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Recent applications of kernel methods in machine learning have seen a renewed interest in the Laplacian kernel, due to its stability to the bandwidth hyperparameter in comparison to the Gaussian kernel, as well as its expressivity being equivalent to that of the neural tangent kernel of deep fully connected networks. However, unlike the Gaussian kernel, the Laplacian kernel is not separable. This poses challenges for techniques to approximate it, especially via the random Fourier features (RFF) methodology and its variants. In this work, we provide random features for the Laplacian kernel and its two generalizations: Mat\'{e}rn kernel and the Exponential power kernel. We provide efficiently implementable schemes to sample weight matrices so that random features approximate these kernels. These weight matrices have a weakly coupled heavy-tailed randomness. Via numerical experiments on real datasets we demonstrate the efficacy of these random feature maps.

Advancements in Large Language Models (LLMs) and their increasing use in medical question-answering necessitate rigorous evaluation of their reliability. A critical challenge lies in hallucination, where models generate plausible yet factually incorrect outputs. In the medical domain, this poses serious risks to patient safety and clinical decision-making. To address this, we introduce MedHallu, the first benchmark specifically designed for medical hallucination detection. MedHallu comprises 10,000 high-quality question-answer pairs derived from PubMedQA, with hallucinated answers systematically generated through a controlled pipeline. Our experiments show that state-of-the-art LLMs, including GPT-4o, Llama-3.1, and the medically fine-tuned UltraMedical, struggle with this binary hallucination detection task, with the best model achieving an F1 score as low as 0.625 for detecting "hard" category hallucinations. Using bidirectional entailment clustering, we show that harder-to-detect hallucinations are semantically closer to ground truth. Through experiments, we also show incorporating domain-specific knowledge and introducing a "not sure" category as one of the answer categories improves the precision and F1 scores by up to 38% relative to baselines., Comment: Code and dataset are available at https://medhallu.github.io/

People exhibit unique emotional responses. In the same scenario, the emotional reactions of two individuals can be either similar or vastly different. For instance, consider one person's reaction to an invitation to smoke versus another person's response to a query about their sleep quality. The identification of these individual traits through the observation of common physical parameters opens the door to a wide range of applications, including psychological analysis, criminology, disease prediction, addiction control, and more. While there has been previous research in the fields of psychometrics, inertial sensors, computer vision, and audio analysis, this paper introduces a novel technique for identifying human traits in real time using brainwave data. To achieve this, we begin with an extensive study of brainwave data collected from 80 participants using a portable EEG headset. We also conduct a statistical analysis of the collected data utilizing box plots. Our analysis uncovers several new insights, leading us to a groundbreaking unified approach for identifying diverse human traits by leveraging machine learning techniques on EEG data. Our analysis demonstrates that this proposed solution achieves high accuracy. Moreover, we explore two deep-learning models to compare the performance of our solution. Consequently, we have developed an integrated, real-time trait identification solution using EEG data, based on the insights from our analysis. To validate our approach, we conducted a rigorous user evaluation with an additional 20 participants. The outcomes of this evaluation illustrate both high accuracy and favorable user ratings, emphasizing the robust potential of our proposed method to serve as a versatile solution for human trait identification., Comment: 11th International Conference on Networking, Systems, and Security (NSysS '24)

Classical kernel machines have historically faced significant challenges in scaling to large datasets and model sizes--a key ingredient that has driven the success of neural networks. In this paper, we present a new methodology for building kernel machines that can scale efficiently with both data size and model size. Our algorithm introduces delayed projections to Preconditioned Stochastic Gradient Descent (PSGD) allowing the training of much larger models than was previously feasible, pushing the practical limits of kernel-based learning. We validate our algorithm, EigenPro4, across multiple datasets, demonstrating drastic training speed up over the existing methods while maintaining comparable or better classification accuracy., Comment: arXiv admin note: text overlap with arXiv:2302.02605

Recent advances in machine learning have led to increased interest in reproducing kernel Banach spaces (RKBS) as a more general framework that extends beyond reproducing kernel Hilbert spaces (RKHS). These works have resulted in the formulation of representer theorems under several regularized learning schemes. However, little is known about an optimization method that encompasses these results in this setting. This paper addresses a learning problem on Banach spaces endowed with a reproducing kernel, focusing on efficient optimization within RKBS. To tackle this challenge, we propose an algorithm based on mirror descent (MDA). Our approach involves an iterative method that employs gradient steps in the dual space of the Banach space using the reproducing kernel. We analyze the convergence properties of our algorithm under various assumptions and establish two types of results: first, we identify conditions under which a linear convergence rate is achievable, akin to optimization in the Euclidean setting, and provide a proof of the linear rate; second, we demonstrate a standard convergence rate in a constrained setting. Moreover, to instantiate this algorithm in practice, we introduce a novel family of RKBSs with $p$-norm ($p \neq 2$), characterized by both an explicit dual map and a kernel., Comment: 42 pages, 3 figures

This systematic review explores the theoretical foundations, evolution, applications, and future potential of Kolmogorov-Arnold Networks (KAN), a neural network model inspired by the Kolmogorov-Arnold representation theorem. KANs distinguish themselves from traditional neural networks by using learnable, spline-parameterized functions instead of fixed activation functions, allowing for flexible and interpretable representations of high-dimensional functions. This review details KAN's architectural strengths, including adaptive edge-based activation functions that improve parameter efficiency and scalability in applications such as time series forecasting, computational biomedicine, and graph learning. Key advancements, including Temporal-KAN, FastKAN, and Partial Differential Equation (PDE) KAN, illustrate KAN's growing applicability in dynamic environments, enhancing interpretability, computational efficiency, and adaptability for complex function approximation tasks. Additionally, this paper discusses KAN's integration with other architectures, such as convolutional, recurrent, and transformer-based models, showcasing its versatility in complementing established neural networks for tasks requiring hybrid approaches. Despite its strengths, KAN faces computational challenges in high-dimensional and noisy data settings, motivating ongoing research into optimization strategies, regularization techniques, and hybrid models. This paper highlights KAN's role in modern neural architectures and outlines future directions to improve its computational efficiency, interpretability, and scalability in data-intensive applications.

Quantization is a powerful tool for accelerating large language model (LLM) inference, but the accuracy-performance trade-offs across different formats remain unclear. In this paper, we conduct the most comprehensive empirical study to date, evaluating FP8, INT8, and INT4 quantization across academic benchmarks and real-world tasks on the entire Llama-3.1 model family. Through over 500,000 evaluations, our investigation yields several key findings: (1) FP8 (W8A8-FP) is effectively lossless across all model scales, (2) well-tuned INT8 (W8A8-INT) achieves surprisingly low (1-3\%) accuracy degradation, and (3) INT4 weight-only (W4A16-INT) is more competitive than expected, rivaling 8-bit quantization. Further, we investigate the optimal quantization format for different deployments by analyzing inference performance through the popular vLLM framework. Our analysis provides clear deployment recommendations: W4A16 is the most cost-efficient for synchronous setups, while W8A8 dominates in asynchronous continuous batching. For mixed workloads, the optimal choice depends on the specific use case. Our findings offer practical, data-driven guidelines for deploying quantized LLMs at scale -- ensuring the best balance between speed, efficiency, and accuracy.

Ensuring faithfulness to context in large language models (LLMs) and retrieval-augmented generation (RAG) systems is crucial for reliable deployment in real-world applications, as incorrect or unsupported information can erode user trust. Despite advancements on standard benchmarks, faithfulness hallucination-where models generate responses misaligned with the provided context-remains a significant challenge. In this work, we introduce FaithEval, a novel and comprehensive benchmark tailored to evaluate the faithfulness of LLMs in contextual scenarios across three diverse tasks: unanswerable, inconsistent, and counterfactual contexts. These tasks simulate real-world challenges where retrieval mechanisms may surface incomplete, contradictory, or fabricated information. FaithEval comprises 4.9K high-quality problems in total, validated through a rigorous four-stage context construction and validation framework, employing both LLM-based auto-evaluation and human validation. Our extensive study across a wide range of open-source and proprietary models reveals that even state-of-the-art models often struggle to remain faithful to the given context, and that larger models do not necessarily exhibit improved faithfulness.Project is available at: \url{https://github.com/SalesforceAIResearch/FaithEval}.

Voice cloning is a prominent feature in personalized speech interfaces. A neural vocal cloning system can mimic someone's voice using just a few audio samples. Both speaker encoding and speaker adaptation are topics of research in the field of voice cloning. Speaker adaptation relies on fine-tuning a multi-speaker generative model, which involves training a separate model to infer a new speaker embedding used for speaker encoding. Both methods can achieve excellent performance, even with a small number of cloning audios, in terms of the speech's naturalness and similarity to the original speaker. Speaker encoding approaches are more appropriate for low-resource deployment since they require significantly less memory and have a faster cloning time than speaker adaption, which can offer slightly greater naturalness and similarity. The main goal is to create a vocal cloning system that produces audio output with a Nepali accent or that sounds like Nepali. For the further advancement of TTS, the idea of transfer learning was effectively used to address several issues that were encountered in the development of this system, including the poor audio quality and the lack of available data., Comment: 6 pages, 10 figures

Catastrophic interference, the loss of previously learned information when learning new information, remains a major challenge in machine learning. Since living organisms do not seem to suffer from this problem, researchers have taken inspiration from biology to improve memory retention in artificial intelligence systems. However, previous attempts to use bio-inspired mechanisms have typically resulted in systems that rely on task boundary information during training and/or explicit task identification during inference, information that is not available in real-world scenarios. Here, we show that neuro-inspired mechanisms such as synaptic consolidation and metaplasticity can mitigate catastrophic interference in a spiking neural network, using only synapse-local information, with no need for task awareness, and with a fixed memory size that does not need to be increased when training on new tasks. Our model, TACOS, combines neuromodulation with complex synaptic dynamics to enable new learning while protecting previous information. We evaluate TACOS on sequential image recognition tasks and demonstrate its effectiveness in reducing catastrophic interference. Our results show that TACOS outperforms existing regularization techniques in domain-incremental learning scenarios. We also report the results of an ablation study to elucidate the contribution of each neuro-inspired mechanism separately.

The implementation of Artificial Intelligence (AI) in the healthcare industry has garnered considerable attention, attributable to its prospective enhancement of clinical outcomes, expansion of access to superior healthcare, cost reduction, and elevation of patient satisfaction. Nevertheless, the primary hurdle that persists is related to the quality of accessible multi-modal healthcare data in conjunction with the evolution of AI methodologies. This study delves into the adoption of large language models to address specific challenges, specifically, the standardization of healthcare data. We advocate the use of these models to identify and map clinical data schemas to established data standard attributes, such as the Fast Healthcare Interoperability Resources. Our results illustrate that employing large language models significantly diminishes the necessity for manual data curation and elevates the efficacy of the data standardization process. Consequently, the proposed methodology has the propensity to expedite the integration of AI in healthcare, ameliorate the quality of patient care, whilst minimizing the time and financial resources necessary for the preparation of data for AI., Comment: 11 pages, 2 figures, 4 tables

Kernel ridge regression (KRR) is a popular class of machine learning models that has become an important tool for understanding deep learning. Much of the focus has been on studying the proportional asymptotic regime, $n \asymp d$, where $n$ is the number of training samples and $d$ is the dimension of the dataset. In this regime, under certain conditions on the data distribution, the kernel random matrix involved in KRR exhibits behavior akin to that of a linear kernel. In this work, we extend the study of kernel regression to the quadratic asymptotic regime, where $n \asymp d^2$. In this regime, we demonstrate that a broad class of inner-product kernels exhibit behavior similar to a quadratic kernel. Specifically, we establish an operator norm approximation bound for the difference between the original kernel random matrix and a quadratic kernel random matrix with additional correction terms compared to the Taylor expansion of the kernel functions. The approximation works for general data distributions under a Gaussian-moment-matching assumption with a covariance structure. This new approximation is utilized to obtain a limiting spectral distribution of the original kernel matrix and characterize the precise asymptotic training and generalization errors for KRR in the quadratic regime when $n/d^2$ converges to a non-zero constant. The generalization errors are obtained for both deterministic and random teacher models. Our proof techniques combine moment methods, Wick's formula, orthogonal polynomials, and resolvent analysis of random matrices with correlated entries., Comment: 75 pages

Neural networks trained to solve modular arithmetic tasks exhibit grokking, a phenomenon where the test accuracy starts improving long after the model achieves 100% training accuracy in the training process. It is often taken as an example of "emergence", where model ability manifests sharply through a phase transition. In this work, we show that the phenomenon of grokking is not specific to neural networks nor to gradient descent-based optimization. Specifically, we show that this phenomenon occurs when learning modular arithmetic with Recursive Feature Machines (RFM), an iterative algorithm that uses the Average Gradient Outer Product (AGOP) to enable task-specific feature learning with general machine learning models. When used in conjunction with kernel machines, iterating RFM results in a fast transition from random, near zero, test accuracy to perfect test accuracy. This transition cannot be predicted from the training loss, which is identically zero, nor from the test loss, which remains constant in initial iterations. Instead, as we show, the transition is completely determined by feature learning: RFM gradually learns block-circulant features to solve modular arithmetic. Paralleling the results for RFM, we show that neural networks that solve modular arithmetic also learn block-circulant features. Furthermore, we present theoretical evidence that RFM uses such block-circulant features to implement the Fourier Multiplication Algorithm, which prior work posited as the generalizing solution neural networks learn on these tasks. Our results demonstrate that emergence can result purely from learning task-relevant features and is not specific to neural architectures nor gradient descent-based optimization methods. Furthermore, our work provides more evidence for AGOP as a key mechanism for feature learning in neural networks.

This paper introduces a collaborative, human-centred taxonomy of AI, algorithmic and automation harms. We argue that existing taxonomies, while valuable, can be narrow, unclear, typically cater to practitioners and government, and often overlook the needs of the wider public. Drawing on existing taxonomies and a large repository of documented incidents, we propose a taxonomy that is clear and understandable to a broad set of audiences, as well as being flexible, extensible, and interoperable. Through iterative refinement with topic experts and crowdsourced annotation testing, we propose a taxonomy that can serve as a powerful tool for civil society organisations, educators, policymakers, product teams and the general public. By fostering a greater understanding of the real-world harms of AI and related technologies, we aim to increase understanding, empower NGOs and individuals to identify and report violations, inform policy discussions, and encourage responsible technology development and deployment., Comment: 21 pages, 2 figures; typos corrected, reference missing fields fixed, printer-friendly version of a diagram added

Phishing, whether through email, SMS, or malicious websites, poses a major threat to organizations by using social engineering to trick users into revealing sensitive information. It not only compromises company's data security but also incurs significant financial losses. In this paper, we investigate whether the remarkable performance of Large Language Models (LLMs) can be leveraged for particular task like text classification, particularly detecting malicious content and compare its results with state-of-the-art Deberta V3 (DeBERTa using ELECTRA-Style Pre-Training with Gradient-Disentangled Embedding Sharing) model. We systematically assess the potential and limitations of both approaches using comprehensive public datasets comprising diverse data sources such as email, HTML, URL, SMS, and synthetic data generation. Additionally, we demonstrate how LLMs can generate convincing phishing emails, making it harder to spot scams and evaluate the performance of both models in this context. Our study delves further into the challenges encountered by DeBERTa V3 during its training phases, fine-tuning methodology and transfer learning processes. Similarly, we examine the challenges associated with LLMs and assess their respective performance. Among our experimental approaches, the transformer-based DeBERTa method emerged as the most effective, achieving a test dataset (HuggingFace phishing dataset) recall (sensitivity) of 95.17% closely followed by GPT-4 providing a recall of 91.04%. We performed additional experiments with other datasets on the trained DeBERTa V3 model and LLMs like GPT 4 and Gemini 1.5. Based on our findings, we provide valuable insights into the effectiveness and robustness of these advanced language models, offering a detailed comparative analysis that can inform future research efforts in strengthening cybersecurity measures for detecting and mitigating phishing threats., Comment: Preprint. 10 pages, Accepted in IEEE 7th International Conference on Big Data and Artificial Intelligence (BDAI 2024)

We introduce Venn Diagram (VD) Prompting, an innovative prompting technique which allows Large Language Models (LLMs) to combine and synthesize information across complex, diverse and long-context documents in knowledge-intensive question-answering tasks. Generating answers from multiple documents involves numerous steps to extract relevant and unique information and amalgamate it into a cohesive response. To improve the quality of the final answer, multiple LLM calls or pretrained models are used to perform different tasks such as summarization, reorganization and customization. The approach covered in the paper focuses on replacing the multi-step strategy via a single LLM call using VD prompting. Our proposed technique also aims to eliminate the inherent position bias in the LLMs, enhancing consistency in answers by removing sensitivity to the sequence of input information. It overcomes the challenge of inconsistency traditionally associated with varying input sequences. We also explore the practical applications of the VD prompt based on our examination of the prompt's outcomes. In the experiments performed on four public benchmark question-answering datasets, VD prompting continually matches or surpasses the performance of a meticulously crafted instruction prompt which adheres to optimal guidelines and practices., Comment: Preprint. 10 pages, Accepted in 2024 the 6th World Symposium on Artificial Intelligence (WSAI 2024)

Kernel methods are a popular class of nonlinear predictive models in machine learning. Scalable algorithms for learning kernel models need to be iterative in nature, but convergence can be slow due to poor conditioning. Spectral preconditioning is an important tool to speed-up the convergence of such iterative algorithms for training kernel models. However computing and storing a spectral preconditioner can be expensive which can lead to large computational and storage overheads, precluding the application of kernel methods to problems with large datasets. A Nystrom approximation of the spectral preconditioner is often cheaper to compute and store, and has demonstrated success in practical applications. In this paper we analyze the trade-offs of using such an approximated preconditioner. Specifically, we show that a sample of logarithmic size (as a function of the size of the dataset) enables the Nystrom-based approximated preconditioner to accelerate gradient descent nearly as well as the exact preconditioner, while also reducing the computational and storage overheads.

Automatic assessment of impairment and disease severity is a key challenge in data-driven medicine. We propose a novel framework to address this challenge, which leverages AI models trained exclusively on healthy individuals. The COnfidence-Based chaRacterization of Anomalies (COBRA) score exploits the decrease in confidence of these models when presented with impaired or diseased patients to quantify their deviation from the healthy population. We applied the COBRA score to address a key limitation of current clinical evaluation of upper-body impairment in stroke patients. The gold-standard Fugl-Meyer Assessment (FMA) requires in-person administration by a trained assessor for 30-45 minutes, which restricts monitoring frequency and precludes physicians from adapting rehabilitation protocols to the progress of each patient. The COBRA score, computed automatically in under one minute, is shown to be strongly correlated with the FMA on an independent test cohort for two different data modalities: wearable sensors ($\rho = 0.845$, 95% CI [0.743,0.908]) and video ($\rho = 0.746$, 95% C.I [0.594, 0.847]). To demonstrate the generalizability of the approach to other conditions, the COBRA score was also applied to quantify severity of knee osteoarthritis from magnetic-resonance imaging scans, again achieving significant correlation with an independent clinical assessment ($\rho = 0.644$, 95% C.I [0.585,0.696])., Comment: 32 pages, 10 figures

Understanding the mechanism of how convolutional neural networks learn features from image data is a fundamental problem in machine learning and computer vision. In this work, we identify such a mechanism. We posit the Convolutional Neural Feature Ansatz, which states that covariances of filters in any convolutional layer are proportional to the average gradient outer product (AGOP) taken with respect to patches of the input to that layer. We present extensive empirical evidence for our ansatz, including identifying high correlation between covariances of filters and patch-based AGOPs for convolutional layers in standard neural architectures, such as AlexNet, VGG, and ResNets pre-trained on ImageNet. We also provide supporting theoretical evidence. We then demonstrate the generality of our result by using the patch-based AGOP to enable deep feature learning in convolutional kernel machines. We refer to the resulting algorithm as (Deep) ConvRFM and show that our algorithm recovers similar features to deep convolutional networks including the notable emergence of edge detectors. Moreover, we find that Deep ConvRFM overcomes previously identified limitations of convolutional kernels, such as their inability to adapt to local signals in images and, as a result, leads to sizable performance improvement over fixed convolutional kernels.

We introduce Jais and Jais-chat, new state-of-the-art Arabic-centric foundation and instruction-tuned open generative large language models (LLMs). The models are based on the GPT-3 decoder-only architecture and are pretrained on a mixture of Arabic and English texts, including source code in various programming languages. With 13 billion parameters, they demonstrate better knowledge and reasoning capabilities in Arabic than any existing open Arabic and multilingual models by a sizable margin, based on extensive evaluation. Moreover, the models are competitive in English compared to English-centric open models of similar size, despite being trained on much less English data. We provide a detailed description of the training, the tuning, the safety alignment, and the evaluation of the models. We release two open versions of the model -- the foundation Jais model, and an instruction-tuned Jais-chat variant -- with the aim of promoting research on Arabic LLMs. Available at https://huggingface.co/inception-mbzuai/jais-13b-chat, Comment: Arabic-centric, foundation model, large-language model, LLM, generative model, instruction-tuned, Jais, Jais-chat

Generative Adversarial Networks (GANs) are a popular formulation to train generative models for complex high dimensional data. The standard method for training GANs involves a gradient descent-ascent (GDA) procedure on a minimax optimization problem. This procedure is hard to analyze in general due to the nonlinear nature of the dynamics. We study the local dynamics of GDA for training a GAN with a kernel-based discriminator. This convergence analysis is based on a linearization of a non-linear dynamical system that describes the GDA iterations, under an \textit{isolated points model} assumption from [Becker et al. 2022]. Our analysis brings out the effect of the learning rates, regularization, and the bandwidth of the kernel discriminator, on the local convergence rate of GDA. Importantly, we show phase transitions that indicate when the system converges, oscillates, or diverges. We also provide numerical simulations that verify our claims.

Recent studies indicate that kernel machines can often perform similarly or better than deep neural networks (DNNs) on small datasets. The interest in kernel machines has been additionally bolstered by the discovery of their equivalence to wide neural networks in certain regimes. However, a key feature of DNNs is their ability to scale the model size and training data size independently, whereas in traditional kernel machines model size is tied to data size. Because of this coupling, scaling kernel machines to large data has been computationally challenging. In this paper, we provide a way forward for constructing large-scale general kernel models, which are a generalization of kernel machines that decouples the model and data, allowing training on large datasets. Specifically, we introduce EigenPro 3.0, an algorithm based on projected dual preconditioned SGD and show scaling to model and data sizes which have not been possible with existing kernel methods., Comment: Code is available at github.com/EigenPro/EigenPro3

In recent years neural networks have achieved impressive results on many technological and scientific tasks. Yet, the mechanism through which these models automatically select features, or patterns in data, for prediction remains unclear. Identifying such a mechanism is key to advancing performance and interpretability of neural networks and promoting reliable adoption of these models in scientific applications. In this paper, we identify and characterize the mechanism through which deep fully connected neural networks learn features. We posit the Deep Neural Feature Ansatz, which states that neural feature learning occurs by implementing the average gradient outer product to up-weight features strongly related to model output. Our ansatz sheds light on various deep learning phenomena including emergence of spurious features and simplicity biases and how pruning networks can increase performance, the "lottery ticket hypothesis." Moreover, the mechanism identified in our work leads to a backpropagation-free method for feature learning with any machine learning model. To demonstrate the effectiveness of this feature learning mechanism, we use it to enable feature learning in classical, non-feature learning models known as kernel machines and show that the resulting models, which we refer to as Recursive Feature Machines, achieve state-of-the-art performance on tabular data.

Generative Adversarial Networks (GANs) are a widely-used tool for generative modeling of complex data. Despite their empirical success, the training of GANs is not fully understood due to the min-max optimization of the generator and discriminator. This paper analyzes these joint dynamics when the true samples, as well as the generated samples, are discrete, finite sets, and the discriminator is kernel-based. A simple yet expressive framework for analyzing training called the $\textit{Isolated Points Model}$ is introduced. In the proposed model, the distance between true samples greatly exceeds the kernel width, so each generated point is influenced by at most one true point. Our model enables precise characterization of the conditions for convergence, both to good and bad minima. In particular, the analysis explains two common failure modes: (i) an approximate mode collapse and (ii) divergence. Numerical simulations are provided that predictably replicate these behaviors.

The practical success of overparameterized neural networks has motivated the recent scientific study of interpolating methods, which perfectly fit their training data. Certain interpolating methods, including neural networks, can fit noisy training data without catastrophically bad test performance, in defiance of standard intuitions from statistical learning theory. Aiming to explain this, a body of recent work has studied benign overfitting, a phenomenon where some interpolating methods approach Bayes optimality, even in the presence of noise. In this work we argue that while benign overfitting has been instructive and fruitful to study, many real interpolating methods like neural networks do not fit benignly: modest noise in the training set causes nonzero (but non-infinite) excess risk at test time, implying these models are neither benign nor catastrophic but rather fall in an intermediate regime. We call this intermediate regime tempered overfitting, and we initiate its systematic study. We first explore this phenomenon in the context of kernel (ridge) regression (KR) by obtaining conditions on the ridge parameter and kernel eigenspectrum under which KR exhibits each of the three behaviors. We find that kernels with powerlaw spectra, including Laplace kernels and ReLU neural tangent kernels, exhibit tempered overfitting. We then empirically study deep neural networks through the lens of our taxonomy, and find that those trained to interpolation are tempered, while those stopped early are benign. We hope our work leads to a more refined understanding of overfitting in modern learning., Comment: NM and JS co-first authors

Randomly initialized wide neural networks transition to linear functions of weights as the width grows, in a ball of radius $O(1)$ around initialization. A necessary condition for this result is that all layers of the network are wide enough, i.e., all widths tend to infinity. However, the transition to linearity breaks down when this infinite width assumption is violated. In this work we show that linear networks with a bottleneck layer learn bilinear functions of the weights, in a ball of radius $O(1)$ around initialization. In general, for $B-1$ bottleneck layers, the network is a degree $B$ multilinear function of weights. Importantly, the degree only depends on the number of bottlenecks and not the total depth of the network.

``Benign overfitting'', the ability of certain algorithms to interpolate noisy training data and yet perform well out-of-sample, has been a topic of considerable recent interest. We show, using a fixed design setup, that an important class of predictors, kernel machines with translation-invariant kernels, does not exhibit benign overfitting in fixed dimensions. In particular, the estimated predictor does not converge to the ground truth with increasing sample size, for any non-zero regression function and any (even adaptive) bandwidth selection. To prove these results, we give exact expressions for the generalization error, and its decomposition in terms of an approximation error and an estimation error that elicits a trade-off based on the selection of the kernel bandwidth. Our results apply to commonly used translation-invariant kernels such as Gaussian, Laplace, and Cauchy.

Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization properties of neural networks. Many recent works analyze such models in a certain high-dimensional regime where the covariates are independent and the number of samples and the number of covariates grow at a fixed ratio (i.e. proportional asymptotics). In this work we show that for a large class of kernels, including the neural tangent kernel of fully connected networks, kernel methods can only perform as well as linear models in this regime. More surprisingly, when the data is generated by a kernel model where the relationship between input and the response could be very nonlinear, we show that linear models are in fact optimal, i.e. linear models achieve the minimum risk among all models, linear or nonlinear. These results suggest that more complex models for the data other than independent features are needed for high-dimensional analysis.

Automatic colorization of images without human intervention has been a subject of interest in the machine learning community for a brief period of time. Assigning color to an image is a highly ill-posed problem because of its innate nature of possessing very high degrees of freedom; given an image, there is often no single color-combination that is correct. Besides colorization, another problem in reconstruction of images is Single Image Super Resolution, which aims at transforming low resolution images to a higher resolution. This research aims to provide an automated approach for the problem by focusing on a very specific domain of images, namely astronomical images, and process them using Generative Adversarial Networks (GANs). We explore the usage of various models in two different color spaces, RGB and L*a*b. We use transferred learning owing to a small data set, using pre-trained ResNet-18 as a backbone, i.e. encoder for the U-net and fine-tune it further. The model produces visually appealing images which hallucinate high resolution, colorized data in these results which does not exist in the original image. We present our results by evaluating the GANs quantitatively using distance metrics such as L1 distance and L2 distance in each of the color spaces across all channels to provide a comparative analysis. We use Frechet inception distance (FID) to compare the distribution of the generated images with the distribution of the real image to assess the model's performance., Comment: 14 pages, 10 figures, 7 tables

Stroke rehabilitation seeks to increase neuroplasticity through the repeated practice of functional motions, but may have minimal impact on recovery because of insufficient repetitions. The optimal training content and quantity are currently unknown because no practical tools exist to measure them. Here, we present PrimSeq, a pipeline to classify and count functional motions trained in stroke rehabilitation. Our approach integrates wearable sensors to capture upper-body motion, a deep learning model to predict motion sequences, and an algorithm to tally motions. The trained model accurately decomposes rehabilitation activities into component functional motions, outperforming competitive machine learning methods. PrimSeq furthermore quantifies these motions at a fraction of the time and labor costs of human experts. We demonstrate the capabilities of PrimSeq in previously unseen stroke patients with a range of upper extremity motor impairment. We expect that these advances will support the rigorous measurement required for quantitative dosing trials in stroke rehabilitation.

Meta Learning has been in focus in recent years due to the meta-learner model's ability to adapt well and generalize to new tasks, thus, reducing both the time and data requirements for learning. However, a major drawback of meta learner is that, to reach to a state from where learning new tasks becomes feasible with less data, it requires a large number of iterations and a lot of time. We address this issue by proposing various acceleration techniques to speed up meta learning algorithms such as MAML (Model Agnostic Meta Learning). We present 3.73X acceleration on a well known RNN optimizer based meta learner proposed in literature [11]. We introduce a novel method of training tasks in clusters, which not only accelerates the meta learning process but also improves model accuracy performance. Keywords: Meta learning, RNN optimizer, AGI, Performance optimization

Effective and reliable screening of patients via Computer-Aided Diagnosis can play a crucial part in the battle against COVID-19. Most of the existing works focus on developing sophisticated methods yielding high detection performance, yet not addressing the issue of predictive uncertainty. In this work, we introduce uncertainty estimation to detect confusing cases for expert referral to address the unreliability of state-of-the-art (SOTA) DNNs on COVID-19 detection. To the best of our knowledge, we are the first to address this issue on the COVID-19 detection problem. In this work, we investigate a number of SOTA uncertainty estimation methods on publicly available COVID dataset and present our experimental findings. In collaboration with medical professionals, we further validate the results to ensure the viability of the best performing method in clinical practice., Comment: AAAI, TAIH workshop, 2021

In this research, we propose a new low-precision framework, TENT, to leverage the benefits of a tapered fixed-point numerical format in TinyML models. We introduce a tapered fixed-point quantization algorithm that matches the numerical format's dynamic range and distribution to that of the deep neural network model's parameter distribution at each layer. An accelerator architecture for the tapered fixed-point with TENT framework is proposed. Results show that the accuracy on classification tasks improves up to ~31 % with an energy overhead of ~17-30 % as compared to fixed-point, for ConvNet and ResNet-18 models., Comment: poster presented at the first tinyML Research Symposium, March 26, 2021

Contemporary wisdom based on empirical studies suggests that standard recurrent neural networks (RNNs) do not perform well on tasks requiring long-term memory. However, precise reasoning for this behavior is still unknown. This paper provides a rigorous explanation of this property in the special case of linear RNNs. Although this work is limited to linear RNNs, even these systems have traditionally been difficult to analyze due to their non-linear parameterization. Using recently-developed kernel regime analysis, our main result shows that linear RNNs learned from random initializations are functionally equivalent to a certain weighted 1D-convolutional network. Importantly, the weightings in the equivalent model cause an implicit bias to elements with smaller time lags in the convolution and hence, shorter memory. The degree of this bias depends on the variance of the transition kernel matrix at initialization and is related to the classic exploding and vanishing gradients problem. The theory is validated in both synthetic and real data experiments., Comment: 30 pages, 4 figures

We study the usage of EfficientNets and their applications to Galaxy Morphology Classification. We explore the usage of EfficientNets into predicting the vote fractions of the 79,975 testing images from the Galaxy Zoo 2 challenge on Kaggle. We evaluate this model using the standard competition metric i.e. rmse score and rank among the top 3 on the public leaderboard with a public score of 0.07765. We propose a fine-tuned architecture using EfficientNetB5 to classify galaxies into seven classes - completely round smooth, in-between smooth, cigarshaped smooth, lenticular, barred spiral, unbarred spiral and irregular. The network along with other popular convolutional networks are used to classify 29,941 galaxy images. Different metrics such as accuracy, recall, precision, F1 score are used to evaluate the performance of the model along with a comparative study of other state of the art convolutional models to determine which one performs the best. We obtain an accuracy of 93.7% on our classification model with an F1 score of 0.8857. EfficientNets can be applied to large scale galaxy classification in future optical space surveys which will provide a large amount of data such as the Large Synoptic Space Telescope., Comment: 13 pages, 7 figures, 8 tables

Sports data has become widely available in the recent past. With the improvement of machine learning techniques, there have been attempts to use sports data to analyze not only the outcome of individual games but also to improve insights and strategies. The outbreak of COVID-19 has interrupted sports leagues globally, giving rise to increasing questions and speculations about the outcome of this season's leagues. What if the season was not interrupted and concluded normally? Which teams would end up winning trophies? Which players would perform the best? Which team would end their season on a high and which teams would fail to keep up with the pressure? We aim to tackle this problem and develop a solution. In this paper, we proposeUCLData, which is a dataset containing detailed information of UEFA Champions League games played over the past six years. We also propose a novel autoencoder based machine learning pipeline that can come up with a story on how the rest of the season will pan out.

This paper considers the problem of neural decoding from parallel neural measurements systems such as micro-electrocorticography ($\mu$-ECoG). In systems with large numbers of array elements at very high sampling rates, the dimension of the raw measurement data may be large. Learning neural decoders for this high-dimensional data can be challenging, particularly when the number of training samples is limited. To address this challenge, this work presents a novel neural network decoder with a low-rank structure in the first hidden layer. The low-rank constraints dramatically reduce the number of parameters in the decoder while still enabling a rich class of nonlinear decoder maps. The low-rank decoder is illustrated on $\mu$-ECoG data from the primary auditory cortex (A1) of awake rats. This decoding problem is particularly challenging due to the complexity of neural responses in the auditory cortex and the presence of confounding signals in awake animals. It is shown that the proposed low-rank decoder significantly outperforms models using standard dimensionality reduction techniques such as principal component analysis (PCA)., Comment: 4 pages, 3 figures

At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our understanding of their generalization capabilities is incomplete. This task is made harder by the non-convexity of the underlying learning problems. We provide a general framework to characterize the asymptotic generalization error for single-layer neural networks (i.e., generalized linear models) with arbitrary non-linearities, making it applicable to regression as well as classification problems. This framework enables analyzing the effect of (i) over-parameterization and non-linearity during modeling; and (ii) choices of loss function, initialization, and regularizer during learning. Our model also captures mismatch between training and test distributions. As examples, we analyze a few special cases, namely linear regression and logistic regression. We are also able to rigorously and analytically explain the \emph{double descent} phenomenon in generalized linear models., Comment: 20 pages, 4 figures

Recovery after stroke is often incomplete, but rehabilitation training may potentiate recovery by engaging endogenous neuroplasticity. In preclinical models of stroke, high doses of rehabilitation training are required to restore functional movement to the affected limbs of animals. In humans, however, the necessary dose of training to potentiate recovery is not known. This ignorance stems from the lack of objective, pragmatic approaches for measuring training doses in rehabilitation activities. Here, to develop a measurement approach, we took the critical first step of automatically identifying functional primitives, the basic building block of activities. Forty-eight individuals with chronic stroke performed a variety of rehabilitation activities while wearing inertial measurement units (IMUs) to capture upper body motion. Primitives were identified by human labelers, who labeled and segmented the associated IMU data. We performed automatic classification of these primitives using machine learning. We designed a convolutional neural network model that outperformed existing methods. The model includes an initial module to compute separate embeddings of different physical quantities in the sensor data. In addition, it replaces batch normalization (which performs normalization based on statistics computed from the training data) with instance normalization (which uses statistics computed from the test data). This increases robustness to possible distributional shifts when applying the method to new patients. With this approach, we attained an average classification accuracy of 70%. Thus, using a combination of IMU-based motion capture and deep learning, we were able to identify primitives automatically. This approach builds towards objectively-measured rehabilitation training, enabling the identification and counting of functional primitives that accrues to a training dose.

We consider the problem of inferring the input and hidden variables of a stochastic multi-layer neural network from an observation of the output. The hidden variables in each layer are represented as matrices. This problem applies to signal recovery via deep generative prior models, multi-task and mixed regression and learning certain classes of two-layer neural networks. A unified approximation algorithm for both MAP and MMSE inference is proposed by extending a recently-developed Multi-Layer Vector Approximate Message Passing (ML-VAMP) algorithm to handle matrix-valued unknowns. It is shown that the performance of the proposed Multi-Layer Matrix VAMP (ML-Mat-VAMP) algorithm can be exactly predicted in a certain random large-system limit, where the dimensions $N\times d$ of the unknown quantities grow as $N\rightarrow\infty$ with $d$ fixed. In the two-layer neural-network learning problem, this scaling corresponds to the case where the number of input features and training samples grow to infinity but the number of hidden nodes stays fixed. The analysis enables a precise prediction of the parameter and test error of the learning., Comment: 3 figures, 6 pages (two-column) + Appendix. arXiv admin note: text overlap with arXiv:1911.03409

Deep generative priors offer powerful models for complex-structured data, such as images, audio, and text. Using these priors in inverse problems typically requires estimating the input and/or hidden signals in a multi-layer deep neural network from observation of its output. While these approaches have been successful in practice, rigorous performance analysis is complicated by the non-convex nature of the underlying optimization problems. This paper presents a novel algorithm, Multi-Layer Vector Approximate Message Passing (ML-VAMP), for inference in multi-layer stochastic neural networks. ML-VAMP can be configured to compute maximum a priori (MAP) or approximate minimum mean-squared error (MMSE) estimates for these networks. We show that the performance of ML-VAMP can be exactly predicted in a certain high-dimensional random limit. Furthermore, under certain conditions, ML-VAMP yields estimates that achieve the minimum (i.e., Bayes-optimal) MSE as predicted by the replica method. In this way, ML-VAMP provides a computationally efficient method for multi-layer inference with an exact performance characterization and testable conditions for optimality in the large-system limit., Comment: 50 pages, double-spaced

We consider the problem of estimating the parameters of a multivariate Bernoulli process with auto-regressive feedback in the high-dimensional setting where the number of samples available is much less than the number of parameters. This problem arises in learning interconnections of networks of dynamical systems with spiking or binary-valued data. We allow the process to depend on its past up to a lag $p$, for a general $p \ge 1$, allowing for more realistic modeling in many applications. We propose and analyze an $\ell_1$-regularized maximum likelihood estimator (MLE) under the assumption that the parameter tensor is approximately sparse. Rigorous analysis of such estimators is made challenging by the dependent and non-Gaussian nature of the process as well as the presence of the nonlinearities and multi-level feedback. We derive precise upper bounds on the mean-squared estimation error in terms of the number of samples, dimensions of the process, the lag $p$ and other key statistical properties of the model. The ideas presented can be used in the high-dimensional analysis of regularized $M$-estimators for other sparse nonlinear and non-Gaussian processes with long-range dependence., Comment: To appear at AISTATS 2019 titled "Sparse Multivariate Bernoulli Processes in High Dimensions"

We derive the mapping between two of the most pervasive utility functions, the mean square error ($MSE$) and the concordance correlation coefficient (CCC, $\rho_c$). Despite its drawbacks, $MSE$ is one of the most popular performance metrics (and a loss function); along with lately $\rho_c$ in many of the sequence prediction challenges. Despite the ever-growing simultaneous usage, e.g., inter-rater agreement, assay validation, a mapping between the two metrics is missing, till date. While minimisation of $L_p$ norm of the errors or of its positive powers (e.g., $MSE$) is aimed at $\rho_c$ maximisation, we reason the often-witnessed ineffectiveness of this popular loss function with graphical illustrations. The discovered formula uncovers not only the counterintuitive revelation that `$MSE_1\rho_{c_2}$', but also provides the precise range for the $\rho_c$ metric for a given $MSE$. We discover the conditions for $\rho_c$ optimisation for a given $MSE$; and as a logical next step, for a given set of errors. We generalise and discover the conditions for any given $L_p$ norm, for an even p. We present newly discovered, albeit apparent, mathematical paradoxes. The study inspires and anticipates a growing use of $\rho_c$-inspired loss functions e.g., $\left|\frac{MSE}{\sigma_{XY}}\right|$, replacing the traditional $L_p$-norm loss functions in multivariate regressions., Comment: Why this discovery, or the mapping formulation is important: MSE1CCC2. In other words, MSE minimisation does not necessarily guarantee CCC maximisation