Physics informed cell representations for variational formulation of multiscale problems

With the rapid advancement of graphical processing units, Physics-Informed Neural Networks (PINNs) are emerging as a promising tool for solving partial differential equations (PDEs). However, PINNs are not well suited for solving PDEs with multiscale features, particularly suffering from slow convergence and poor accuracy. To address this limitation of PINNs, this article proposes physics-informed cell representations for resolving multiscale Poisson problems using a model architecture consisting of multilevel multiresolution grids coupled with a multilayer perceptron (MLP). The grid parameters (i.e., the level-dependent feature vectors) and the MLP parameters (i.e., the weights and biases) are determined using gradient-descent based optimization. The variational (weak) form based loss function accelerates computation by allowing the linear interpolation of feature vectors within grid cells. This cell-based MLP model also facilitates the use of a decoupled training scheme for Dirichlet boundary conditions and a parameter-sharing scheme for periodic boundary conditions, delivering superior accuracy compared to conventional PINNs. Furthermore, the numerical examples highlight improved speed and accuracy in solving PDEs with nonlinear or high-frequency boundary conditions and provide insights into hyperparameter selection. In essence, by cell-based MLP model along with the parallel tiny-cuda-nn library, our implementation improves convergence speed and numerical accuracy.

Zero-shot Prompt-based Video Encoder for Surgical Gesture Recognition

Purpose: Surgical video is an important data stream for gesture recognition. Thus, robust visual encoders for those data-streams is similarly important. Methods: Leveraging the Bridge-Prompt framework, we fine-tune a pre-trained vision-text model (CLIP) for gesture recognition in surgical videos. This can utilize extensive outside video data such as text, but also make use of label meta-data and weakly supervised contrastive losses. Results: Our experiments show that prompt-based video encoder outperforms standard encoders in surgical gesture recognition tasks. Notably, it displays strong performance in zero-shot scenarios, where gestures/tasks that were not provided during the encoder training phase are included in the prediction phase. Additionally, we measure the benefit of inclusion text descriptions in the feature extractor training schema. Conclusion: Bridge-Prompt and similar pre-trained+fine-tuned video encoder models present significant visual representation for surgical robotics, especially in gesture recognition tasks. Given the diverse range of surgical tasks (gestures), the ability of these models to zero-shot transfer without the need for any task (gesture) specific retraining makes them invaluable.

One Category One Prompt: Dataset Distillation using Diffusion Models

The extensive amounts of data required for training deep neural networks pose significant challenges on storage and transmission fronts. Dataset distillation has emerged as a promising technique to condense the information of massive datasets into a much smaller yet representative set of synthetic samples. However, traditional dataset distillation approaches often struggle to scale effectively with high-resolution images and more complex architectures due to the limitations in bi-level optimization. Recently, several works have proposed exploiting knowledge distillation with decoupled optimization schemes to scale up dataset distillation. Although these methods effectively address the scalability issue, they rely on extensive image augmentations requiring the storage of soft labels for augmented images. In this paper, we introduce Dataset Distillation using Diffusion Models (D3M) as a novel paradigm for dataset distillation, leveraging recent advancements in generative text-to-image foundation models. Our approach utilizes textual inversion, a technique for fine-tuning text-to-image generative models, to create concise and informative representations for large datasets. By employing these learned text prompts, we can efficiently store and infer new samples for introducing data variability within a fixed memory budget. We show the effectiveness of our method through extensive experiments across various computer vision benchmark datasets with different memory budgets.

Efficient Solvers for Partial Gromov-Wasserstein

The partial Gromov-Wasserstein (PGW) problem facilitates the comparison of measures with unequal masses residing in potentially distinct metric spaces, thereby enabling unbalanced and partial matching across these spaces. In this paper, we demonstrate that the PGW problem can be transformed into a variant of the Gromov-Wasserstein problem, akin to the conversion of the partial optimal transport problem into an optimal transport problem. This transformation leads to two new solvers, mathematically and computationally equivalent, based on the Frank-Wolfe algorithm, that provide efficient solutions to the PGW problem. We further establish that the PGW problem constitutes a metric for metric measure spaces. Finally, we validate the effectiveness of our proposed solvers in terms of computation time and performance on shape-matching and positive-unlabeled learning problems, comparing them against existing baselines.

Stereographic Spherical Sliced Wasserstein Distances

Comparing spherical probability distributions is of great interest in various fields, including geology, medical domains, computer vision, and deep representation learning. The utility of optimal transport-based distances, such as the Wasserstein distance, for comparing probability measures has spurred active research in developing computationally efficient variations of these distances for spherical probability measures. This paper introduces a high-speed and highly parallelizable distance for comparing spherical measures using the stereographic projection and the generalized Radon transform, which we refer to as the Stereographic Spherical Sliced Wasserstein (S3W) distance. We carefully address the distance distortion caused by the stereographic projection and provide an extensive theoretical analysis of our proposed metric and its rotationally invariant variation. Finally, we evaluate the performance of the proposed metrics and compare them with recent baselines in terms of both speed and accuracy through a wide range of numerical studies, including gradient flows and self-supervised learning.

BrainWash: A Poisoning Attack to Forget in Continual Learning

Continual learning has gained substantial attention within the deep learning community, offering promising solutions to the challenging problem of sequential learning. Yet, a largely unexplored facet of this paradigm is its susceptibility to adversarial attacks, especially with the aim of inducing forgetting. In this paper, we introduce "BrainWash," a novel data poisoning method tailored to impose forgetting on a continual learner. By adding the BrainWash noise to a variety of baselines, we demonstrate how a trained continual learner can be induced to forget its previously learned tasks catastrophically, even when using these continual learning baselines. An important feature of our approach is that the attacker requires no access to previous tasks' data and is armed merely with the model's current parameters and the data belonging to the most recent task. Our extensive experiments highlight the efficacy of BrainWash, showcasing degradation in performance across various regularization-based continual learning methods.

CovarNav: Machine Unlearning via Model Inversion and Covariance Navigation

The rapid progress of AI, combined with its unprecedented public adoption and the propensity of large neural networks to memorize training data, has given rise to significant data privacy concerns. To address these concerns, machine unlearning has emerged as an essential technique to selectively remove the influence of specific training data points on trained models. In this paper, we approach the machine unlearning problem through the lens of continual learning. Given a trained model and a subset of training data designated to be forgotten (i.e., the "forget set"), we introduce a three-step process, named CovarNav, to facilitate this forgetting. Firstly, we derive a proxy for the model's training data using a model inversion attack. Secondly, we mislabel the forget set by selecting the most probable class that deviates from the actual ground truth. Lastly, we deploy a gradient projection method to minimize the cross-entropy loss on the modified forget set (i.e., learn incorrect labels for this set) while preventing forgetting of the inverted samples. We rigorously evaluate CovarNav on the CIFAR-10 and Vggface2 datasets, comparing our results with recent benchmarks in the field and demonstrating the efficacy of our proposed approach.

LCOT: Linear circular optimal transport

The optimal transport problem for measures supported on non-Euclidean spaces has recently gained ample interest in diverse applications involving representation learning. In this paper, we focus on circular probability measures, i.e., probability measures supported on the unit circle, and introduce a new computationally efficient metric for these measures, denoted as Linear Circular Optimal Transport (LCOT). The proposed metric comes with an explicit linear embedding that allows one to apply Machine Learning (ML) algorithms to the embedded measures and seamlessly modify the underlying metric for the ML algorithm to LCOT. We show that the proposed metric is rooted in the Circular Optimal Transport (COT) and can be considered the linearization of the COT metric with respect to a fixed reference measure. We provide a theoretical analysis of the proposed metric and derive the computational complexities for pairwise comparison of circular probability measures. Lastly, through a set of numerical experiments, we demonstrate the benefits of LCOT in learning representations of circular measures.

NOLA: Networks as Linear Combination of Low Rank Random Basis

Large Language Models (LLMs) have recently gained popularity due to their impressive few-shot performance across various downstream tasks. However, fine-tuning all parameters and storing a unique model for each downstream task or domain becomes impractical because of the massive size of checkpoints (e.g., 350GB in GPT-3). Current literature, such as LoRA, showcases the potential of low-rank modifications to the original weights of an LLM, enabling efficient adaptation and storage for task-specific models. These methods can reduce the number of parameters needed to fine-tune an LLM by several orders of magnitude. Yet, these methods face two primary limitations: 1) the parameter reduction is lower-bounded by the rank one decomposition, and 2) the extent of reduction is heavily influenced by both the model architecture and the chosen rank. For instance, in larger models, even a rank one decomposition might exceed the number of parameters truly needed for adaptation. In this paper, we introduce NOLA, which overcomes the rank one lower bound present in LoRA. It achieves this by re-parameterizing the low-rank matrices in LoRA using linear combinations of randomly generated matrices (basis) and optimizing the linear mixture coefficients only. This approach allows us to decouple the number of trainable parameters from both the choice of rank and the network architecture. We present adaptation results using GPT-2 and ViT in natural language and computer vision tasks. NOLA performs as well as, or better than models with equivalent parameter counts. Furthermore, we demonstrate that we can halve the parameters in larger models compared to LoRA with rank one, without sacrificing performance.

Partial Transport for Point-Cloud Registration

Point cloud registration plays a crucial role in various fields, including robotics, computer graphics, and medical imaging. This process involves determining spatial relationships between different sets of points, typically within a 3D space. In real-world scenarios, complexities arise from non-rigid movements and partial visibility, such as occlusions or sensor noise, making non-rigid registration a challenging problem. Classic non-rigid registration methods are often computationally demanding, suffer from unstable performance, and, importantly, have limited theoretical guarantees. The optimal transport problem and its unbalanced variations (e.g., the optimal partial transport problem) have emerged as powerful tools for point-cloud registration, establishing a strong benchmark in this field. These methods view point clouds as empirical measures and provide a mathematically rigorous way to quantify the `correspondence' between (the transformed) source and target points. In this paper, we approach the point-cloud registration problem through the lens of optimal transport theory and first propose a comprehensive set of non-rigid registration methods based on the optimal partial transportation problem. Subsequently, leveraging the emerging work on efficient solutions to the one-dimensional optimal partial transport problem, we extend our proposed algorithms via slicing to gain significant computational efficiency, resulting in fast and robust non-rigid registration algorithms. We demonstrate the effectiveness of our proposed methods and compare them against baselines on various 3D and 2D non-rigid registration problems where the source and target point clouds are corrupted by random noise.