Curvature-Informed SGD via General Purpose Lie-Group Preconditioners

We present a novel approach to accelerate stochastic gradient descent (SGD) by utilizing curvature information obtained from Hessian-vector products or finite differences of parameters and gradients, similar to the BFGS algorithm. Our approach involves two preconditioners: a matrix-free preconditioner and a low-rank approximation preconditioner. We update both preconditioners online using a criterion that is robust to stochastic gradient noise and does not require line search or damping. To preserve the corresponding symmetry or invariance, our preconditioners are constrained to certain connected Lie groups. The Lie group's equivariance property simplifies the preconditioner fitting process, while its invariance property eliminates the need for damping, which is commonly required in second-order optimizers. As a result, the learning rate for parameter updating and the step size for preconditioner fitting are naturally normalized, and their default values work well in most scenarios. Our proposed approach offers a promising direction for improving the convergence of SGD with low computational overhead. We demonstrate that Preconditioned SGD (PSGD) outperforms SoTA on Vision, NLP, and RL tasks across multiple modern deep-learning architectures. We have provided code for reproducing toy and large scale experiments in this paper.

Towards Composable Distributions of Latent Space Augmentations

We propose a composable framework for latent space image augmentation that allows for easy combination of multiple augmentations. Image augmentation has been shown to be an effective technique for improving the performance of a wide variety of image classification and generation tasks. Our framework is based on the Variational Autoencoder architecture and uses a novel approach for augmentation via linear transformation within the latent space itself. We explore losses and augmentation latent geometry to enforce the transformations to be composable and involuntary, thus allowing the transformations to be readily combined or inverted. Finally, we show these properties are better performing with certain pairs of augmentations, but we can transfer the latent space to other sets of augmentations to modify performance, effectively constraining the VAE's bottleneck to preserve the variance of specific augmentations and features of the image which we care about. We demonstrate the effectiveness of our approach with initial results on the MNIST dataset against both a standard VAE and a Conditional VAE. This latent augmentation method allows for much greater control and geometric interpretability of the latent space, making it a valuable tool for researchers and practitioners in the field.

Generating High Fidelity Synthetic Data via Coreset selection and Entropic Regularization

Generative models have the ability to synthesize data points drawn from the data distribution, however, not all generated samples are high quality. In this paper, we propose using a combination of coresets selection methods and ``entropic regularization'' to select the highest fidelity samples. We leverage an Energy-Based Model which resembles a variational auto-encoder with an inference and generator model for which the latent prior is complexified by an energy-based model. In a semi-supervised learning scenario, we show that augmenting the labeled data-set, by adding our selected subset of samples, leads to better accuracy improvement rather than using all the synthetic samples.

Improving Levenberg-Marquardt Algorithm for Neural Networks

We explore the usage of the Levenberg-Marquardt (LM) algorithm for regression (non-linear least squares) and classification (generalized Gauss-Newton methods) tasks in neural networks. We compare the performance of the LM method with other popular first-order algorithms such as SGD and Adam, as well as other second-order algorithms such as L-BFGS , Hessian-Free and KFAC. We further speed up the LM method by using adaptive momentum, learning rate line search, and uphill step acceptance.

Hypothesis Testing using Causal and Causal Variational Generative Models

Hypothesis testing and the usage of expert knowledge, or causal priors, has not been well explored in the context of generative models. We propose a novel set of generative architectures, Causal Gen and Causal Variational Gen, that can utilize nonparametric structural causal knowledge combined with a deep learning functional approximation. We show how, using a deliberate (non-random) split of training and testing data, these models can generalize better to similar, but out-of-distribution data points, than non-causal generative models and prediction models such as Variational autoencoders and Fully Connected Neural Networks. We explore using this generalization error as a proxy for causal model hypothesis testing. We further show how dropout can be used to learn functional relationships of structural models that are difficult to learn with traditional methods. We validate our methods on a synthetic pendulum dataset, as well as a trauma surgery ground level fall dataset.

Adaptive Second Order Coresets for Data-efficient Machine Learning

Training machine learning models on massive datasets incurs substantial computational costs. To alleviate such costs, there has been a sustained effort to develop data-efficient training methods that can carefully select subsets of the training examples that generalize on par with the full training data. However, existing methods are limited in providing theoretical guarantees for the quality of the models trained on the extracted subsets, and may perform poorly in practice. We propose AdaCore, a method that leverages the geometry of the data to extract subsets of the training examples for efficient machine learning. The key idea behind our method is to dynamically approximate the curvature of the loss function via an exponentially-averaged estimate of the Hessian to select weighted subsets (coresets) that provide a close approximation of the full gradient preconditioned with the Hessian. We prove rigorous guarantees for the convergence of various first and second-order methods applied to the subsets chosen by AdaCore. Our extensive experiments show that AdaCore extracts coresets with higher quality compared to baselines and speeds up training of convex and non-convex machine learning models, such as logistic regression and neural networks, by over 2.9x over the full data and 4.5x over random subsets.

De-Biasing Generative Models using Counterfactual Methods

Variational autoencoders (VAEs) and other generative methods have garnered growing interest not just for their generative properties but also for the ability to dis-entangle a low-dimensional latent variable space. However, few existing generative models take causality into account. We propose a new decoder based framework named the Causal Counterfactual Generative Model (CCGM), which includes a partially trainable causal layer in which a part of a causal model can be learned without significantly impacting reconstruction fidelity. By learning the causal relationships between image semantic labels or tabular variables, we can analyze biases, intervene on the generative model, and simulate new scenarios. Furthermore, by modifying the causal structure, we can generate samples outside the domain of the original training data and use such counterfactual models to de-bias datasets. Thus, datasets with known biases can still be used to train the causal generative model and learn the causal relationships, but we can produce de-biased datasets on the generative side. Our proposed method combines a causal latent space VAE model with specific modification to emphasize causal fidelity, enabling finer control over the causal layer and the ability to learn a robust intervention framework. We explore how better disentanglement of causal learning and encoding/decoding generates higher causal intervention quality. We also compare our model against similar research to demonstrate the need for explicit generative de-biasing beyond interventions. Our initial experiments show that our model can generate images and tabular data with high fidelity to the causal framework and accommodate explicit de-biasing to ignore undesired relationships in the causal data compared to the baseline.

Diverse Imitation Learning via Self-Organizing Generative Models

Imitation learning is the task of replicating expert policy from demonstrations, without access to a reward function. This task becomes particularly challenging when the expert exhibits a mixture of behaviors. Prior work has introduced latent variables to model variations of the expert policy. However, our experiments show that the existing works do not exhibit appropriate imitation of individual modes. To tackle this problem, we adopt an encoder-free generative model for behavior cloning (BC) to accurately distinguish and imitate different modes. Then, we integrate it with GAIL to make the learning robust towards compounding errors at unseen states. We show that our method significantly outperforms the state of the art across multiple experiments.