Grokking, a delayed generalization in neural networks after perfect training performance, has been observed in Transformers and MLPs, but the components driving it remain underexplored. We show that embeddings are central to grokking: introducing them into MLPs induces delayed generalization in modular arithmetic tasks, whereas MLPs without embeddings can generalize immediately. Our analysis identifies two key mechanisms: (1) Embedding update dynamics, where rare tokens stagnate due to sparse gradient updates and weight decay, and (2) Bilinear coupling, where the interaction between embeddings and downstream weights introduces saddle points and increases sensitivity to initialization. To confirm these mechanisms, we investigate frequency-aware sampling, which balances token updates by minimizing gradient variance, and embedding-specific learning rates, derived from the asymmetric curvature of the bilinear loss landscape. We prove that an adaptive learning rate ratio, \(\frac{η_E}{η_W} \propto \frac{σ_{\max}(E)}{σ_{\max}(W)} \cdot \frac{f_W}{f_E}\), mitigates bilinear coupling effects, accelerating convergence. Our methods not only improve grokking dynamics but also extend to broader challenges in Transformer optimization, where bilinear interactions hinder efficient training.

Proximal Policy Optimization (PPO) is a widely used reinforcement learning algorithm that heavily relies on accurate advantage estimates for stable and efficient training. However, raw advantage signals can exhibit significant variance, noise, and scale-related issues, impeding optimal learning performance. To address this challenge, we introduce Advantage Modulation PPO (AM-PPO), a novel enhancement of PPO that adaptively modulates advantage estimates using a dynamic, non-linear scaling mechanism. This adaptive modulation employs an alpha controller that dynamically adjusts the scaling factor based on evolving statistical properties of the advantage signals, such as their norm, variance, and a predefined target saturation level. By incorporating a tanh-based gating function driven by these adaptively scaled advantages, AM-PPO reshapes the advantage signals to stabilize gradient updates and improve the conditioning of the policy gradient landscape. Crucially, this modulation also influences value function training by providing consistent and adaptively conditioned learning targets. Empirical evaluations across standard continuous control benchmarks demonstrate that AM-PPO achieves superior reward trajectories, exhibits sustained learning progression, and significantly reduces the clipping required by adaptive optimizers. These findings underscore the potential of advantage modulation as a broadly applicable technique for enhancing reinforcement learning optimization.

The rapid adoption of generative AI has driven an explosion in the size of datasets consumed and produced by AI models. Traditional methods for unstructured data visualization, such as t-SNE and UMAP, have not kept up with the pace of dataset scaling. This presents a significant challenge for AI explainability, which relies on methods such as t-SNE and UMAP for exploratory data analysis. In this paper, we introduce Negative Or Mean Affinity Discrimination (NOMAD) Projection, the first method for unstructured data visualization via nonlinear dimensionality reduction that can run on multiple GPUs at train time. W e provide theory that situates NOMAD Projection as an approximate upper bound on the InfoNC-t-SNE loss, and empirical results that demonstrate NOMAD Projection's superior performance and speed profile compared to existing state-of-the-art methods. W e demonstrate the scalability of NOMAD Projection by computing the first complete data map of Multilingual Wikipedia. CVPR 2025 Tutorial - Identifying Structure in Data: All you need to know about Dimensionality Reduction, Clustering, and More 1. Introduction The discovery of neural scaling laws has resulted in an explosion in the size of datasets consumed and produced by AI models [11] [9]. Traditional algorithms for unstructured data visualization, such as t-SNE [14] and UMAP [15], have not kept up with the pace of dataset scaling. The presents a significant challenge for data-centric AI explainability, since it relies upon methods like t-SNE and UMAP for exploratory data analysis.

Authorship analysis plays an important role in diverse domains, including forensic linguistics, academia, cybersecurity, and digital content authentication. This paper presents a systematic literature review on two key sub-tasks of authorship analysis; Author Attribution and Author Verification. The review explores SOTA methodologies, ranging from traditional ML approaches to DL models and LLMs, highlighting their evolution, strengths, and limitations, based on studies conducted from 2015 to 2024. Key contributions include a comprehensive analysis of methods, techniques, their corresponding feature extraction techniques, datasets used, and emerging challenges in authorship analysis. The study highlights critical research gaps, particularly in low-resource language processing, multilingual adaptation, cross-domain generalization, and AI-generated text detection. This review aims to help researchers by giving an overview of the latest trends and challenges in authorship analysis. It also points out possible areas for future study. The goal is to support the development of better, more reliable, and accurate authorship analysis system in diverse textual domain.

Understanding the neural mechanisms underlying speech production is essential for both advancing cognitive neuroscience theory and developing practical communication technologies. In this study, we investigated magnetoencephalography signals to decode phones from brain activity during speech production and perception (passive listening and voice playback) tasks. Using a dataset comprising 17 participants, we performed pairwise phone classification, extending our analysis to 15 phonetic pairs. Multiple machine learning approaches, including regularized linear models and neural network architectures, were compared to determine their effectiveness in decoding phonetic information. Our results demonstrate significantly higher decoding accuracy during speech production (76.6%) compared to passive listening and playback modalities (~51%), emphasizing the richer neural information available during overt speech. Among the models, the Elastic Net classifier consistently outperformed more complex neural networks, highlighting the effectiveness of traditional regularization techniques when applied to limited and high-dimensional MEG datasets. Besides, analysis of specific brain frequency bands revealed that low-frequency oscillations, particularly Delta (0.2-3 Hz) and Theta (4-7 Hz), contributed the most substantially to decoding accuracy, suggesting that these bands encode critical speech production-related neural processes. Despite using advanced denoising methods, it remains unclear whether decoding solely reflects neural activity or if residual muscular or movement artifacts also contributed, indicating the need for further methodological refinement. Overall, our findings underline the critical importance of examining overt speech production paradigms, which, despite their complexity, offer opportunities to improve brain-computer interfaces to help individuals with severe speech impairments.

Out-of-Distribution (OoD) detection is vital for the reliability of deep neural networks, the key of which lies in effectively characterizing the disparities between OoD and In-Distribution (InD) data. In this work, such disparities are exploited through a fresh perspective of non-linear feature subspace. That is, a discriminative non-linear subspace is learned from InD features to capture representative patterns of InD, while informative patterns of OoD features cannot be well captured in such a subspace due to their different distribution. Grounded on this perspective, we exploit the deviations of InD and OoD features in such a non-linear subspace for effective OoD detection. To be specific, we leverage the framework of Kernel Principal Component Analysis (KPCA) to attain the discriminative non-linear subspace and deploy the reconstruction error on such subspace to distinguish InD and OoD data. Two challenges emerge: (i) the learning of an effective non-linear subspace, i.e., the selection of kernel function in KPCA, and (ii) the computation of the kernel matrix with large-scale InD data. For the former, we reveal two vital non-linear patterns that closely relate to the InD-OoD disparity, leading to the establishment of a Cosine-Gaussian kernel for constructing the subspace. For the latter, we introduce two techniques to approximate the Cosine-Gaussian kernel with significantly cheap computations. In particular, our approximation is further tailored by incorporating the InD data confidence, which is demonstrated to promote the learning of discriminative subspaces for OoD data. Our study presents new insights into the non-linear feature subspace for OoD detection and contributes practical explorations on the associated kernel design and efficient computations, yielding a KPCA detection method with distinctively improved efficacy and efficiency.

Self-supervised learning has emerged as a powerful paradigm for training deep neural networks, particularly in medical imaging where labeled data is scarce. While current approaches typically rely on synthetic augmentations of single images, we propose VET-DINO, a framework that leverages a unique characteristic of medical imaging: the availability of multiple standardized views from the same study. Using a series of clinical veterinary radiographs from the same patient study, we enable models to learn view-invariant anatomical structures and develop an implied 3D understanding from 2D projections. We demonstrate our approach on a dataset of 5 million veterinary radiographs from 668,000 canine studies. Through extensive experimentation, including view synthesis and downstream task performance, we show that learning from real multi-view pairs leads to superior anatomical understanding compared to purely synthetic augmentations. VET-DINO achieves state-of-the-art performance on various veterinary imaging tasks. Our work establishes a new paradigm for self-supervised learning in medical imaging that leverages domain-specific properties rather than merely adapting natural image techniques.

We introduce cumulative polynomial Kolmogorov-Arnold networks (CP-KAN), a neural architecture combining Chebyshev polynomial basis functions and quadratic unconstrained binary optimization (QUBO). Our primary contribution involves reformulating the degree selection problem as a QUBO task, reducing the complexity from $O(D^N)$ to a single optimization step per layer. This approach enables efficient degree selection across neurons while maintaining computational tractability. The architecture performs well in regression tasks with limited data, showing good robustness to input scales and natural regularization properties from its polynomial basis. Additionally, theoretical analysis establishes connections between CP-KAN's performance and properties of financial time series. Our empirical validation across multiple domains demonstrates competitive performance compared to several traditional architectures tested, especially in scenarios where data efficiency and numerical stability are important. Our implementation, including strategies for managing computational overhead in larger networks is available in Ref.~\citep{cpkan_implementation}.

Group distributionally robust optimization (GDRO) aims to develop models that perform well across $m$ distributions simultaneously. Existing GDRO algorithms can only process a fixed number of samples per iteration, either 1 or $m$, and therefore can not support scenarios where the sample size varies dynamically. To address this limitation, we investigate GDRO with flexible sample queries and cast it as a two-player game: one player solves an online convex optimization problem, while the other tackles a prediction with limited advice (PLA) problem. Within such a game, we propose a novel PLA algorithm, constructing appropriate loss estimators for cases where the sample size is either 1 or not, and updating the decision using follow-the-regularized-leader. Then, we establish the first high-probability regret bound for non-oblivious PLA. Building upon the above approach, we develop a GDRO algorithm that allows an arbitrary and varying sample size per round, achieving a high-probability optimization error bound of $O\left(\frac{1}{t}\sqrt{\sum_{j=1}^t \frac{m}{r_j}\log m}\right)$, where $r_t$ denotes the sample size at round $t$. This result demonstrates that the optimization error decreases as the number of samples increases and implies a consistent sample complexity of $O(m\log (m)/ε^2)$ for any fixed sample size $r\in[m]$, aligning with existing bounds for cases of $r=1$ or $m$. We validate our approach on synthetic binary and real-world multi-class datasets.

Recent advancements in deep models have highlighted the need for intelligent systems that combine continual learning (CL) for knowledge acquisition with machine unlearning (MU) for data removal, forming the Continual Learning-Unlearning (CLU) paradigm. While existing work treats CL and MU as separate processes, we reveal their intrinsic connection through a unified optimization framework based on Kullback-Leibler divergence minimization. This framework decomposes gradient updates for approximate CLU into four components: learning new knowledge, unlearning targeted data, preserving existing knowledge, and modulation via weight saliency. A critical challenge lies in balancing knowledge update and retention during sequential learning-unlearning cycles. To resolve this stability-plasticity dilemma, we introduce a remain-preserved manifold constraint to induce a remaining Hessian compensation for CLU iterations. A fast-slow weight adaptation mechanism is designed to efficiently approximate the second-order optimization direction, combined with adaptive weighting coefficients and a balanced weight saliency mask, proposing a unified implementation framework for gradient-based CLU. Furthermore, we pioneer task-agnostic CLU scenarios that support fine-grained unlearning at the cross-task category and random sample levels beyond the traditional task-aware setups. Experiments demonstrate that the proposed UG-CLU framework effectively coordinates incremental learning, precise unlearning, and knowledge stability across multiple datasets and model architectures, providing a theoretical foundation and methodological support for dynamic, compliant intelligent systems.