Grokking, or sudden generalization that occurs after prolonged overfitting, is a surprising phenomenon that has challenged our understanding of deep learning. While a lot of progress has been made in understanding grokking, it is still not clear why generalization is delayed and why grokking often does not happen without regularization. In this work we argue that without regularization, grokking tasks push models to the edge of numerical stability, introducing floating point errors in the Softmax that we refer to as Softmax Collapse (SC). We show that SC prevents grokking and that mitigating SC leads to grokking without regularization. Investigating the root cause of SC, we find that beyond the point of overfitting, the gradients strongly align with what we call the naïve loss minimization (NLM) direction. This component of the gradient does not change the predictions of the model but decreases the loss by scaling the logits, usually through the scaling of the weights along their current direction. We show that this scaling of the logits explains the delay in generalization characteristic of grokking, and eventually leads to SC, stopping learning altogether. To validate these hypotheses, we introduce two key contributions that mitigate the issues faced in grokking tasks: (i) StableMax, a new activation function that prevents SC and enables grokking without regularization, and (ii) Grad, a training algorithm that leads to quick generalization in grokking tasks by preventing NLM altogether. These contributions provide new insights into grokking, shedding light on its delayed generalization, reliance on regularization, and the effectiveness of known grokking-inducing methods. Code for this paper can be found at: https://github.com/LucasPrietoAl/ Deep learning has been transformative for a variety of fields such as natural language processing (Devlin et al., 2019), computer vision (Krizhevsky et al., 2012), geometry processing (Qi et al., 2017), and 3D vision (Deng et al., 2018). This rapid proliferation has brought with it surprising phenomena that defy the predictions of classical statistical learning theory. In this paper we explore one such recently observed phenomenon known as grokking, first described by Power et al. (2022) as a sudden and unexpected generalization occurring after prolonged overfitting.

We introduce a new multimodal optimization approach called Natural Variational Annealing (NVA) that combines the strengths of three foundational concepts to simultaneously search for multiple global and local modes of black-box nonconvex objectives. First, it implements a simultaneous search by using variational posteriors, such as, mixtures of Gaussians. Second, it applies annealing to gradually trade off exploration for exploitation. Finally, it learns the variational search distribution using natural-gradient learning where updates resemble well-known and easy-to-implement algorithms. The three concepts come together in NVA giving rise to new algorithms and also allowing us to incorporate "fitness shaping", a core concept from evolutionary algorithms. We assess the quality of search on simulations and compare them to methods using gradient descent and evolution strategies. We also provide an application to a real-world inverse problem in planetary science.

Advancements in artificial intelligence (AI) and deep learning have led to neural networks being used to generate lightning-speed answers to complex questions, to paint like Monet, or to write like Proust. Leveraging their computational speed and flexibility, neural networks are also being used to facilitate fast, likelihood-free statistical inference. However, it is not straightforward to use neural networks with data that for various reasons are incomplete, which precludes their use in many applications. A recently proposed approach to remedy this issue inputs an appropriately padded data vector and a vector that encodes the missingness pattern to a neural network. While computationally efficient, this "masking" approach can result in statistically inefficient inferences. Here, we propose an alternative approach that is based on the Monte Carlo expectation-maximization (EM) algorithm. Our EM approach is likelihood-free, substantially faster than the conventional EM algorithm as it does not require numerical optimization at each iteration, and more statistically efficient than the masking approach. This research represents a prototype problem that indicates how improvements could be made in AI by introducing Bayesian statistical thinking. We compare the two approaches to missingness using simulated incomplete data from two models: a spatial Gaussian process model, and a spatial Potts model. The utility of the methodology is shown on Arctic sea-ice data and cryptocurrency data.

Learning parity functions is a canonical problem in learning theory, which although computationally tractable, is not amenable to standard learning algorithms such as gradient-based methods. This hardness is usually explained via statistical query lower bounds [Kearns, 1998]. However, these bounds only imply that for any given algorithm, there is some worst-case parity function that will be hard to learn. Thus, they do not explain why fixed parities - say, the full parity function over all coordinates - are difficult to learn in practice, at least with standard predictors and gradient-based methods [Abbe and Boix-Adsera, 2022]. In this paper, we address this open problem, by showing that for any fixed parity of some minimal size, using it as a target function to train one-hidden-layer ReLU networks with perturbed gradient descent will fail to produce anything meaningful. To establish this, we prove a new result about the decay of the Fourier coefficients of linear threshold (or weighted majority) functions, which may be of independent interest.

How can we attribute the behaviors of machine learning models to their training data? While the classic influence function sheds light on the impact of individual samples, it often fails to capture the more complex and pronounced collective influence of a set of samples. To tackle this challenge, we study the Most Influential Subset Selection (MISS) problem, which aims to identify a subset of training samples with the greatest collective influence. We conduct a comprehensive analysis of the prevailing approaches in MISS, elucidating their strengths and weaknesses. Our findings reveal that influence-based greedy heuristics, a dominant class of algorithms in MISS, can provably fail even in linear regression. We delineate the failure modes, including the errors of influence function and the non-additive structure of the collective influence. Conversely, we demonstrate that an adaptive version of these heuristics which applies them iteratively, can effectively capture the interactions among samples and thus partially address the issues. Experiments on real-world datasets corroborate these theoretical findings and further demonstrate that the merit of adaptivity can extend to more complex scenarios such as classification tasks and non-linear neural networks. We conclude our analysis by emphasizing the inherent trade-off between performance and computational efficiency, questioning the use of additive metrics such as the Linear Datamodeling Score, and offering a range of discussions.

Reinforcement learning (RL) aims to estimate the action to take given a (time-varying) state, with the goal of maximizing a cumulative reward function. Predominantly, there are two families of algorithms to solve RL problems: value-based and policy-based methods, with the latter designed to learn a probabilistic parametric policy from states to actions. Most contemporary approaches implement this policy using a neural network (NN). However, NNs usually face issues related to convergence, architectural suitability, hyper-parameter selection, and underutilization of the redundancies of the state-action representations (e.g. locally similar states). This paper postulates multi-linear mappings to efficiently estimate the parameters of the RL policy. More precisely, we leverage the PARAFAC decomposition to design tensor low-rank policies. The key idea involves collecting the policy parameters into a tensor and leveraging tensor-completion techniques to enforce low rank. We establish theoretical guarantees of the proposed methods for various policy classes and validate their efficacy through numerical experiments. Specifically, we demonstrate that tensor low-rank policy models reduce computational and sample complexities in comparison to NN models while achieving similar rewards.

CRISPR-based diagnostics have gained increasing attention as biosensing tools able to address limitations in contemporary molecular diagnostic tests. To maximise the performance of CRISPR-based assays, much effort has focused on optimizing the chemistry and biology of the biosensing reaction. However, less attention has been paid to improving the techniques used to analyse CRISPR-based diagnostic data. To date, diagnostic decisions typically involve various forms of slope-based classification. Such methods are superior to traditional methods based on assessing absolute signals, but still have limitations. Herein, we establish performance benchmarks (total accuracy, sensitivity, and specificity) using common slope-based methods. We compare the performance of these benchmark methods with three different quadratic empirical distribution function statistical tests, finding significant improvements in diagnostic speed and accuracy when applied to a clinical data set. Two of the three statistical techniques, the Kolmogorov-Smirnov and Anderson-Darling tests, report the lowest time-to-result and highest total test accuracy. Furthermore, we developed a long short-term memory recurrent neural network to classify CRISPR-biosensing data, achieving 100% specificity on our model data set. Finally, we provide guidelines on choosing the classification method and classification method parameters that best suit a diagnostic assays needs.

Long-term and Large-scale Wireless Traffic Forecasting (LL-WTF) is pivotal for strategic network management and comprehensive planning on a macro scale. However, LL-WTF poses greater challenges than short-term ones due to the pronounced non-stationarity of extended wireless traffic and the vast number of nodes distributed at the city scale. To cope with this, we propose a Progressive Supervision method based on Label Decomposition (PSLD). Specifically, we first introduce a Random Subgraph Sampling (RSS) algorithm designed to sample a tractable subset from large-scale traffic data, thereby enabling efficient network training. Then, PSLD employs label decomposition to obtain multiple easy-to-learn components, which are learned progressively at shallow layers and combined at deep layers to effectively cope with the non-stationary problem raised by LL-WTF tasks. Finally, we compare the proposed method with various state-of-the-art (SOTA) methods on three large-scale WT datasets. Extensive experimental results demonstrate that the proposed PSLD significantly outperforms existing methods, with an average 2%, 4%, and 11% performance improvement on three WT datasets, respectively. In addition, we built an open source library for WT forecasting (WTFlib) to facilitate related research, which contains numerous SOTA methods and provides a strong benchmark.Experiments can be reproduced through https://github.com/Anoise/WTFlib.

Online Continual Learning (OCL) is a critical area in machine learning, focusing on enabling models to adapt to evolving data streams in real-time while addressing challenges such as catastrophic forgetting and the stability-plasticity trade-off. This study conducts the first comprehensive Systematic Literature Review (SLR) on OCL, analyzing 81 approaches, extracting over 1,000 features (specific tasks addressed by these approaches), and identifying more than 500 components (sub-models within approaches, including algorithms and tools). We also review 83 datasets spanning applications like image classification, object detection, and multimodal vision-language tasks. Our findings highlight key challenges, including reducing computational overhead, developing domain-agnostic solutions, and improving scalability in resource-constrained environments. Furthermore, we identify promising directions for future research, such as leveraging self-supervised learning for multimodal and sequential data, designing adaptive memory mechanisms that integrate sparse retrieval and generative replay, and creating efficient frameworks for real-world applications with noisy or evolving task boundaries. By providing a rigorous and structured synthesis of the current state of OCL, this review offers a valuable resource for advancing this field and addressing its critical challenges and opportunities. The complete SLR methodology steps and extracted data are publicly available through the provided link: https://github.com/kiyan-rezaee/ Systematic-Literature-Review-on-Online-Continual-Learning

The widespread acceptance of empirically derived codal provisions and equations in civil engineering stands in stark contrast to the skepticism facing machine learning (ML) models, despite their shared statistical foundations. This paper examines this philosophical tension through the lens of structural engineering and explores how integrating ML challenges traditional engineering philosophies and professional identities. Recent efforts have documented how ML enhances predictive accuracy, optimizes designs, and analyzes complex behaviors. However, one might also raise concerns about the diminishing role of human intuition and the interpretability of algorithms. To showcase this rarely explored front, this paper presents how ML can be successfully integrated into various engineering problems by means of formulation via deduction, induction, and abduction. Then, this paper identifies three principal paradoxes that could arise when adopting ML: analysis paralysis (increased prediction accuracy leading to a reduced understanding of physical mechanisms), infeasible solutions (optimization resulting in unconventional designs that challenge engineering intuition), and the Rashomon effect (where contradictions in explainability methods and physics arise). This paper concludes by addressing these paradoxes and arguing the need to rethink epistemological shifts in engineering and engineering education and methodologies to harmonize traditional principles with ML.