Despite the success of reinforcement learning from human feedback (RLHF) in aligning language models, current reward modeling heavily relies on explicit preference data with high collection costs. In this work, we study implicit reward modeling---learning reward models from implicit human feedback---which offers a cost-effective alternative. We identify two fundamental challenges in implicit reward modeling: (1) Implicit preference data lacks definitive negative samples, which makes standard positive-negative classification methods inapplicable; (2) Implicit preference data suffers from user preference bias, where different responses have different propensities to elicit user feedback actions, which exacerbates the difficulty of distinguishing definitive negative samples. To address these challenges, we propose ImplicitRM, which aims to learn unbiased reward models from implicit preference data. ImplicitRM stratifies training samples into four latent groups via a stratification model. Building on this, it derives a learning objective through likelihood maximization, which we prove is theoretically unbiased, effectively resolving both challenges. Experiments demonstrate that ImplicitRM learns accurate reward models across implicit preference datasets. Code is available at https://anonymous.4open.science/r/ImplicitRM-5FB3.
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Applications · Health / Medicine
Mislabeled samples in training datasets severely degrade the performance of deep networks, as overparameterized models tend to memorize erroneous labels. We address this challenge by proposing a novel approach for mislabeled data detection that leverages training dynamics. Our method is grounded in the key observation that correctly labeled samples exhibit consistent entropy decrease during training, while mislabeled samples maintain relatively high entropy throughout the training process. Building on this insight, we introduce a signed entropy integral (SEI) statistic that captures both the magnitude and temporal trend of prediction entropy across training epochs. SEI is broadly applicable to classification networks and demonstrates particular effectiveness when integrated with contrastive language-image pretraining (CLIP) architectures. Through extensive experiments on three medical imaging datasets---a domain particularly susceptible to labeling errors due to diagnostic complexity---spanning diverse modalities and pathologies, we demonstrate that SEI achieves state-of-the-art performance in mislabeled data identification, outperforming existing methods while maintaining computational efficiency and implementation simplicity.
Deep Learning · Algorithms
In-context learning (ICL) is a practical way to adapt large models, yet under strict context limits it remains unclear how to spend scarce tokens without being misled by noisy, redundant, or conflicting demonstrations. We address this gap by targeting token-budgeted context construction: how to select and compress demonstrations so the prompt carries maximal task-relevant signal with minimal predictive distortion. We propose RDCO, a deterministic, training-free optimizer that scores demonstrations by marginal task information per token, penalizes redundancy and prefix-conditioned conflicts, and compacts the selected context under a bounded predictive divergence constraint to control drift. Across a 10-dataset ICL suite spanning classification and structured generation, RDCO achieves the best average performance (63.26 Acc. on classification and 56.26 EM on generation) and improves the overall average by +2.20 points over the strongest baseline under the same budget. Our results suggest that viewing prompts as finite-capacity messages yields a principled and effective path to more reliable and token-efficient ICL.
Deep Learning · Graph Neural Networks
Graph Convolutional Networks (GCNs) are defined based on aggregating the node information of adjacent nodes, that are usually treated as equally important as each other, limiting the representational power of existing GCNs for graph classification. To address this shortcoming, we propose a novel Global Interacted Graph Convolutional Network (GI-GCN), that can leverage the solution vectors maintained during the iterative updates of the Dominant Set to adaptively characterize the global importance distribution of different nodes. Specifically, at each convolution layer, this distribution is adopted to adaptively modulate the importance weights of different node features before performing the local message passing. We show that this convolution strategy can effectively capture the highly correlated information between nonadjacent nodes through the Dominant Set algorithm, not only emphasizing the critical information at the graph level but also enhancing the discriminative power of graph representations. Furthermore, we optimize the spatial complexity of the framework, significantly reducing the memory overhead associated with the global interaction modeling. Experiments demonstrate the effectiveness of the proposed GI-GCN.
Deep Learning · Algorithms
Deep networks often exhibit a preference for "simple" solutions, and such a simplicity bias is widely believed to play a key role in generalization. Yet a broadly applicable, quantitative measure of simplicity remains elusive. We introduce _polynomial representations_ as a distribution-aware, low-dimensional surrogate for neural functions: we approximate a network’s predictive behavior along data-dependent interpolation paths using orthogonal polynomial bases, yielding a compact functional representation. We show that the _effective degree_ of this representation serves as a practical simplicity metric that is predictive of generalization across tasks and architectures, and consistently outperforms existing generalization proxies such as sharpness. Finally, polynomial representations naturally yield a _differentiable_ simplicity regularizer, which consistently improves generalization in image and text classification, fine-tuning contrastive vision–language models, and reinforcement learning.
Social Aspects · Everything Else
Conformal prediction (CP) has become a cornerstone of distribution-free uncertainty quantification, conventionally evaluated by its coverage and interval length. This work critically examines the sufficiency of these standard metrics. We demonstrate that the interval length might be deceptively improved through a counter-intuitive approach termed Prejudicial Trick (PT), while the coverage remains valid. Specifically, for any given test sample, PT probabilistically returns an interval, which is either null or constructed using an adjusted confidence level, thereby preserving marginal coverage. While PT potentially yields a deceptively lower interval length, it introduces practical vulnerabilities: the same input can yield completely different prediction intervals across repeated runs of the algorithm. We formally derive the conditions under which PT achieves these misleading improvements and provide extensive empirical evidence across various regression and classification tasks. Furthermore, we introduce a new metric interval stability which helps detect whether a new CP method implicitly improves the length based on such PT-like techniques.
Deep Learning · Attention Mechanisms
Transformers can perform in-context classification from a few labeled examples, yet the inference-time algorithm remains opaque. We study multi-class linear classification in the hard no-margin regime and make the computation identifiable by enforcing feature- and label-permutation equivariance at every layer. This enables interpretability while maintaining functional equivalence and yields highly structured weights. From these models we extract an explicit depth-indexed recursion---an end-to-end identified, emergent update rule inside a standard softmax transformer, to our knowledge the first of its kind. Attention matrices formed from mixed feature--label Gram structure drive coupled updates of training points, labels, and the test probe. The resulting dynamics implement label-aware mean-shift, which provably amplifies class separation and yields robust expected class alignment.
Deep Learning · Large Language Models
Uncertainty quantification (UQ) is an important technique for ensuring the trustworthiness of LLMs, given their tendency to hallucinate. Existing state-of-the-art UQ approaches for free-form generation rely heavily on sampling, which incurs high computational cost and variance. In this work, we propose the first gradient-based UQ method for free-form generation, SemGrad, which is sampling-free and computationally efficient. Unlike prior gradient-based methods developed for classification tasks that operates in parameter space, we propose to consider gradients in semantic space. Our method builds on the key intuition that a confident LLM should maintain stable output distributions under semantically equivalent input perturbations. We interpret the stability as the gradients in semantic space and introduce a Semantic Preservation Score (SPS) to identify embeddings that best capture semantics, with respect to which gradients are computed. We further propose HybridGrad, which combines the strengths of SemGrad and parameter gradients. Experiments demonstrate that both of our methods provide efficient and effective uncertainty estimates, achieving superior performance than state-of-the-art methods, particularly in settings with multiple valid responses.
Social Aspects · Accountability, Transparency, and Interpretability
Regression trees are among the most interpretable yet expressive model classes in machine learning. Historically, greedy induction has been the dominant approach for constructing well-performing regression trees. While optimal methods based on dynamic programming and branch-and-bound exist, they are computationally prohibitive for general linear regression trees, despite often achieving substantially better performance than greedy approaches. Recent work has shown that specialized lookahead strategies can dramatically improve runtime while maintaining near-optimal performance, primarily in classification settings. In this work, we develop a novel algorithm for near-optimal, sparse, piecewise linear regression trees that combines a lookahead-style search strategy with efficient rank-one Cholesky updates of the Gram matrix. We demonstrate, both theoretically and empirically, that our method achieves a favorable trade-off between computational efficiency, predictive accuracy, and sparsity, and scales significantly better than the current state of the art.
General Machine Learning · Representation Learning
In this paper, we propose a discrete roto-reflection group equivariant vision transformer with convolutional attention. Roto-reflection equivariant networks preserve the rotational, flip and positional symmetry in feature maps, making them useful for tasks where orientation of the inputs is relevant to the model outputs. In image classification and object detection, most of the studies on roto-reflection equivariant models have focused on using convolutional neural networks rather than vision transformers. In this paper, we examine the challenges involved in achieving equivariance in vision transformers, and we propose a simpler way to implement a discretized roto-reflection group equivariant vision transformer. The experimental results demonstrate that our approach outperforms the existing approaches for developing discrete roto-reflection group equivariant neural networks for image classification.
Deep Learning · Foundation Models
Traditional time series models are often task-specific and rely heavily on manual feature engineering. While Transformer-based architectures have revolutionized sequence modeling in language and vision, their potential for general-purpose time series representation learning remains underexplored, particularly for heterogeneous sensor data. We introduce CHARM (Channel-Aware Representation Model), a model designed to improve representations for multivariate time series by incorporating channel-level textual descriptions into its architecture. This allows the model to leverage contextual information associated with individual sensors while remaining invariant to channel order. CHARM is trained using a Joint Embedding Predictive Architecture (JEPA) with a novel loss that promotes informative and temporally stable embeddings. We find that CHARM’s latent-space prediction encourages robustness to sensor-level noise and supports learning underlying temporal structure. In addition, the description-aware gating mechanism provides a degree of interpretability through learned inter-channel relationships. Across a range of downstream tasks—including univariate and multivariate anomaly detection, classification, and short- and long-term forecasting—the learned embeddings achieve strong performance using only a lightweight linear probe.
General Machine Learning · Representation Learning
Most multimodal learning assumes redundant views (such as image–caption pairs), yet many applications require combining complementary modalities that provide distinct evidence (such as an X-ray and medical history). We term this setting *Complementary Multimodal Classification* (CMC). In CMC, existing explainable-by-design methods often force an accuracy–interpretability trade-off because single shared similarity metrics fail under asymmetric, class-conditional evidence. To address this, we propose Coherent Alignment of Multimodal Prototypes (CAMP). CAMP enforces coherent multimodal reasoning by aligning class-wise evidence via optimal transport and imposing geometric constraints to counter modality dominance and representation collapse. We provide theoretical guarantees showing that these mechanisms eliminate such degeneracies without restricting expressivity. Empirically, across 17 public CMC datasets, CAMP matches or exceeds large ($>$100M parameter) AutoML baselines with fewer than 1M trainable parameters, and when fine-tuned end-to-end it achieves state-of-the-art performance. To the best of our knowledge, this work is the first modality-agnostic prototype-learning framework designed for complementary multimodal tasks.
Theory · Learning Theory
Statistical evaluation aims to estimate the generalization performance of a model using held-out i.i.d. test data sampled from the ground-truth distribution. In supervised learning settings such as classification, performance metrics such as error rate are well-defined, and test error reliably approximates population error given sufficiently large datasets. In contrast, evaluation is more challenging for generative models due to their open-ended nature: it is unclear which metrics are appropriate and whether such metrics can be reliably evaluated from finite samples. In this work, we introduce a theoretical framework for evaluating language models and establish evaluability results for commonly used metrics. We study two categories of metrics: test-based metrics, including integral probability metrics (IPMs), and similarity-based metrics, including Rényi and KL divergences. We show that IPMs with respect to any bounded test class can be evaluated from finite samples up to multiplicative and additive approximation errors. Moreover, when the test class has finite fat-shattering dimension, IPMs can be evaluated with arbitrary precision. In contrast, similarity-based metrics, including Rényi and KL divergences, are not evaluable from finite samples, as their values can be critically determined by rare events. We also analyze the potential and limitations of perplexity as an evaluation method.
General Machine Learning · Methodology
We introduce Convex Distance Operator Transport (CDOT), the first convex optimal transport framework that aligns distributions across heterogeneous domains by jointly preserving feature correspondence and intrinsic geometric structure. Specifically, CDOT employs an operator-based regularization that aligns aggregated distance structures by introducing distance and conditional expectation operators. Consequently, the proposed regularization improves the robustness to local geometric variations. We further prove that the resulting CDOT discrepancy is a valid pseudometric on the space of attributed compact metric-measure spaces. In addition, we characterize the relationship between CDOT and Gromov--Wasserstien (GW) through a new notion of dispersion gap, formally elucidating the geometric source of non-convexity in GW compared to the convexity of CDOT. In the finite-sample regime, we derive a non-asymptotic risk bound decomposed into optimization and statistical errors, establishing risk consistency under a globally convergent Frank--Wolfe algorithm. Experiments on synthetic point clouds, brain connectomes, and graph classification benchmarks demonstrate better performance over existing methods, with stable and reliable behavior in practice.
Large language model (LLM) activations are notoriously difficult to understand, with most existing techniques using complex, specialized methods for interpreting them. Recent work has proposed a simpler approach known as LatentQA: training LLMs to directly accept LLM activations as inputs and answer arbitrary questions about them in natural language. However, prior work has focused on narrow task settings for both training and evaluation. In this paper, we instead take a generalist perspective. We evaluate LatentQA-trained models, which we call Activation Oracles (AOs), in far out-of-distribution settings and examine how performance scales with training data diversity. We find that AOs can recover information fine-tuned into a model (e.g., biographical knowledge or malign propensities) that does not appear in the input text, despite never being trained with activations from a fine-tuned model. Our main evaluations are four downstream tasks where we can compare to prior white- and black-box techniques. We find that even narrowly-trained LatentQA models can generalize well, and that adding additional training datasets (such as classification tasks and a self-supervised context prediction task) yields consistent further improvements. Our best AOs match or exceed white-box baselines on all four tasks and the best overall baseline on 3 of 4. These results suggest that diversified training to answer natural-language queries imparts a general capability to verbalize information about LLM activations.
Applications · Computer Vision
Prompt tuning introduces learnable prompt vectors that adapt pretrained vision-language models to downstream tasks in a parameter-efficient manner. However, under limited supervision, prompt tuning alters pretrained representations and drives downstream features away from the pretrained manifold toward directions that are unfavorable for transfer. This drift degrades generalization. To address this limitation, we propose ManiPT, a framework that performs prompt tuning on the pretrained manifold. ManiPT introduces cosine consistency constraints in both the text and image modalities to confine the learned representations within the pretrained geometric neighborhood. Furthermore, we introduce a structural bias that enforces incremental corrections, guiding the adaptation along transferable directions to mitigate reliance on shortcut learning. From a theoretical perspective, ManiPT alleviates overfitting tendencies under limited data. Our experiments cover four downstream settings: unseen-class generalization, few-shot classification, cross-dataset transfer, and domain generalization. Across these settings, ManiPT achieves higher average performance than baseline methods. Notably, ManiPT provides an explicit perspective on how prompt tuning overfits under limited supervision.
Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Modern models are trained on massive datasets, yet these are vanishingly small compared to the full combinatorial space of possible data, raising the question of whether models can reliably generalize to unseen combinations. To formalize what this requires, we propose a set of practically motivated desiderata that any compositionally generalizing system must satisfy, and analyze their implications under standard training with linear classification heads. We show that these desiderata necessitate \emph{linear factorization}, where representations decompose additively into per-concept components, and further imply near-orthogonality across factors. We establish dimension bounds that link the number of concepts to the geometry of representations. Empirically, we survey CLIP and SigLIP families, finding strong evidence for linear factorization, approximate orthogonality, and a tight correlation between the quality of factorization and compositional generalization. Together, our results identify the structural conditions that embeddings must satisfy for compositional generalization, and provide both theoretical clarity and empirical diagnostics for developing foundation models that generalize compositionally.
Deep Learning · Other Representation Learning
Multi-modal dataset distillation (MDD) seeks to compress large-scale multi-modal datasets into a compact set of synthetic pairs. Existing methods employ a dual-trajectory matching framework to align the teacher and student models within each modality. While effective, this paradigm incurs non-negligible memory and computational overhead due to the checkpoint storage and bi-level optimization over synthetic data. To address these limitations, we propose analytic parameter matching (APM), which theoretically derives the analytic parameters of modal projectors to replace the inner-loop optimization, and then aligns the analytic projector parameters of teacher and student models. APM offers two key advantages: (1) it replaces checkpoint-intensive storage with only two cached matrices, significantly reducing memory consumption; and (2) it computes analytic parameters in a single forward pass, thereby avoiding costly bi-level optimization. Empirically, APM achieves up to 65$\times$ storage reduction and 9.6$\times$ faster distillation, while scaling to 1,000 synthetic pairs. Extensive experiments on image-text and audio-text benchmarks demonstrate the effectiveness of APM in cross-modal retrieval tasks, \eg, 12.8 IR@1 and 17.8 TR@1 in Flickr30k with 100 synthetic pairs. Moreover, APM exhibits notable generalization performance in cross-architecture evaluation and zero-shot classification tasks.
Deep Learning · Robustness
The detection of synthetic images has traditionally been framed as a binary classification problem. However, we argue that this formulation overlooks a fundamental structural property of generative datasets: synthetic images are not independent samples, but are implicitly paired with real images sharing the same semantic source. Existing methods treat real and fake images as independent instances, failing to capture generation-induced relational discrepancies in real–fake pairs. Moreover, models tend to rapidly overfit to seen fake patterns, leading to poor generalization to unseen ones. To overcome these challenges, we propose a novel detection framework that explicitly mines real–fake pairs by constructing source-guided mappings or leveraging nearest-neighbor relationships in the CLIP embedding space. We then introduce pair-wise discrepancy learning that explicitly enlarges generation-induced deviations and discrepancy inversion to mitigate overfitting. Moreover, to preserve pretrained semantic representations while improving generalization, we adopt a bias-only fine-tuning scheme that restricts model capacity during adaptation. Extensive experiments show that our approach achieves superior generalization across unseen fake patterns.
Theory · Deep Learning
Muon updates matrix parameters via the matrix sign of the gradient and has shown strong empirical gains, yet its dynamics and scaling behavior remain unclear in theory. We study Muon in a linear associative memory model with softmax retrieval and a hierarchical frequency spectrum over query–answer pairs, with and without label noise. In this setting, we show that Gradient Descent (GD) learns frequency components at highly imbalanced rates, leading to slow convergence bottlenecked by low-frequency components. In contrast, the Muon optimizer mitigates this imbalance, leading to faster and more uniform progress. Specifically, in the noiseless case, Muon achieves an exponential speedup over GD; in the noisy case with a power-decay frequency spectrum, we derive Muon's optimization scaling law and demonstrate its superior scaling efficiency over GD. Furthermore, we show that Muon can be interpreted as an implicit matrix preconditioner arising from adaptive task alignment and block-symmetric gradient structure. In contrast, the preconditioner with coordinate-wise sign operator could match Muon under oracle access to unknown task representations, which is infeasible for SignGD in practice. Experiments on synthetic long-tail classification and LLaMA-style pre-training corroborate the theory.