Beyond Closure Models: Learning Chaotic-Systems via Physics-Informed Neural Operators

Accurately predicting the long-term behavior of chaotic systems is crucial for various applications such as climate modeling. However, achieving such predictions typically requires iterative computations over a dense spatiotemporal grid to account for the unstable nature of chaotic systems, which is expensive and impractical in many real-world situations. An alternative approach to such a full-resolved simulation is using a coarse grid and then correcting its errors through a \textit{closure model}, which approximates the overall information from fine scales not captured in the coarse-grid simulation. Recently, ML approaches have been used for closure modeling, but they typically require a large number of training samples from expensive fully-resolved simulations (FRS). In this work, we prove an even more fundamental limitation, i.e., the standard approach to learning closure models suffers from a large approximation error for generic problems, no matter how large the model is, and it stems from the non-uniqueness of the mapping. We propose an alternative end-to-end learning approach using a physics-informed neural operator (PINO) that overcomes this limitation by not using a closure model or a coarse-grid solver. We first train the PINO model on data from a coarse-grid solver and then fine-tune it with (a small amount of) FRS and physics-based losses on a fine grid. The discretization-free nature of neural operators means that they do not suffer from the restriction of a coarse grid that closure models face, and they can provably approximate the long-term statistics of chaotic systems. In our experiments, our PINO model achieves a 120x speedup compared to FRS with a relative error $\sim 5\%$. In contrast, the closure model coupled with a coarse-grid solver is $58$x slower than PINO while having a much higher error $\sim205\%$ when the closure model is trained on the same FRS dataset.

Trajectory Regularization Enhances Self-Supervised Geometric Representation

Self-supervised learning (SSL) has proven effective in learning high-quality representations for various downstream tasks, with a primary focus on semantic tasks. However, its application in geometric tasks remains underexplored, partially due to the absence of a standardized evaluation method for geometric representations. To address this gap, we introduce a new pose-estimation benchmark for assessing SSL geometric representations, which demands training without semantic or pose labels and achieving proficiency in both semantic and geometric downstream tasks. On this benchmark, we study enhancing SSL geometric representations without sacrificing semantic classification accuracy. We find that leveraging mid-layer representations improves pose-estimation performance by 10-20%. Further, we introduce an unsupervised trajectory-regularization loss, which improves performance by an additional 4% and improves generalization ability on out-of-distribution data. We hope the proposed benchmark and methods offer new insights and improvements in self-supervised geometric representation learning.

Deep Multimodal Fusion for Surgical Feedback Classification

Quantification of real-time informal feedback delivered by an experienced surgeon to a trainee during surgery is important for skill improvements in surgical training. Such feedback in the live operating room is inherently multimodal, consisting of verbal conversations (e.g., questions and answers) as well as non-verbal elements (e.g., through visual cues like pointing to anatomic elements). In this work, we leverage a clinically-validated five-category classification of surgical feedback: "Anatomic", "Technical", "Procedural", "Praise" and "Visual Aid". We then develop a multi-label machine learning model to classify these five categories of surgical feedback from inputs of text, audio, and video modalities. The ultimate goal of our work is to help automate the annotation of real-time contextual surgical feedback at scale. Our automated classification of surgical feedback achieves AUCs ranging from 71.5 to 77.6 with the fusion improving performance by 3.1%. We also show that high-quality manual transcriptions of feedback audio from experts improve AUCs to between 76.5 and 96.2, which demonstrates a clear path toward future improvements. Empirically, we find that the Staged training strategy, with first pre-training each modality separately and then training them jointly, is more effective than training different modalities altogether. We also present intuitive findings on the importance of modalities for different feedback categories. This work offers an important first look at the feasibility of automated classification of real-world live surgical feedback based on text, audio, and video modalities.

Tracking the Dynamics of the Tear Film Lipid Layer

Dry Eye Disease (DED) is one of the most common ocular diseases: over five percent of US adults suffer from DED. Tear film instability is a known factor for DED, and is thought to be regulated in large part by the thin lipid layer that covers and stabilizes the tear film. In order to aid eye related disease diagnosis, this work proposes a novel paradigm in using computer vision techniques to numerically analyze the tear film lipid layer (TFLL) spread. Eleven videos of the tear film lipid layer spread are collected with a micro-interferometer and a subset are annotated. A tracking algorithm relying on various pillar computer vision techniques is developed. Our method can be found at https://easytear-dev.github.io/.

Unsupervised Scene Sketch to Photo Synthesis

Sketches make an intuitive and powerful visual expression as they are fast executed freehand drawings. We present a method for synthesizing realistic photos from scene sketches. Without the need for sketch and photo pairs, our framework directly learns from readily available large-scale photo datasets in an unsupervised manner. To this end, we introduce a standardization module that provides pseudo sketch-photo pairs during training by converting photos and sketches to a standardized domain, i.e. the edge map. The reduced domain gap between sketch and photo also allows us to disentangle them into two components: holistic scene structures and low-level visual styles such as color and texture. Taking this advantage, we synthesize a photo-realistic image by combining the structure of a sketch and the visual style of a reference photo. Extensive experimental results on perceptual similarity metrics and human perceptual studies show the proposed method could generate realistic photos with high fidelity from scene sketches and outperform state-of-the-art photo synthesis baselines. We also demonstrate that our framework facilitates a controllable manipulation of photo synthesis by editing strokes of corresponding sketches, delivering more fine-grained details than previous approaches that rely on region-level editing.

Open Long-Tailed Recognition in a Dynamic World

Real world data often exhibits a long-tailed and open-ended (with unseen classes) distribution. A practical recognition system must balance between majority (head) and minority (tail) classes, generalize across the distribution, and acknowledge novelty upon the instances of unseen classes (open classes). We define Open Long-Tailed Recognition++ (OLTR++) as learning from such naturally distributed data and optimizing for the classification accuracy over a balanced test set which includes both known and open classes. OLTR++ handles imbalanced classification, few-shot learning, open-set recognition, and active learning in one integrated algorithm, whereas existing classification approaches often focus only on one or two aspects and deliver poorly over the entire spectrum. The key challenges are: 1) how to share visual knowledge between head and tail classes, 2) how to reduce confusion between tail and open classes, and 3) how to actively explore open classes with learned knowledge. Our algorithm, OLTR++, maps images to a feature space such that visual concepts can relate to each other through a memory association mechanism and a learned metric (dynamic meta-embedding) that both respects the closed world classification of seen classes and acknowledges the novelty of open classes. Additionally, we propose an active learning scheme based on visual memory, which learns to recognize open classes in a data-efficient manner for future expansions. On three large-scale open long-tailed datasets we curated from ImageNet (object-centric), Places (scene-centric), and MS1M (face-centric) data, as well as three standard benchmarks (CIFAR-10-LT, CIFAR-100-LT, and iNaturalist-18), our approach, as a unified framework, consistently demonstrates competitive performance. Notably, our approach also shows strong potential for the active exploration of open classes and the fairness analysis of minority groups.

Recurrent Parameter Generators

We present a generic method for recurrently using the same parameters for many different convolution layers to build a deep network. Specifically, for a network, we create a recurrent parameter generator (RPG), from which the parameters of each convolution layer are generated. Though using recurrent models to build a deep convolutional neural network (CNN) is not entirely new, our method achieves significant performance gain compared to the existing works. We demonstrate how to build a one-layer neural network to achieve similar performance compared to other traditional CNN models on various applications and datasets. Such a method allows us to build an arbitrarily complex neural network with any amount of parameters. For example, we build a ResNet34 with model parameters reduced by more than $400$ times, which still achieves $41.6\%$ ImageNet top-1 accuracy. Furthermore, we demonstrate the RPG can be applied at different scales, such as layers, blocks, or even sub-networks. Specifically, we use the RPG to build a ResNet18 network with the number of weights equivalent to one convolutional layer of a conventional ResNet and show this model can achieve $67.2\%$ ImageNet top-1 accuracy. The proposed method can be viewed as an inverse approach to model compression. Rather than removing the unused parameters from a large model, it aims to squeeze more information into a small number of parameters. Extensive experiment results are provided to demonstrate the power of the proposed recurrent parameter generator.

3D Shape Reconstruction from Free-Hand Sketches

Sketches are the most abstract 2D representations of real-world objects. Although a sketch usually has geometrical distortion and lacks visual cues, humans can effortlessly envision a 3D object from it. This indicates that sketches encode the appropriate information to recover 3D shapes. Although great progress has been achieved in 3D reconstruction from distortion-free line drawings, such as CAD and edge maps, little effort has been made to reconstruct 3D shapes from free-hand sketches. We pioneer to study this task and aim to enhance the power of sketches in 3D-related applications such as interactive design and VR/AR games. Further, we propose an end-to-end sketch-based 3D reconstruction framework. Instead of well-used edge maps, synthesized sketches are adopted as training data. Additionally, we propose a sketch standardization module to handle different sketch styles and distortions. With extensive experiments, we demonstrate the effectiveness of our model and its strong generalizability to various free-hand sketches.

Orthogonal Convolutional Neural Networks

The instability and feature redundancy in CNNs hinders further performance improvement. Using orthogonality as a regularizer has shown success in alleviating these issues. Previous works however only considered the kernel orthogonality in the convolution layers of CNNs, which is a necessary but not sufficient condition for orthogonal convolutions in general. We propose orthogonal convolutions as regularizations in CNNs and benchmark its effect on various tasks. We observe up to 3% gain for CIFAR100 and up to 1% gain for ImageNet classification. Our experiments also demonstrate improved performance on image retrieval, inpainting and generation, which suggests orthogonal convolution improves the feature expressiveness. Empirically, we show that the uniform spectrum and reduced feature redundancy may account for the gain in performance and robustness under adversarial attacks.

Learning Coupled Spatial-temporal Attention for Skeleton-based Action Recognition

In this paper, we propose a coupled spatial-temporal attention (CSTA) model for skeleton-based action recognition, which aims to figure out the most discriminative joints and frames in spatial and temporal domains simultaneously. Conventional approaches usually consider all the joints or frames in a skeletal sequence equally important, which are unrobust to ambiguous and redundant information. To address this, we first learn two sets of weights for different joints and frames through two subnetworks respectively, which enable the model to have the ability of "paying attention to" the relatively informative section. Then, we calculate the cross product based on the weights of joints and frames for the coupled spatial-temporal attention. Moreover, our CSTA mechanisms can be easily plugged into existing hierarchical CNN models (CSTA-CNN) to realize their function. Extensive experimental results on the recently collected UESTC dataset and the currently largest NTU dataset have shown the effectiveness of our proposed method for skeleton-based action recognition.