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

Perspectives on the State and Future of Deep Learning - 2023

The goal of this series is to chronicle opinions and issues in the field of machine learning as they stand today and as they change over time. The plan is to host this survey periodically until the AI singularity paperclip-frenzy-driven doomsday, keeping an updated list of topical questions and interviewing new community members for each edition. In this issue, we probed people's opinions on interpretable AI, the value of benchmarking in modern NLP, the state of progress towards understanding deep learning, and the future of academia.

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.

MultiQG-TI: Towards Question Generation from Multi-modal Sources

We study the new problem of automatic question generation (QG) from multi-modal sources containing images and texts, significantly expanding the scope of most of the existing work that focuses exclusively on QG from only textual sources. We propose a simple solution for our new problem, called MultiQG-TI, which enables a text-only question generator to process visual input in addition to textual input. Specifically, we leverage an image-to-text model and an optical character recognition model to obtain the textual description of the image and extract any texts in the image, respectively, and then feed them together with the input texts to the question generator. We only fine-tune the question generator while keeping the other components fixed. On the challenging ScienceQA dataset, we demonstrate that MultiQG-TI significantly outperforms ChatGPT with few-shot prompting, despite having hundred-times less trainable parameters. Additional analyses empirically confirm the necessity of both visual and textual signals for QG and show the impact of various modeling choices.

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.

Unsupervised Learning of Sampling Distributions for Particle Filters

Accurate estimation of the states of a nonlinear dynamical system is crucial for their design, synthesis, and analysis. Particle filters are estimators constructed by simulating trajectories from a sampling distribution and averaging them based on their importance weight. For particle filters to be computationally tractable, it must be feasible to simulate the trajectories by drawing from the sampling distribution. Simultaneously, these trajectories need to reflect the reality of the nonlinear dynamical system so that the resulting estimators are accurate. Thus, the crux of particle filters lies in designing sampling distributions that are both easy to sample from and lead to accurate estimators. In this work, we propose to learn the sampling distributions. We put forward four methods for learning sampling distributions from observed measurements. Three of the methods are parametric methods in which we learn the mean and covariance matrix of a multivariate Gaussian distribution; each methods exploits a different aspect of the data (generic, time structure, graph structure). The fourth method is a nonparametric alternative in which we directly learn a transform of a uniform random variable. All four methods are trained in an unsupervised manner by maximizing the likelihood that the states may have produced the observed measurements. Our computational experiments demonstrate that learned sampling distributions exhibit better performance than designed, minimum-degeneracy sampling distributions.

Retrieval-based Controllable Molecule Generation

Generating new molecules with specified chemical and biological properties via generative models has emerged as a promising direction for drug discovery. However, existing methods require extensive training/fine-tuning with a large dataset, often unavailable in real-world generation tasks. In this work, we propose a new retrieval-based framework for controllable molecule generation. We use a small set of exemplar molecules, i.e., those that (partially) satisfy the design criteria, to steer the pre-trained generative model towards synthesizing molecules that satisfy the given design criteria. We design a retrieval mechanism that retrieves and fuses the exemplar molecules with the input molecule, which is trained by a new self-supervised objective that predicts the nearest neighbor of the input molecule. We also propose an iterative refinement process to dynamically update the generated molecules and retrieval database for better generalization. Our approach is agnostic to the choice of generative models and requires no task-specific fine-tuning. On various tasks ranging from simple design criteria to a challenging real-world scenario for designing lead compounds that bind to the SARS-CoV-2 main protease, we demonstrate our approach extrapolates well beyond the retrieval database, and achieves better performance and wider applicability than previous methods.

Automated Scoring for Reading Comprehension via In-context BERT Tuning

Automated scoring of open-ended student responses has the potential to significantly reduce human grader effort. Recent advances in automated scoring often leverage textual representations based on pre-trained language models such as BERT and GPT as input to scoring models. Most existing approaches train a separate model for each item/question, which is suitable for scenarios such as essay scoring where items can be quite different from one another. However, these approaches have two limitations: 1) they fail to leverage item linkage for scenarios such as reading comprehension where multiple items may share a reading passage; 2) they are not scalable since storing one model per item becomes difficult when models have a large number of parameters. In this paper, we report our (grand prize-winning) solution to the National Assessment of Education Progress (NAEP) automated scoring challenge for reading comprehension. Our approach, in-context BERT fine-tuning, produces a single shared scoring model for all items with a carefully-designed input structure to provide contextual information on each item. We demonstrate the effectiveness of our approach via local evaluations using the training dataset provided by the challenge. We also discuss the biases, common error types, and limitations of our approach.

Can Neural Nets Learn the Same Model Twice? Investigating Reproducibility and Double Descent from the Decision Boundary Perspective

We discuss methods for visualizing neural network decision boundaries and decision regions. We use these visualizations to investigate issues related to reproducibility and generalization in neural network training. We observe that changes in model architecture (and its associate inductive bias) cause visible changes in decision boundaries, while multiple runs with the same architecture yield results with strong similarities, especially in the case of wide architectures. We also use decision boundary methods to visualize double descent phenomena. We see that decision boundary reproducibility depends strongly on model width. Near the threshold of interpolation, neural network decision boundaries become fragmented into many small decision regions, and these regions are non-reproducible. Meanwhile, very narrows and very wide networks have high levels of reproducibility in their decision boundaries with relatively few decision regions. We discuss how our observations relate to the theory of double descent phenomena in convex models. Code is available at https://github.com/somepago/dbViz

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