy while exhibiting performance competitive with existing robust methods.

On-policy self-distillation (OPSD) adapts a language model by distilling guidance from a frozen teacher on trajectories sampled from the student. Its effectiveness, however, depends critically on the quality of those trajectories. We show that when student rollouts drift from target trajectories, conditioning the teacher on off-target prefixes substantially weakens its task-relevant supervision. Controlled prefix-corruption experiments expose this failure mode, which we term rollout-conditioned signal degradation. To address this problem, we propose a unified training framework that separates two complementary supervision pathways. The first retains rollout-conditioned distribution matching, providing guidance on states the student actually visits. The second applies supervised cross-entropy on canonical ground-truth contexts, avoiding the incompatibility of imposing target tokens on erroneous rollout prefixes. Token-level rollout-target alignment is used to adapt the strength of the canonical-context anchor, emphasizing it during cold start and relaxing it as rollout quality improves. Experiments across multiple model scales, two task families, and general-reasoning benchmarks show that the proposed approach improves task acquisition over OPSD while preserving general capabilities, resulting in a more favorable empirical plasticity-stability trade-off. These findings identify context quality as a central bottleneck in on-policy self-distillation and demonstrate the value of separating rollout-conditioned guidance from canonical supervision.

Multivariate time series forecasting presents unique challenges because future variables often co-evolve under shared system dynamics. While existing studies mainly focus on cross-variable dependencies in historical observations, dependencies among future values are much less explored. Specifically, modern forecasting models largely follow the Direct Forecasting (DF) paradigm, generating multi-step forecasts with point-wise objectives that do not explicitly constrain cross-variable structure. In this work, we show that the DF objective is mismatched in the presence of cross-variable and lagged dependencies, revealing an objective gap. To address this issue, we propose \textbf{C}ross-\textbf{V}ariable \textbf{Loss} (CvLoss), a plug-in structural regularizer that constrains forecast residuals on a cross-variable graph. CvLoss penalizes inconsistent edge-wise residual differences over forecast patches, encouraging consistency across both synchronous and asynchronous interactions. Our experiments show that CvLoss consistently improves competitive forecasting models, outperforms representative learning objectives, and is compatible with a variety of forecasting backbones.

In medical multiple-choice question answering (MCQA), Retrieval-Augmented Generation (RAG) can supplement the domain knowledge of language models (LMs). However, since vanilla RAG indiscriminately utilizes retrieved documents, it can degrade LM performance. To address this, we propose MedJudgeRAG. Our framework represents retrieved documents as a dynamic knowledge graph (KG) composed of entities and relations. For each option, the model judges an evidence verdict from the retrieved documents and the KG. Based on the verdict combination, the model determines a knowledge utilization strategy to reason toward the final answer. These capabilities are trained via supervised fine-tuning using structured reasoning traces generated by a teacher LM. The training employs a weighted cross-entropy loss that differentially weights the KG and reasoning segments. Experiments on two medical MCQA benchmarks demonstrate that MedJudgeRAG consistently outperforms both vanilla RAG and parametric baselines. Furthermore, ablation analysis reveals that the dynamic KG is more effective as graph-conditioned supervision at training time than as an explicit output at inference time. Our code is available at https://github.com/hyu-amllab/medjudgerag, and the generated reasoning traces are released at https://huggingface.co/datasets/youarethewon/medjudgerag.

Discrete flow matching provides a flexible framework for generative modeling on discrete structures. However, the standard factorized training objective exposes the model to targets of varying difficulty, mixing well-conditioned, predictable tokens with ambiguous, high-entropy ones. We empirically demonstrate that the uncertainty over the value of each token is closely related to the density of available context in its neighborhood. Motivated by this observation, we propose a simple modification to the underlying continuous-time Markov chain (CTMC) that incorporates local context information. Our context-weighted sampler improves generation quality with negligible computational overhead, while our scaled cross-entropy loss function reweights the training signal from different tokens and reduces generative perplexity by up to 63% on OpenWebText. Moreover, our approach matches a strong semi-autoregressive block diffusion baseline in quality while retaining the ability to perform generation in any order. These results highlight the role of local context as an important factor in discrete generative modeling and show that simple context-aware modifications can significantly improve both sampling and training efficiency.

Semantic segmentation of 3D point clouds faces severe class imbalance, yet the effectiveness of specialized imbalance-aware methods from 2D computer vision remains unclear in 3D contexts. We systematically evaluate 11 imbalance mitigation approaches across datasets with extreme (641:1) and moderate (56:1) imbalance ratios, revealing a surprising finding: standard cross-entropy with uniform weighting achieves competitive performance, typically within 0.8-3.3% mIoU of specialized methods across architectures and datasets. Through multifaceted mechanistic analysis of error patterns, decision boundaries, and the geometry of the optimization landscape, our analyses suggest that imbalance severity shapes the topology, creating narrow solution basins under extreme imbalance and flat plateaus under moderate imbalance. This appears to constrain the effectiveness of loss-level modifications, as all methods must navigate these geometric constraints. Our findings offer practical guidance; standard cross-entropy provides a robust baseline, with specialized methods offering modest improvements (0.8-3.3% mIoU) that vary by architecture and dataset but risk substantial degradation if poorly tuned. This work provides the first mechanistic explanation for why techniques proven effective in 2D do not readily transfer to point-based 3D point cloud segmentation, validated across two representative architectures.

We present a novel viewpoint for uncertainty quantification. Uncertainty measures are not primitives, in need of axioms and argumentation, but instead consequences, of higher-level modelling decisions. We show how epistemic and aleatoric uncertainty measures can be derived via decomposition of a subjective risk, based on a strictly proper loss. Reverse cross entropy provides a prominent example, where decomposition recovers the classic information-theoretic uncertainty terms. The same approach recovers numerous measures previously proposed across the UQ literature, providing them a common theoretical foundation. This suggests a new approach to UQ: given a modelling scenario and strictly proper loss, the corresponding epistemic and aleatoric terms are induced by the subjective-risk decomposition. We then extend our view to learning theory: we introduce and analyse subjective risk analogues of excess risk, approximation error and estimation error, and identify the connections to UQ. We consider this a first step towards a full learning-theoretic framework for uncertainty quantification.

While autoregressive models optimize the exact data likelihood via the chain rule, diffusion models are typically trained with denoising objectives. We develop conservation laws based on generalized extrinsic information transfer (GEXIT) functions for a broad class of memoryless noise processes, showing that the data--model cross-entropy (CE) can be characterized exactly as an integral of local information-theoretic derivatives along the noise path. This yields a unified characterization of the likelihood for discrete and continuous diffusion, with the Gaussian case reducing to the well-known mutual information--minimum mean-square error (I-MMSE) relationship. An immediate implication is a locality property: one can compute the information-theoretic derivatives using only the marginal posteriors along the noise path. As a result, training reduces to learning the marginal posteriors by minimizing the negative log-likelihood. While the conservation law implies that the entropy does not depend on the noise path, finite-capacity denoisers approximate the posteriors with varying accuracy across noise types, leading to differences in performance. We validate these predictions on synthetic Markov sources and standard benchmarks, including text8 and CIFAR-10.

Similarity search is a primary application of embedding models trained by contrastive learning. For one of the most popular contrastive learning loss functions, InfoNCE, we show that the population risk with $k$ negative samples is $O(1/k)$ close to an expected cross-entropy which quantifies deviation between i) a softmax similarity search over unseen data using the learned embedding function, and ii) an idealised softmax search over the same data but using similarity implicitly represented in the positive sample generator. This complements existing interpretations of InfoNCE in the $k\to\infty$ limit which are phrased in terms of mutual information, and alignment versus uniformity in embeddings. To quantify generalisation performance, we introduce a new continuity bound for the InfoNCE loss, obtained via Gâteaux differentiation. The bound preserves the structure of averaging over negative samples present in the loss function and features an ``inverse temperature'' parameter which can be tuned to account for the algorithmic temperature. For embedding functions which are Lipschitz in a parameter, this yields a simple demonstration that the averaging effect of $k$ negative samples in the InfoNCE loss carries over to stabilisation of the generalisation error as $k$ grows.

Subjective NLP tasks often exhibit systematic annotator disagreement, requiring models that represent uncertainty rather than collapse it. We introduce Ensemble Diversity Optimization (EDO), a prediction-space framework that jointly optimizes ensemble weights, effective cardinality, and calibration through a unified differentiable objective. EDO learns ensemble composition and size end-to-end via Gumbel-Softmax relaxation and incorporates a signed diversity regularizer, tuned on validation data, to steer optimization toward either preserving or suppressing disagreement. This regularization prevents ensemble collapse and enables controlled navigation of the utility-calibration trade-off. The framework integrates a soft F1 surrogate, class-weighted cross-entropy to address imbalance, and reliability-weighted diversity to regulate intra-ensemble variability. Experiments on four subjective text-classification benchmarks (ArMIS, ConvAbuse, HS-Brexit, MD-Agreement) show that EDO substantially improves probabilistic calibration, reducing cross-entropy (40-78% depending on baseline) and lowering Brier scores relative to Soft-CE, Soft-MD, Top-5 Voting, and WEL, while maintaining competitive F1 and better alignment with annotator distributions. These results demonstrate that jointly optimizing ensemble structure with a signed diversity regularizer provides an efficient, model-agnostic approach for modeling human subjectivity in supervised learning.

Training target speaker extraction (TSE) models for real conversational mixtures remains challenging because large-scale training corpora and clean target speech for supervision are unavailable. We present PS4, a proxy-supervised training framework for TSE in real conversational mixtures, with two main contributions. First, we construct a large-scale corpus of 71,771 training samples derived from four public datasets, covering both Chinese and English scenarios. Each sample contains an overlapping speech mixture, per-speaker enrollment audio, a ground-truth transcript, and frame-level voice activity labels. Second, we propose a proxy-supervised joint training strategy that fine-tunes a BSRNN-based TSE model using four complementary differentiable objectives: ASR cross-entropy, speaker similarity, frame-level voice activity detection, and perceptual audio quality. Starting from a publicly available pre-trained checkpoint, only the BSRNN separator is updated during fine-tuning. On the REAL-T challenge leaderboard, PS4 ranks 2nd overall, achieving the best speaker similarity and timing F1 among all submitted systems.

Background: Graph neural networks improve computational prediction of polypharmacy side effects, but standard binary cross-entropy training allocates equal capacity to well-classified and difficult examples, potentially missing clinically significant interactions. We evaluated whether an asymmetric focal objective could improve multi-relational drug-drug interaction (DDI) prediction by emphasizing difficult positive interactions. Methods: ClinicalFocal loss was integrated into a relation-aware graph convolutional network using molecular fingerprints, physicochemical descriptors, and learned embeddings. The model was evaluated on TWOSIDES using five-fold cross-validation with identical experimental conditions (architecture, features, data partitions, hyperparameters, and random seeds) for ClinicalFocal loss and binary cross-entropy baseline. Results: ClinicalFocal loss increased accuracy from 0.699 to 0.892 (+19.3 percentage points) and F1 score from 0.700 to 0.894 (+19.4 percentage points). AUROC increased from 0.766 to 0.914, and AUCPR increased from 0.714 to 0.860. The false-negative rate decreased from 29.8% to 9.1%, while specificity increased from 69.6% to 87.5%. Overall classification error decreased from 30.1% to 10.8%, corresponding to a 64.1% relative reduction. Improvements were consistent across all five folds. Conclusions: Asymmetric focal optimization improved classification and ranking performance while achieving 90.9% recall for observed interaction triples, without modifying the underlying architecture. Loss-function design is a direct, tunable lever for improving graph-based DDI prediction.

Reliable seam segmentation is essential for autonomous robotic welding in construction, where harsh illumination, specular reflections, and thin weld geometries often degrade segmentation performance. This study proposes a reflection-robust seam segmentation framework that enhances a BiSeNetV2 backbone through transfer learning and a hybrid Cross-Entropy--Lovász loss. Rather than increasing architectural complexity, the proposed framework improves reflection robustness through learning-stability-oriented optimization. Experimental results show that the proposed method achieves 81.76% Joint IoU and 90.73% mIoU, improving Joint IoU by +22.36 percentage points over the OHEM-based baseline while maintaining identical FLOPs, parameter count, and inference speed. The proposed approach also recovers 96.33% of severe zero-IoU failure cases under reflective conditions. Comparative experiments across BiSeNetV2, DeepLabV3+, UNet, and SegFormer further demonstrate that the proposed optimization strategy is particularly effective for lightweight real-time segmentation architectures. Qualitative analyses additionally show improved seam continuity and reflection robustness in challenging welding environments. These findings suggest that the proposed framework provides a practical and lightweight perception solution for robotic welding applications involving reflective metallic surfaces.

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.

Speculative decoding accelerates autoregressive generation by drafting a block of tokens that the target model verifies left-to-right, committing only the longest accepted prefix. Block (DLM-style) drafters predict the whole block in parallel, which is fast but trained with a full-block cross-entropy that supervises every position against the gold continuation -- even though inference discards every token after the first rejection. Recent acceptance-aware objectives patch this by reweighting the full-block loss; we instead use teacher-forced learning as a motivation for how supervision should concentrate on the accepted prefix. A mask-only block drafter has no input-side channel for gold-prefix conditioning, so AUF approximates that prefix-sensitive supervision on the loss side by keeping the cross-entropy support only through the drafter's first predicted failure. AUF is a single, detached change to the CE support -- no auxiliary objective, no verifier rollouts, and no change to the inference pipeline or the exactness contract. Within fixed drafter backbones and serving settings on Qwen3-8B, AUF raises the DFlash drafter's average emitted length $τ$, averaged over six benchmarks, from 2.40 to 2.61, with a gain on every benchmark, and transfers to Domino's two-branch head (2.56 to 2.68). Two findings sharpen the picture: the decay-only baseline reaches higher token accuracy on the shared block mask yet decodes worse, and on DFlash, once AUF truncates the support, the standard exponential position-decay weighting becomes empirically inert.

Why do neural networks memorize algorithmic training data long before they generalize? We present a geometric case study demonstrating that, on tasks where generalization requires discovering structured low-dimensional circuits, the memorization-generalization delay is driven by radial inflation of hidden representations under cross-entropy optimization. We formalize a radial-angular decomposition of activation-space dynamics and derive three testable propositions: (i) that penalizing radial inflation induces anisotropic, data-dependent weight regularization; (ii) that it suppresses radial gradient energy below the isotropic random baseline, forcing predominantly angular updates; and (iii) that it biases convergence toward flatter minima. To empirically validate these propositions, we study a single-hyperparameter norm penalty that softly constrains activations to a sqrt(d)-radius hypersphere. On modular arithmetic, this penalty accelerates grokking up to 6x across MLPs and Transformers, and halves training steps for a 10M-parameter nanoGPT on 3-digit addition.

Despite rapid progress in learning-based stereo matching, high accuracy is often achieved at the cost of heavy backbones and computationally intensive 3D cost volume processing, resulting in substantial memory and runtime overhead. More critically, these methods frequently struggle to generalize across domains, limiting their practical deployment. We present \textit{LiteMatch}, a lightweight stereo matching framework that achieves strong zero-shot generalization through cost volume stabilization-without expensive 3D convolutions. LiteMatch employs two complementary encoders: a Cross-View Correspondence Encoder (CVCE) to capture global cross-view interactions, and a High-Frequency Encoder (HFE) that enhances fine structural details via FFT-based frequency cues. To stabilize the cost volume, we introduce the \textit{Cost Volume Consistency Loss (CVC-Loss)}, a voxel-wise binary cross-entropy objective applied to softmax-normalized cost distributions. By encouraging sharp and unimodal disparity probabilities, CVC-Loss promotes stable cost distributions and enables rapid convergence. A lightweight refinement module further produces sharp full-resolution disparities with low-iteration updates, avoiding heavy recurrent refinement. With a flexible design ranging from 3.36M to 9.58M parameters, LiteMatch achieves exceptional zero-shot generalization, delivering competitive EPE and D1 performance across Scene Flow, KITTI, Middlebury, ETH3D, and DrivingStereo. Our results establish that lightweight architectures can indeed generalize across domains without sacrificing accuracy. \href{https://mdraqibkhan.github.io/Litematch}{\textcolor{blue}{Code}}

In many prediction problems in medical applications, target labels exhibit an inherent ordinal structure, where class ordering reflects clinically meaningful severity levels. The cost associated with misclassification is often non-uniform and asymmetric, as errors between distant ordinal categories may have substantially more severe consequences than errors between adjacent ones, and overestimating disease severity may have different clinical implications than underestimating it. Traditional loss functions such as multi-class cross-entropy treat all misclassifications equally and fail to incorporate this ordering information. Recent advances in ordinal regression aim to address this limitation by integrating rank-based structures into deep learning models. In this work, we introduce the \textbf{Ordinal Cross-Entropy (OCE)} framework, a general and architecture-independent approach for learning from ordinal data. The proposed method extends the standard cross-entropy formulation to account for misclassification severity through an ordinal cost matrix while preserving the probabilistic interpretation and optimization benefits of the conventional loss. We provide a theoretical analysis of the OCE gradient behavior and show that it yields smoother optimization dynamics and improved ordinal consistency. Experiments on benchmark datasets show that our method achieves lower prediction error costs and better calibration compared to existing state-of-the-art ordinal approaches, establishing OCE as a simple yet effective solution for ordinal regression in deep neural networks.

The Categorical Jacobian of Zhang et al. (2024) reads protein contacts from a language model by perturbing every residue with every alternative amino acid, about $19L$ forward passes. We show the signal it reconstructs is already concentrated in a small subset of attention heads: averaging the top-$K$ contact-relevant heads -- selected on as few as 10 labeled proteins, with no fitted per-pair or per-head weights -- recovers contacts in a single forward pass and matches or beats the Categorical Jacobian for every bidirectional model where it is defined (bar the smallest, 8M). Our primary test is leakage-clean: on a CAMEO split where neither selection nor evaluation touches data the models have plausibly memorized, the head readout beats the Categorical Jacobian on ESM-2-650M by +9pp ($N = 29$, $p < 0.001$), with the within-model margin reproducing across architectures. Ablations localize the gain to labeled head selection, not to averaging: at a matched label budget the unweighted mean ties a supervised $L_1$ logistic regression on the same heads. Both methods fall 30-36pp from their in-distribution Zhang numbers to the leakage-clean split, which we read as an upper bound on how much prior numbers reflect pretraining overlap. We additionally introduce representation-CJ, a hidden-state generalization of the Jacobian to architectures without a masked-LM head (the output-head-independent analogue of logit-CJ), agreeing with the Categorical Jacobian where both are defined (per-protein Pearson $r \approx 0.95$); show that the optimal $K$ tracks how diffusely a model spreads its contact heads; and find both methods lose the signal on the two causal LMs we test, suggesting attention-encoded pair structure may depend on bidirectional pretraining.

Table Structure Recognition (TSR) using a pointer network achieves impressive results by predicting HTML sequences while aligning tags to detected text (or cell) regions. However, our analysis reveals that when pointer networks fail, 79.6% of errors occur between spatially adjacent cells (Manhattan distance <= 2). Despite this, standard cross-entropy loss weights all negative candidates equally. In this work, we propose Geometry-Aware Pointer (GAP) Loss, which reweights the cross-entropy objective based on spatial proximity to ground truth. By applying inverse distance weighting, GAP focuses gradient flow where the model struggles most: immediate neighbors receive stronger gradients than distant cells. Our approach requires only a straightforward modification to the loss computation, maintaining the same model architecture with zero additional inference cost. Extensive experiments on PubTabNet and SynthTabNet demonstrate that GAP consistently reduces adjacent-cell errors, achieving new state-of-the-art performance. Our findings suggest that incorporating geometric inductive biases at the loss level provides a simple yet effective approach to robust TSR. Our code is available at https://github.com/teamreboott/GAP

Grokking, the delayed jump from memorization to generalization, is usually tied to the weight norm: a smaller norm generalizes sooner. We ask what the norm actually controls. Holding the weight norm fixed by clamping and varying only an output temperature, we slide the grokking delay across its entire norm-induced range under cross-entropy; matching the effective logit scale back to baseline recovers about 85% of the delay at two moduli. Across a grid of norms and temperatures the delay collapses onto the logit scale alone (R2 = 0.97), with the norm adding 1-2% beyond it. The effect is loss-dependent: under mean-squared error the logit scale is pinned and the norm acts through a different route. A memorization control, a float64 softmax-collapse audit, and a no-LayerNorm transformer point to the same channel. Forking arms from one identical state, the delay follows the held norm value and not the clamp operation, which closes a rescaling-artifact concern. The proximal variable is the logit scale and the softmax saturation it drives; the weight norm is only an upstream handle. All numbers, tables, and figures reproduce from released code and data.

Looped language models turn hidden states into runtime state: each state is decoded for prediction and fed back into future computation. This creates a basic supervision question: which state variables does cross-entropy actually control? We show that dense per-loop cross-entropy controls the variables exposed by the readout, not every variable active in the recurrent transition. Hidden-state scale gives a concrete failure mode. Scale-invariant readouts such as RMSNorm and LayerNorm hide radial scale from the immediate cross-entropy loss, while pre-norm residual recurrence continues to carry and update that same scale. Thus per-loop loss can make early exits usable without controlling recurrent scale. In 44M and 129M looped transformers without inter-loop normalization, per-loop cross-entropy through RMSNorm readouts still drives final hidden-state norms into the thousands or tens of thousands. Scale-visible readouts and explicit norm penalties keep norms in the tens, and scale-removing recurrence is the complementary architectural fix. The resulting design rule is simple: dense supervision trains exits; recurrent scale control requires either making scale visible to a loss or removing it from the loop. Consistent with this rule, scale-controlled variants achieve lower perplexity at matched inference-depth operating points in our variable-depth benchmarks.

Deep learning has driven many recent advances in process analytics, especially for predictive and prescriptive monitoring. However, standard objectives such as cross-entropy optimize local next-step likelihoods and only implicitly capture control-flow structure. As a result, models can achieve high token-level accuracy while permitting imprecise global behaviour. We introduce DIFF-ERO, a conformance-aware loss function for deep learning models on process data. DIFF-ERO is a differentiable formulation of entropy-based stochastic conformance that incorporates control-flow information during training. Our approach constructs batch-level stochastic transition matrices with soft edge memberships, allowing structural precision and recall signals to directly inform backpropagation. The loss is model-agnostic and can be applied whenever the final representation parametrizes stochastic transitions. We instantiate DIFF-ERO in transformer encoder-decoder pipelines for next-activity prediction and use it jointly with cross-entropy to analyse its theoretical components with respect to convergence. Across benchmarks comparing other loss functions and targets, DIFF-ERO shows improved predictive performance where structure matters most while maintaining parity elsewhere. At the same time, the learned stochastic automaton converges towards the structural ground truth, indicating that the network internalizes process model structure.

Learning compatible representations aims to learn feature representations that can be used interchangeably over time whenever a model undergoes updates. In this paper, we demonstrate that stationary representations learned by d-Simplex fixed classifiers imply compatibility as in its formal definition. This result establishes a foundation for future works and can be directly exploited in practical learning scenarios. We address the challenge of learning compatibility using $d$-Simplex fixed classifiers when the model is sequentially fine-tuned. Learning according to a d-Simplex fixed classifier with the cross-entropy loss aligns feature distributions at the first-order statistics. Consequently, it may not fully capture higher-order dependencies in the representation between model updates. To address this issue, we demonstrate that training the model using a $d$-Simplex fixed classifier through a convex combination of the cross-entropy loss and a contrastive loss not only captures higher-order dependencies, but is also equivalent to learning with the cross-entropy under the compatibility constraints. We confirm our findings with extensive experiments also considering a new scenario where a pre-trained model is sequentially fine-tuned and occasionally replaced with an improved model. We show that stationary representations enable uninterrupted retrieval services (without reprocessing gallery images) while improving performance during model updates and replacements, achieving state-of-the-art. Code at https://github.com/miccunifi/iamcl2r.

Audio-visual captioning generates natural language descriptions from video and audio content. Multimodal LLMs have advanced this task, but both modalities contribute many tokens to the LLM input, where prefill self-attention scales quadratically. Existing token-pruning methods usually retain tokens by attention, saliency, or cross-entropy loss, yet the hard threshold selection makes it difficult to retain tokens that are truly valuable, especially for high-confusing tokens near the decision boundary. To this end, we propose a AVEX-Prune, an RL-based audio-visual dynamic token pruning method in this work. In our AVEX-Prune, an audio-visual token exchange strategy is proposed to select truly valuable tokens by replacing low-confidence retained tokens with high-confidence candidate tokens from the same or the other modality, and measuring the differences in caption generation from token swaps. AVEX-Prune preserves full-token quality at a 40% retention ratio on both VILA 1.5-8B (54.5 vs. 54.6) and VideoLLaMA 2 (57.0 vs. 56.8).

Large language models (LLMs) can generate factually inconsistent claims, motivating accurate and scalable hallucination detectors. Prior work largely enlarges training sets via synthesis or new annotations, introducing increasing cost and potential bias while underusing the consistency implied by semantically equivalent paraphrases. We propose Consistency-Constrained Hallucination Detector (CCHD), which formulates training as a constrained optimization problem. The standard cross-entropy on original document-claim pairs is complemented by (i) paraphrase-consistency constraints bounding divergence across paraphrased views, and (ii) label-preservation constraints tying paraphrases to ground truth. We solve the problem by gradient descent-ascent over model parameters and per-view Lagrange multipliers, adding only a few scalar dual variables and no inference-time overhead. With DeBERTa and Flan-T5 backbones, CCHD consistently outperforms strong baselines (FactCG, MiniCheck, and AlignScore) on standard factuality benchmarks, demonstrating its superiority on hallucination detection.

End-to-end planners for autonomous driving typically generate a set of candidate trajectories, score each one, and return the highest-scoring candidate. However, the scorer is applied only after the proposals are generated and cannot influence the set of trajectories: a weak set of candidates limits planning performance regardless of the scorer's quality. We instead treat the scorer as a learned trajectory-level reward function and search for trajectories that maximize it. Our method, TOAD, runs the Cross-Entropy Method at test time, warm-started from the planner's proposals. It requires no retraining and is plug-and-play for existing planners. Across six base planners, TOAD improves results on NAVSIM-v1 (94.7 PDMS), NAVSIM-v2 (56.3 EPDMS), and the closed-loop HUGSIM benchmark. The code will be made publicly available via the project page: https://valeoai.github.io/TOAD/.

Grokking suggests that fitting the training data and learning a simple underlying rule may occur on different time scales. We formalize this phenomenon by separating the fast decay of the classification loss from the slower simplification of the learned representation, and we call the resulting pair of stopping times two training clocks. For deep linear networks, we show that a post-margin gap-growth or one-step tail-contraction condition reduces the cross-entropy loss to level epsilon on a logarithmic time scale. In contrast, when layerwise weight decay is present, the induced regularization on the end-to-end map can be expressed as a Schatten-type penalty; under a sharp late-time Kurdyka-Lojasiewicz tail, this structural energy closes on a polynomial time scale. The two clocks, therefore, separate fitting from representation simplification. We then explain how the same mechanism can appear in ReLU MLPs. In regions where the activation patterns on the training set remain fixed, the network reduces to a linear model in the active coordinates. In a two-layer ReLU embedding model, chain-rule estimates further show that the classifier head can receive larger effective gradients than the embedding block under controlled downstream norms. This supports a two-stage mechanism in which the classifier fits first, while the representation continues to simplify later. We use modular addition as the main experimental setting. The deep linear theory provides the rigorous core of the analysis. But the ReLU results are formulated as conditional reductions that account for empirical behavior without claiming a global proof for nonlinear training dynamics.

Reasoning models have advanced rapidly, but the dominant reinforcement learning from verifiable rewards (RLVR) recipe remains surprisingly narrow: sample many responses and reward each with a single bit indicating whether the final answer is correct. Yet many settings provide rich feedback, including execution traces, tool outputs, expert corrections, and model self-evaluations. We study how to use such feedback through a distributional variant of the classic imitation learning algorithm DAgger, where the learner has local access to an expert distribution on states visited by the current policy. This yields a simple forward cross-entropy objective that admits a blackbox expert and whose sequence-level gradient {conduct rich credit assignment by propagating} future expert-student disagreement back to earlier decisions. We show that prior RL with self-distillation objectives based on reverse KL or Jensen-Shannon fail to guarantee monotonic policy improvement: even when the expert has higher reward, their updates may increase probability on worse actions. In contrast, we show that forward cross-entropy admits monotonic policy improvement and enjoys guarantees on regret. We further show that our objective optimizes a lower bound on teacher-weighted likelihood of success, leading to improved Pass@N. Empirically, our approach, DistIL, improves over RLVR and RL with self-distillation baselines across a variety of domains: scientific reasoning, coding, and solving hard mathematical problems.

Complementarity is the case in which a human--AI interaction (HAI) outperforms the best prediction benchmark available among its members. Although this idea is central in HAI research, formal work on complementarity remains limited. Existing frameworks do not model how agents' predictions compose into workflow-sensitive multi-agent protocols. We close this gap by introducing a tree-based formalization of complementarity in multi-agent HAI. An HAI protocol is represented by an ordered agent-role configuration together with a rooted planar binary tree whose leaves are decorated by prediction vectors. A local binary composition rule is evaluated recursively along the tree, yielding a tree-relative complementarity functional relative to a pointwise-min oracle benchmark. We prove four results. First, selector-based HAIs, including self- or AI-reliance, cannot achieve complementarity regardless of task, loss, or prediction quality. Second, in regression under squared loss, complementarity is equivalent to Euclidean distance minimization from the ground-truth vector; for $N=2$, the optimal linear-pooling weight has a closed form and a residual-correction interpretation. Third, under linear local composition, every protocol tree defines a barycentric coordinate chart on the simplex of leaf weights; Tamari-cover reparameterizations of protocol trees preserve complementarity, and for $N=4$, they satisfy the pentagon identity. Fourth, in binary classification, no internal local composition can achieve complementarity under endpoint-monotone losses, including standard Bregman and many finite Bernoulli $f$-divergence losses; an analogous obstruction holds for multiclass aggregation under cross-entropy. In summary, our framework shows that complementarity is attainable in multi-agent regression, but obstructed in classification under natural conditions on local aggregation and loss functions.

LLMs have become the state-of-the-art algorithms for solving NLP tasks. However, they typically come at huge computational and memory costs, thus making them difficult to deploy on embedded systems. Toward this, state-of-the-art methods typically employ uniform post-training quantization (PTQ) across attention blocks of the network, hence overlooking the potential of applying different quantization levels in the same network. They also employ complex operations to mitigate the negative impact of activation outliers, hence incurring high computational overheads. Moreover, they have not considered evaluation using emerging LLMs with non-conventional attention architectures (e.g., state-space models), which pose different challenges in applying quantization. To address these limitations, we propose QuBLAST, a novel PTQ methodology that employs block-level compression approach with activation scaling strategy for LLMs. Block-level compression approach enables mixed-precision quantization across blocks of the network, while activation scaling strategy efficiently mitigates the negative impact of activation outliers. Specifically, QuBLAST first analyzes the sensitivity of different attention blocks in the pre-trained model through the cross-entropy loss analysis. QuBLAST leverages this sensitivity analysis to determine the weight quantization level for each attention block in the model. Furthermore, QuBLAST employs the activation scaling map for each block to control the range of activation values and mitigate the negative impact of activation outliers, thereby enabling better quantization results. Experimental results show that, QuBLAST reduces model sizes by 40%-45.2% across different model architectures (i.e., Qwen3-8B, Llama3-8B, Mistral v0.1-8B, and Falcon H1R-7B), while maintaining the performance within 5% perplexity increase for the WikiText-2 and WikiText-103 datasets.

Existing analyses of the edge of stability (EoS) treat it as a global property of optimization. We show that it is also selective: the stability constraint redistributes learning across subsets of the training distribution, amplifying progress on some groups while suppressing progress on others. Using a branching intervention that enters or exits the EoS regime from the same training state, we causally demonstrate this trade-off and identify two necessary conditions for a group to benefit. First, its aggregate gradient must align with the top Hessian eigenvector. We isolate this mechanism with a controlled perturbation that preserves distance but randomizes direction, destroying alignment and eliminating the advantage. Second, the group must sustain non-vanishing gradient magnitude over time. Under cross-entropy loss, gradient saturation decouples confidently classified groups, shifting the advantage to output-outliers, whose gradients persist. Together, these results show that EoS functions not only as a stability boundary, but as a mechanism governing the allocation of learning across the data distribution.

Generalized segmentation of medical images prevents performance degradation when different imaging devices and clinical protocols are used across multiple domains. The Whitening Transform-based Probabilistic Shape Regularization Extractor (WT-PSE), published in IEEE Transactions on Medical Imaging in 2024, addresses this challenge by employing feature decorrelation and Wasserstein distance-based knowledge distillation to achieve robust cross-domain segmentation. This study systematically examines improvements to the WT-PSE learning framework. Four limitations in the original implementation are identified: limited training augmentations that fail to simulate real scanner variations, reliance on per-pixel binary cross-entropy loss that is sensitive to edge noise, the absence of a scheduled loss weighting strategy that may destabilize early training, and the lack of ablation switches for controlled scientific comparison. To address these issues, we propose four enhancements: (1) domain-adaptive augmentation including random erasing, gamma correction, and salt-and-pepper noise; (2) a hybrid BCE and Dice loss function for improved edge-aware segmentation under noisy conditions; (3) a curriculum-based Dice weight scheduling strategy; and (4) command-line control flags for systematic ablation studies. Experiments on the fundus optic disc segmentation benchmark demonstrate that the improved pipeline achieves a final epoch optic-disc Dice score of 0.956 and an ASD score of 13.31, outperforming the baseline epoch-5 Dice score of 0.939. These results indicate that training-level improvements can provide consistent performance gains without modifying the underlying WT-PSE architecture.

Randomized smoothing (RS) uses a smoothed classifier to provide architecture-agnostic certificates of $\ell_2$ classification robustness, but its dependence on per-input Monte Carlo (MC) sampling undermines its use in real-time systems. We argue that this cost is structural rather than fundamental, such that it can be significantly reduced by sharing information across the deployment stream. We introduce RRISE, an RS framework that compresses certification into a single forward pass through a learned surrogate. RRISE trains the surrogate against precomputed MC class-count targets via a soft-label cross-entropy loss and converts surrogate predictions into provably conservative certified radii through a one-time conformal calibration step. The resulting certificate is deployment-verifiable: whenever the calibrated radius is positive, the surrogate's prediction provably matches the smoothed classifier's and the smoothed classifier is constant on a ball of that radius around the input. Across image classification benchmarks, RRISE matches fixed-budget MC certified accuracy within $0.84$ percentage points while replacing up to $10^4$ noisy base-model evaluations per query with a single surrogate forward pass, recouping MC training cost after $\approx 10^5$ deployment queries. On CIFAR-100 and Tiny ImageNet, where the only prior offline-surrogate method collapses, RRISE achieves $1.23$ to $1.91\times$ higher certified accuracy, establishing efficient randomized smoothing as a practical path to certified robustness in repeated-deployment settings.

In RLHF, each training example contains a prompt $x$ and two candidate responses $y,y'$, and annotators provide pairwise preferences between these responses. The learning problem is to convert these heterogeneous pairwise judgments into a single scalar reward $r(x,y)$ that measures response quality for each prompt. Classical social choice implies an impossibility because heterogeneous annotator samples can induce pooled preferences with Condorcet cycles, so no scalar reward can evaluate all compared response pairs consistently. A growing literature analyzes RLHF as a social-choice problem, but usually assumes a fixed finite set of alternatives, i.e., a pre-enumerated finite set of candidate responses for each prompt. Modern pipelines instead score responses through a learned representation $φ(x,y)$ before a scalar head, so $φ$ determines which responses are treated as distinguishable alternatives and which comparisons are visible to the reward model. Once this embedding is part of the problem, the impossibility results from social choice theory become a tradeoff. We show that the excess cross-entropy loss of any reward built on $φ$ decomposes exactly into a representational term, which a richer $φ$ shrinks, and an aggregation term, which a richer $φ$ enlarges by exposing more comparisons that no scalar can rank consistently. The same results extend to direct preference optimization (DPO), and jointly training the embedding and the reward cannot guarantee to recover the sweet spot of this tradeoff. Experiments on synthetic data and real preference datasets corroborate our results.

Large language models (LLMs) are increasingly used as generators in iterative neural architecture search (NAS), yet no formal convergence theory exists for this class of algorithms. We model iterative LLM-NAS as a parametric Cross-Entropy (CE) method over executable programs and prove six results: (1) iterative LLM fine-tuning on elite architectures is equivalent to the CE update restricted to the LLM parametric family; (2) expected architecture quality is monotonically non-decreasing across cycles; (3) elite-set probability converges to a fixed point at a geometric rate C_t >= 1-(1-rho_0)^t; (4) delta-based generation achieves a strictly higher valid-generation rate than full-code generation under a first-order Markov token-error model; (5) the MinHash-Jaccard novelty filter prevents mode collapse; (6) proxy reliability admits the closed-form rho_S = (6/pi) arcsin(rho_P(SNR)/2), yielding the practical diagnostic sigma^2_arch >> sigma^2_noise as a necessary condition for trustworthy proxy-based rankings. Testing against a 22-cycle, three-LLM, six-dataset experiment with 3,300 generated architectures confirms two predictions quantitatively, two at direction-of-effect level, and explains the proxy-reliability ceiling effect previously reported empirically but left unexplained.

Bayesian Networks (BNs) are of interest from an explainable AI viewpoint, offering transparent probabilistic models for decision support. Baymex is a recently introduced multi-objective evolutionary algorithm for learning discretized BNs, enabling experts to trade-off different objectives of interest, such as likelihood, model complexity, and prior beliefs. While Baymex has been shown to outperform state-of-the-art BN learning approaches, Baymex still 1) requires a lot of computation time and 2) has only been evaluated on synthetic data. To improve scalability, we introduce a parallelization strategy as well as a mechanism that enables adaptively steering optimization toward networks that overfit less. We furthermore reconfigure Baymex to train a BN classifier through multi-objective optimization of cross-entropy loss and the BIC complexity term so as to evaluate its performance on real-world clinical classification tasks. Besides observing speedups up to over 54 times on a 16-core CPU, comparisons against clinically familiar baselines (decision trees, logistic regression, naive Bayes, and random forests) on two open-source (RADCURE and SUPPORT) and one in-house dataset, show that Baymex obtains statistically similar or better predictive performance while producing compact, clinically inspectable BNs. Importantly, Baymex finds multiple plausible BN classifiers that contain predictors consistent with established clinical factors.

Post-training large language models with reinforcement learning is bottlenecked by the reward signal. Existing approaches require either ground-truth verifiable rewards, restricting training to domains with automatic correctness checks (e.g., mathematics, code execution), or human preference labels, which are expensive to collect and prone to reward hacking. Recent label-free methods replace ground-truth verifiers with self-referential signals like majority voting or token entropy over a model's own outputs, but risk reinforcing a model's own errors. In this work we propose Cross-Model Entropy (CME), the mean log-likelihood of a generator's response under a separate verifier model, as a label-free reward signal for RL post-training. CME is continuous, training-free, and grounded in the principle that responses a verifier finds unsurprising are likely correct or high quality. Because the verifier is independent of the generator, the signal cannot be gamed through self-consistency. We integrate CME into GRPO with no other changes to the training loop, extending label-free RL to open-ended instruction following -- a regime where self-referential signals are inapplicable or poorly suited. On open-ended instruction following (UltraFeedback prompts, evaluated on AlpacaEval 2.0), CME rewards beat the untrained base in head-to-head LLM-as-Judge comparisons across four model families (Qwen, Llama, Gemma, OLMo) and three training regimes (pretrained, SFT, and instruction-tuned), with tie-adjusted win rates ranging from 52.5% to 71.4%. Code will be released upon publication.

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.

We present Frost Training, a method for improving Monte Carlo-based policy optimization for a large family of LLM-as-a-judge tasks called Cross-Entropy Games. The key idea is to exploit the gradient of the reward function in embedding space. This signal is used in the Greedy Coordinate Gradient (GCG) jailbreaking technique; we demonstrate for the first time that it can also be used to boost model training. We validate our method using GRPO training for maximum-likelihood infilling. Frost Training improves the model's ability to generate high-scoring outputs, reaching higher maximum scores in a best-of-k setting, and does so at an increased speed.

In strategic classification, an institution (e.g., a bank) anticipates adaptation from users who change their features to increase utility in a classification task (e.g., loan repayment). Since a key challenge is the distribution shift induced by users, we turn to causal models, which have been shown to bound the worst-case out-of-distribution (OOD) risk, and establish several new results that link causality and strategic classification. First, we show that causal classification leads to optimal classification error after any sufficiently large adaptation, when the noise is bounded in a certain way. Second, when these assumptions do not hold, we show OOD cross-entropy risk of optimal classifiers decomposes into an OOD bias term and a term arising from not using all observable features, allowing us to understand when causal classifiers have an advantage. Finally, we show that the use of causal features can allow alignment of long-term incentives between institutions and users, contrasting with previous work that highlights social costs of such approaches. We validate our theory empirically on synthetic data, finding that our results predict behavior in practice.

We study the mean-squared error of $k$-fold cross-validation as a risk estimator, with particular emphasis on how its accuracy depends on the number of folds $k$. Despite the widespread use of cross-validation, principled guidance for choosing $k$ is largely absent, mainly due to the complex dependence between fold-wise error estimates. To obtain sharp and interpretable results, we focus on the majority algorithm in binary classification, a minimal yet nontrivial empirical risk minimization procedure. We provide a fine-grained analysis of its cross-validation behavior, showing that even this simple algorithm exhibits subtle and delicate phenomena for which existing theory provides loose and even vacuous bounds. Leveraging this analysis, we introduce a minimax framework for cross-validation risk estimation and prove that no empirical risk minimization algorithm can achieve an $O(1/n)$ minimax mean-squared error when the number of folds grows with the number of samples $n$; instead, a lower bound of order $Ω(\sqrt{k}/n)$ is unavoidable. Our results reveal fundamental limitations of cross-validation as a data-reuse strategy, clarify gaps and inaccuracies in prior theoretical work, and position the majority algorithm as a natural benchmark that any tight analysis of cross-validation should be able to explain.

Fine-tuning a language model on contexts whose correct completion has a near-synonym competitor often fails silently. The cross-entropy loss decreases monotonically while the correct token never overtakes the competitor in rank. We study this regime across five transformer architectures spanning two families and a fivefold parameter range, on ten hand-selected near-synonym contexts. We instrument these failures with an order parameter combining the predicted distribution and pairwise embedding overlaps. It decomposes additively into a signal, tracking the model's commitment to the correct token over its nearest competitor, and a background drag, set by how the embedding bulk leaks probability into the score. This isolates two failure modes. In kinematic failure the signal stays small. In structural failure the drag actively worsens as fine-tuning proceeds. We observe sharp catapult-like jumps in the order parameter that resemble a phase transition. A central negative result organises the paper. The transitions are phantoms. The spontaneous-symmetry-breaking interpretation is ruled out by direct measurement. Catapult-like jumps still appear under LoRA fine-tuning with the token embedding matrix exactly unchanged during training, where no geometric phase transition is possible. The discontinuity lives entirely in the softmax readout. A small number of dimensionless quantities organise the trajectory across architectures. One is consistent across all five under full fine-tuning. A second sorts architectures into two classes by bulk embedding distribution and predicts LoRA sufficiency. As a blind test, the framework predicts the critical learning rate of a held-out architecture, not used to fit any parameter, to within 2.1% of a subsequent learning-rate sweep. Findings concern the near-synonym mechanism only and should not be extrapolated without recalibration.

We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $M$-component mixture distributions, we propose a family of estimators derived from the stochastic mirror descent (SMD) algorithm. This optimization-based approach provides a principled and flexible framework that generalizes traditional estimators and proposes a variety of novel estimators through the choice of Bregman divergences. A key advantage of our method is that it scales efficiently with the number of candidate components $f_i$; that is, one can employ a large set of basis distributions in the mixture model without incurring significant computational overhead. This enables richer approximations and improved estimation accuracy. Moreover, in the case of categorical distribution (discrete outcomes) our estimators do not require a strict lower bound, in other words our framework does not require the precise knowledge of the support of the distribution. We demonstrate that, under mild conditions, the proposed $\varphi$-SMD estimators achieve near-optimal convergence rates in both Kullback-Leibler (KL) divergence and $\ell_2$-norm and offer practical benefits when computation is expensive. Our numerical analysis highlights improved performance guaranties over classical estimators, particularly in terms of sample efficiency and scalability.

Mean cross-entropy is the standard validation metric for language models, but it can fail to track model quality during training. We examine this in two common scenarios. First, in Qwen2.5-1.5B SFT on synthetic fact-learning, we find that mean CE rises substantially after the initial learning phase while held-out fact-recall accuracy remains near its peak. Second, we find that in top-K distillation on TinyStories, decreasing K improves median CE while worsening mean CE; the Top-5 student attains the highest LLM-judge score and crosses below its teacher on median CE, despite having the worst mean CE. In both cases, median CE correlates much more closely with task performance than does mean CE. Analyzing how bulk and tail percentile CE move during training reveals that training reshapes the empirical per-token CE distribution. In top-K distillation, smaller K yields a distribution with more mass at both extremes, decreasing the median and increasing the mean. In Qwen SFT, the bulk saturates quickly while the tail extends in the latter half of training. In both, the task-evaluation metric appears more sensitive to the bulk than to the tail. Practically, we recommend reporting a small set of percentile CE summaries alongside the mean, and using concordance among them as a tool to keep track of distribution reshaping, as well as a low-cost diagnostic for when mean and median CE disagree on model selection.

CLI agents are the closest thing language models have to an embodied setting: the model emits commands, the terminal executes them, and the returned stream -- stdout, errors, files, logs, and traces -- records the consequences. We argue that this stream is a supervision signal, but standard agent RL discards it: GRPO-style training updates action tokens with sparse outcome-level rewards while ignoring environment responses already in the rollout. Failed rollouts provide little policy-gradient signal despite containing rich evidence about how the environment responds. We introduce ECHO (Environment Cross-entropy Hybrid Objective), a hybrid objective that combines the standard policy-gradient loss on action tokens with an auxiliary loss that trains the policy to predict environment observation tokens resulting from its own actions. ECHO reuses the same forward pass as GRPO, requires no additional rollouts, and turns terminal feedback into dense supervision for all rollouts. ECHO doubles GRPO pass@1 on TerminalBench-2.0: Qwen3-8B improves from 2.70% to 5.17%, and Qwen3-14B from 5.17% to 10.79%. ECHO also produces policies that better predict terminal dynamics, even on trajectories they did not generate: across held-out rollouts, it sharply reduces environment-token cross-entropy while GRPO alone barely changes it. From base Qwen3-8B, ECHO matches expert-SFT-then-GRPO performance on held-out terminal tasks without expert demonstrations, and recovers roughly half of the expert-SFT initialization benefit on TerminalBench-2.0. In some settings, the environment prediction loss alone enables verifier-free self-improvement, allowing policies to improve on unseen OOD tasks by learning only from environment interactions. Together, these results suggest that environment observations are not merely context for future actions, but a dense, on-policy supervision signal already present in every rollout.

Discrete diffusion models are often trained through clean-data prediction, but the prediction can be used in different ways to define the reverse dynamics. In Masked Diffusion Models (MDM) these choices largely coincide, whereas in Uniform Diffusion Models (UDM) they do not. We show that the standard plug-in bridge parameterization for UDM is not optimized by the denoising posterior, but by a leave-one-out posterior that predicts each clean token without using its own noisy observation. This identifies a mismatch between the plug-in ELBO and the usual cross-entropy denoising objective. We characterize the leave-one-out target and derive exact conversions between the denoiser, the leave-one-out posterior, and the score. These conversions allow us to disentangle parameterization and training objective. Our results also lead to inference improvements without any additional training through an informed predictor-corrector sampler and improved temperature sampling based on the leave-one-out predictor. We further introduce an absorbing-state reformulation of uniform diffusion that preserves the UDM joint law while decomposing it into masked-diffusion-like sampling operations, with simpler denoising posteriors, carry-over unmasking, and a natural remasking mechanism. On language modeling, leave-one-out parameterizations consistently improve UDM generation, while the absorbing construction matches or surpasses masked diffusion. These results suggest that the empirical gap between masked and uniform diffusion is driven less by the choice of marginals themselves than by parameterization and sampling design. The code and models can be found at https://github.com/samsongourevitch/rev_udm.

Real-world sensor-based learning systems require uncertainty estimation that is both reliable and computationally efficient. Evidential Deep Learning (EDL) provides single-pass uncertainty estimation by modeling the class probabilities via Dirichlet distributions, where the Dirichlet parameters are predicted by a learned neural network mapping. However, this approach can lead to computational challenges, as Dirichlet expected objectives are more complex than standard supervised learning losses, complicating their analysis and implementation. We address this issue by approximating the objective of the first-order empirical risk minimization problem induced by EDL with a plug-in loss evaluated at the Dirichlet mean and show that, under mild assumptions, the approximation error decays with growing evidence for a broad class of loss functions, including mean-squared error and cross-entropy loss. As a special case, our analysis provides justification for the use of softmax in the context of uncertainty estimation, since under a particular evidence-to-Dirichlet mapping, our framework includes the standard softmax classifier. We validate the proposed simplified objectives on the Google Speech Commands dataset and show that they achieve predictive accuracy and selective prediction performance comparable to classical EDL, while being simpler to implement using standard deep learning losses and training pipelines. To the best of our knowledge, this empirical analysis is the first to obtain coverage-accuracy trade-offs for speech recognition tasks through EDL.

Computational antibody CDR design methods condition on antigen structure to generate binding loops. Yet, the existing architectures conflate two fundamentally distinct sub-problems: identifying which CDR positions will contact the antigen, and selecting amino acids at those positions. This forces models to learn contact reasoning implicitly through uniform message passing, diluting antigen signal across all positions equally. We introduce ConTact, a contact-then-act architecture that explicitly decomposes CDR design into three cascaded stages: learning surface complementarity fingerprints, predicting CDR-antigen contacts, and injecting contact-gated antigen features into the prediction head. A distance-biased cross-attention module encodes geometric priors favoring spatial neighbors, while a contact-weighted cross-entropy loss concentrates gradient signal on binding-critical positions. On the CHIMERA-Bench dataset, ConTact achieves the lowest backbone RMSD on every split (a 5 to 6% improvement over the best baseline) and the best fraction of native contacts, interface RMSD, and epitope F1 on the antigen-fold and temporal splits, while remaining competitive on the harder epitope-group split. The source code is available at: https://github.com/mansoor181/ConTact.git