Convergence Analysis of the Wasserstein Proximal Algorithm beyond Geodesic Convexity

The proximal algorithm is a powerful tool to minimize nonlinear and nonsmooth functionals in a general metric space. Motivated by the recent progress in studying the training dynamics of the noisy gradient descent algorithm on two-layer neural networks in the mean-field regime, we provide in this paper a simple and self-contained analysis for the convergence of the general-purpose Wasserstein proximal algorithm without assuming geodesic convexity of the objective functional. Under a natural Wasserstein analog of the Euclidean Polyak-{\L}ojasiewicz inequality, we establish that the proximal algorithm achieves an unbiased and linear convergence rate. Our convergence rate improves upon existing rates of the proximal algorithm for solving Wasserstein gradient flows under strong geodesic convexity. We also extend our analysis to the inexact proximal algorithm for geodesically semiconvex objectives. In our numerical experiments, proximal training demonstrates a faster convergence rate than the noisy gradient descent algorithm on mean-field neural networks.

Optimal Transport Barycenter via Nonconvex-Concave Minimax Optimization

The optimal transport barycenter (a.k.a. Wasserstein barycenter) is a fundamental notion of averaging that extends from the Euclidean space to the Wasserstein space of probability distributions. Computation of the unregularized barycenter for discretized probability distributions on point clouds is a challenging task when the domain dimension $d > 1$. Most practical algorithms for approximating the barycenter problem are based on entropic regularization. In this paper, we introduce a nearly linear time $O(m \log{m})$ and linear space complexity $O(m)$ primal-dual algorithm, the Wasserstein-Descent $\dot{\mathbb{H}}^1$-Ascent (WDHA) algorithm, for computing the exact barycenter when the input probability density functions are discretized on an $m$-point grid. The key success of the WDHA algorithm hinges on alternating between two different yet closely related Wasserstein and Sobolev optimization geometries for the primal barycenter and dual Kantorovich potential subproblems. Under reasonable assumptions, we establish the convergence rate and iteration complexity of WDHA to its stationary point when the step size is appropriately chosen. Superior computational efficacy, scalability, and accuracy over the existing Sinkhorn-type algorithms are demonstrated on high-resolution (e.g., $1024 \times 1024$ images) 2D synthetic and real data.

Large Language Model is Secretly a Protein Sequence Optimizer

We consider the protein sequence engineering problem, which aims to find protein sequences with high fitness levels, starting from a given wild-type sequence. Directed evolution has been a dominating paradigm in this field which has an iterative process to generate variants and select via experimental feedback. We demonstrate large language models (LLMs), despite being trained on massive texts, are secretly protein sequence optimizers. With a directed evolutionary method, LLM can perform protein engineering through Pareto and experiment-budget constrained optimization, demonstrating success on both synthetic and experimental fitness landscapes.

MADGEN -- Mass-Spec attends to De Novo Molecular generation

The annotation (assigning structural chemical identities) of MS/MS spectra remains a significant challenge due to the enormous molecular diversity in biological samples and the limited scope of reference databases. Currently, the vast majority of spectral measurements remain in the "dark chemical space" without structural annotations. To improve annotation, we propose MADGEN (Mass-spec Attends to De Novo Molecular GENeration), a scaffold-based method for de novo molecular structure generation guided by mass spectrometry data. MADGEN operates in two stages: scaffold retrieval and spectra-conditioned molecular generation starting with the scaffold. In the first stage, given an MS/MS spectrum, we formulate scaffold retrieval as a ranking problem and employ contrastive learning to align mass spectra with candidate molecular scaffolds. In the second stage, starting from the retrieved scaffold, we employ the MS/MS spectrum to guide an attention-based generative model to generate the final molecule. Our approach constrains the molecular generation search space, reducing its complexity and improving generation accuracy. We evaluate MADGEN on three datasets (NIST23, CANOPUS, and MassSpecGym) and evaluate MADGEN's performance with a predictive scaffold retriever and with an oracle retriever. We demonstrate the effectiveness of using attention to integrate spectral information throughout the generation process to achieve strong results with the oracle retriever.

Graph Generative Pre-trained Transformer

Graph generation is a critical task in numerous domains, including molecular design and social network analysis, due to its ability to model complex relationships and structured data. While most modern graph generative models utilize adjacency matrix representations, this work revisits an alternative approach that represents graphs as sequences of node set and edge set. We advocate for this approach due to its efficient encoding of graphs and propose a novel representation. Based on this representation, we introduce the Graph Generative Pre-trained Transformer (G2PT), an auto-regressive model that learns graph structures via next-token prediction. To further exploit G2PT's capabilities as a general-purpose foundation model, we explore fine-tuning strategies for two downstream applications: goal-oriented generation and graph property prediction. We conduct extensive experiments across multiple datasets. Results indicate that G2PT achieves superior generative performance on both generic graph and molecule datasets. Furthermore, G2PT exhibits strong adaptability and versatility in downstream tasks from molecular design to property prediction.

CompCap: Improving Multimodal Large Language Models with Composite Captions

How well can Multimodal Large Language Models (MLLMs) understand composite images? Composite images (CIs) are synthetic visuals created by merging multiple visual elements, such as charts, posters, or screenshots, rather than being captured directly by a camera. While CIs are prevalent in real-world applications, recent MLLM developments have primarily focused on interpreting natural images (NIs). Our research reveals that current MLLMs face significant challenges in accurately understanding CIs, often struggling to extract information or perform complex reasoning based on these images. We find that existing training data for CIs are mostly formatted for question-answer tasks (e.g., in datasets like ChartQA and ScienceQA), while high-quality image-caption datasets, critical for robust vision-language alignment, are only available for NIs. To bridge this gap, we introduce Composite Captions (CompCap), a flexible framework that leverages Large Language Models (LLMs) and automation tools to synthesize CIs with accurate and detailed captions. Using CompCap, we curate CompCap-118K, a dataset containing 118K image-caption pairs across six CI types. We validate the effectiveness of CompCap-118K by supervised fine-tuning MLLMs of three sizes: xGen-MM-inst.-4B and LLaVA-NeXT-Vicuna-7B/13B. Empirical results show that CompCap-118K significantly enhances MLLMs' understanding of CIs, yielding average gains of 1.7%, 2.0%, and 2.9% across eleven benchmarks, respectively.

Adversarial-Robust Transfer Learning for Medical Imaging via Domain Assimilation

In the field of Medical Imaging, extensive research has been dedicated to leveraging its potential in uncovering critical diagnostic features in patients. Artificial Intelligence (AI)-driven medical diagnosis relies on sophisticated machine learning and deep learning models to analyze, detect, and identify diseases from medical images. Despite the remarkable performance of these models, characterized by high accuracy, they grapple with trustworthiness issues. The introduction of a subtle perturbation to the original image empowers adversaries to manipulate the prediction output, redirecting it to other targeted or untargeted classes. Furthermore, the scarcity of publicly available medical images, constituting a bottleneck for reliable training, has led contemporary algorithms to depend on pretrained models grounded on a large set of natural images -- a practice referred to as transfer learning. However, a significant {\em domain discrepancy} exists between natural and medical images, which causes AI models resulting from transfer learning to exhibit heightened {\em vulnerability} to adversarial attacks. This paper proposes a {\em domain assimilation} approach that introduces texture and color adaptation into transfer learning, followed by a texture preservation component to suppress undesired distortion. We systematically analyze the performance of transfer learning in the face of various adversarial attacks under different data modalities, with the overarching goal of fortifying the model's robustness and security in medical imaging tasks. The results demonstrate high effectiveness in reducing attack efficacy, contributing toward more trustworthy transfer learning in biomedical applications.

Does ChatGPT and Whisper Make Humanoid Robots More Relatable?

Humanoid robots are designed to be relatable to humans for applications such as customer support and helpdesk services. However, many such systems, including Softbank's Pepper, fall short because they fail to communicate effectively with humans. The advent of Large Language Models (LLMs) shows the potential to solve the communication barrier for humanoid robotics. This paper outlines the comparison of different Automatic Speech Recognition (ASR) APIs, the integration of Whisper ASR and ChatGPT with the Pepper robot and the evaluation of the system (Pepper-GPT) tested by 15 human users. The comparison result shows that, compared to the Google ASR and Google Cloud ASR, the Whisper ASR performed best as its average Word Error Rate (1.716%) and processing time (2.639 s) are both the lowest. The participants' usability investigations show that 60% of the participants thought the performance of the Pepper-GPT was "excellent", while the rest rated this system as "good" in the subsequent experiments. It is proved that while some problems still need to be overcome, such as the robot's multilingual ability and facial tracking capacity, users generally responded positively to the system, feeling like talking to an actual human.

Physics-informed Deep Learning to Solve Three-dimensional Terzaghi Consolidation Equation: Forward and Inverse Problems

The emergence of neural networks constrained by physical governing equations has sparked a new trend in deep learning research, which is known as Physics-Informed Neural Networks (PINNs). However, solving high-dimensional problems with PINNs is still a substantial challenge, the space complexity brings difficulty to solving large multidirectional problems. In this paper, a novel PINN framework to quickly predict several three-dimensional Terzaghi consolidation cases under different conditions is proposed. Meanwhile, the loss functions for different cases are introduced, and their differences in three-dimensional consolidation problems are highlighted. The tuning strategies for the PINNs framework for three-dimensional consolidation problems are introduced. Then, the performance of PINNs is tested and compared with traditional numerical methods adopted in forward problems, and the coefficients of consolidation and the impact of noisy data in inverse problems are identified. Finally, the results are summarized and presented from three-dimensional simulations of PINNs, which show an accuracy rate of over 99% compared with ground truth for both forward and inverse problems. These results are desirable with good accuracy and can be used for soil settlement prediction, which demonstrates that the proposed PINNs framework can learn the three-dimensional consolidation PDE well. Keywords: Three-dimensional Terzaghi consolidation; Physics-informed neural networks (PINNs); Forward problems; Inverse problems; soil settlement

A dynamic interactive learning framework for automated 3D medical image segmentation

Many deep learning based automated medical image segmentation systems, in reality, face difficulties in deployment due to the cost of massive data annotation and high latency in model iteration. We propose a dynamic interactive learning framework that addresses these challenges by integrating interactive segmentation into end-to-end weak supervised learning with streaming tasks. We develop novel replay and label smoothing schemes that overcome catastrophic forgetting and improve online learning robustness. For each image, our multi-round interactive segmentation module simultaneously optimizes both front-end predictions and deep learning segmenter. In each round, a 3D "proxy mask" is propagated from sparse user inputs based on image registration, serving as weak supervision that enable knowledge distillation from the unknown ground truth. In return, the trained segmenter explicitly guides next step's user interventions according to a spatial residual map from consecutive front or back-end predictions. Evaluation on 3D segmentation tasks (NCI-ISBI2013 and BraTS2015) shows that our framework generates online learning performances that match offline training benchmark. In addition, with a 62% reduction in total annotation efforts, our framework produces competitive dice scores comparing to online and offline learning which equipped with full ground truth. Furthermore, such a framework, with its flexibility and responsiveness, could be deployed behind hospital firewall that guarantees data security and easy maintenance.