Deep Networks Always Grok and Here is Why

Grokking, or delayed generalization, is a phenomenon where generalization in a deep neural network (DNN) occurs long after achieving near zero training error. Previous studies have reported the occurrence of grokking in specific controlled settings, such as DNNs initialized with large-norm parameters or transformers trained on algorithmic datasets. We demonstrate that grokking is actually much more widespread and materializes in a wide range of practical settings, such as training of a convolutional neural network (CNN) on CIFAR10 or a Resnet on Imagenette. We introduce the new concept of delayed robustness, whereby a DNN groks adversarial examples and becomes robust, long after interpolation and/or generalization. We develop an analytical explanation for the emergence of both delayed generalization and delayed robustness based on a new measure of the local complexity of a DNN's input-output mapping. Our local complexity measures the density of the so-called 'linear regions' (aka, spline partition regions) that tile the DNN input space, and serves as a utile progress measure for training. We provide the first evidence that for classification problems, the linear regions undergo a phase transition during training whereafter they migrate away from the training samples (making the DNN mapping smoother there) and towards the decision boundary (making the DNN mapping less smooth there). Grokking occurs post phase transition as a robust partition of the input space emerges thanks to the linearization of the DNN mapping around the training points. Website: https://bit.ly/grok-adversarial

Training Dynamics of Deep Network Linear Regions

The study of Deep Network (DN) training dynamics has largely focused on the evolution of the loss function, evaluated on or around train and test set data points. In fact, many DN phenomenon were first introduced in literature with that respect, e.g., double descent, grokking. In this study, we look at the training dynamics of the input space partition or linear regions formed by continuous piecewise affine DNs, e.g., networks with (leaky)ReLU nonlinearities. First, we present a novel statistic that encompasses the local complexity (LC) of the DN based on the concentration of linear regions inside arbitrary dimensional neighborhoods around data points. We observe that during training, the LC around data points undergoes a number of phases, starting with a decreasing trend after initialization, followed by an ascent and ending with a final descending trend. Using exact visualization methods, we come across the perplexing observation that during the final LC descent phase of training, linear regions migrate away from training and test samples towards the decision boundary, making the DN input-output nearly linear everywhere else. We also observe that the different LC phases are closely related to the memorization and generalization performance of the DN, especially during grokking.

Self-Consuming Generative Models Go MAD

Seismic advances in generative AI algorithms for imagery, text, and other data types has led to the temptation to use synthetic data to train next-generation models. Repeating this process creates an autophagous (self-consuming) loop whose properties are poorly understood. We conduct a thorough analytical and empirical analysis using state-of-the-art generative image models of three families of autophagous loops that differ in how fixed or fresh real training data is available through the generations of training and in whether the samples from previous generation models have been biased to trade off data quality versus diversity. Our primary conclusion across all scenarios is that without enough fresh real data in each generation of an autophagous loop, future generative models are doomed to have their quality (precision) or diversity (recall) progressively decrease. We term this condition Model Autophagy Disorder (MAD), making analogy to mad cow disease.

OOD-Speech: A Large Bengali Speech Recognition Dataset for Out-of-Distribution Benchmarking

We present OOD-Speech, the first out-of-distribution (OOD) benchmarking dataset for Bengali automatic speech recognition (ASR). Being one of the most spoken languages globally, Bengali portrays large diversity in dialects and prosodic features, which demands ASR frameworks to be robust towards distribution shifts. For example, islamic religious sermons in Bengali are delivered with a tonality that is significantly different from regular speech. Our training dataset is collected via massively online crowdsourcing campaigns which resulted in 1177.94 hours collected and curated from $22,645$ native Bengali speakers from South Asia. Our test dataset comprises 23.03 hours of speech collected and manually annotated from 17 different sources, e.g., Bengali TV drama, Audiobook, Talk show, Online class, and Islamic sermons to name a few. OOD-Speech is jointly the largest publicly available speech dataset, as well as the first out-of-distribution ASR benchmarking dataset for Bengali.

BaDLAD: A Large Multi-Domain Bengali Document Layout Analysis Dataset

While strides have been made in deep learning based Bengali Optical Character Recognition (OCR) in the past decade, the absence of large Document Layout Analysis (DLA) datasets has hindered the application of OCR in document transcription, e.g., transcribing historical documents and newspapers. Moreover, rule-based DLA systems that are currently being employed in practice are not robust to domain variations and out-of-distribution layouts. To this end, we present the first multidomain large Bengali Document Layout Analysis Dataset: BaDLAD. This dataset contains 33,695 human annotated document samples from six domains - i) books and magazines, ii) public domain govt. documents, iii) liberation war documents, iv) newspapers, v) historical newspapers, and vi) property deeds, with 710K polygon annotations for four unit types: text-box, paragraph, image, and table. Through preliminary experiments benchmarking the performance of existing state-of-the-art deep learning architectures for English DLA, we demonstrate the efficacy of our dataset in training deep learning based Bengali document digitization models.

SplineCam: Exact Visualization and Characterization of Deep Network Geometry and Decision Boundaries

Current Deep Network (DN) visualization and interpretability methods rely heavily on data space visualizations such as scoring which dimensions of the data are responsible for their associated prediction or generating new data features or samples that best match a given DN unit or representation. In this paper, we go one step further by developing the first provably exact method for computing the geometry of a DN's mapping - including its decision boundary - over a specified region of the data space. By leveraging the theory of Continuous Piece-Wise Linear (CPWL) spline DNs, SplineCam exactly computes a DNs geometry without resorting to approximations such as sampling or architecture simplification. SplineCam applies to any DN architecture based on CPWL nonlinearities, including (leaky-)ReLU, absolute value, maxout, and max-pooling and can also be applied to regression DNs such as implicit neural representations. Beyond decision boundary visualization and characterization, SplineCam enables one to compare architectures, measure generalizability and sample from the decision boundary on or off the manifold. Project Website: bit.ly/splinecam.

Bengali Common Voice Speech Dataset for Automatic Speech Recognition

Bengali is one of the most spoken languages in the world with over 300 million speakers globally. Despite its popularity, research into the development of Bengali speech recognition systems is hindered due to the lack of diverse open-source datasets. As a way forward, we have crowdsourced the Bengali Common Voice Speech Dataset, which is a sentence-level automatic speech recognition corpus. Collected on the Mozilla Common Voice platform, the dataset is part of an ongoing campaign that has led to the collection of over 400 hours of data in 2 months and is growing rapidly. Our analysis shows that this dataset has more speaker, phoneme, and environmental diversity compared to the OpenSLR Bengali ASR dataset, the largest existing open-source Bengali speech dataset. We present insights obtained from the dataset and discuss key linguistic challenges that need to be addressed in future versions. Additionally, we report the current performance of a few Automatic Speech Recognition (ASR) algorithms and set a benchmark for future research.

No More Than 6ft Apart: Robust K-Means via Radius Upper Bounds

Centroid based clustering methods such as k-means, k-medoids and k-centers are heavily applied as a go-to tool in exploratory data analysis. In many cases, those methods are used to obtain representative centroids of the data manifold for visualization or summarization of a dataset. Real world datasets often contain inherent abnormalities, e.g., repeated samples and sampling bias, that manifest imbalanced clustering. We propose to remedy such a scenario by introducing a maximal radius constraint $r$ on the clusters formed by the centroids, i.e., samples from the same cluster should not be more than $2r$ apart in terms of $\ell_2$ distance. We achieve this constraint by solving a semi-definite program, followed by a linear assignment problem with quadratic constraints. Through qualitative results, we show that our proposed method is robust towards dataset imbalances and sampling artifacts. To the best of our knowledge, ours is the first constrained k-means clustering method with hard radius constraints. Codes at https://bit.ly/kmeans-constrained

Polarity Sampling: Quality and Diversity Control of Pre-Trained Generative Networks via Singular Values

We present Polarity Sampling, a theoretically justified plug-and-play method for controlling the generation quality and diversity of pre-trained deep generative networks DGNs). Leveraging the fact that DGNs are, or can be approximated by, continuous piecewise affine splines, we derive the analytical DGN output space distribution as a function of the product of the DGN's Jacobian singular values raised to a power $\rho$. We dub $\rho$ the $\textbf{polarity}$ parameter and prove that $\rho$ focuses the DGN sampling on the modes ($\rho < 0$) or anti-modes ($\rho > 0$) of the DGN output-space distribution. We demonstrate that nonzero polarity values achieve a better precision-recall (quality-diversity) Pareto frontier than standard methods, such as truncation, for a number of state-of-the-art DGNs. We also present quantitative and qualitative results on the improvement of overall generation quality (e.g., in terms of the Frechet Inception Distance) for a number of state-of-the-art DGNs, including StyleGAN3, BigGAN-deep, NVAE, for different conditional and unconditional image generation tasks. In particular, Polarity Sampling redefines the state-of-the-art for StyleGAN2 on the FFHQ Dataset to FID 2.57, StyleGAN2 on the LSUN Car Dataset to FID 2.27 and StyleGAN3 on the AFHQv2 Dataset to FID 3.95. Demo: bit.ly/polarity-demo-colab

MaGNET: Uniform Sampling from Deep Generative Network Manifolds Without Retraining

Deep Generative Networks (DGNs) are extensively employed in Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and their variants to approximate the data manifold, and data distribution on that manifold. However, training samples are often obtained based on preferences, costs, or convenience producing artifacts in the empirical data distribution e.g., the large fraction of smiling faces in the CelebA dataset or the large fraction of dark-haired individuals in FFHQ. These inconsistencies will be reproduced when sampling from the trained DGN, which has far-reaching potential implications for fairness, data augmentation, anomaly detection, domain adaptation, and beyond. In response, we develop a differential geometry based sampler -- coined MaGNET -- that, given any trained DGN, produces samples that are uniformly distributed on the learned manifold. We prove theoretically and empirically that our technique produces a uniform distribution on the manifold regardless of the training set distribution. We perform a range of experiments on various datasets and DGNs. One of them considers the state-of-the-art StyleGAN2 trained on FFHQ dataset, where uniform sampling via MaGNET increases distribution precision and recall by 4.1% & 3.0% and decreases gender bias by 41.2%, without requiring labels or retraining.