Lead Author Spotlight | ICLR 2022

Schrödinger Bridge (SB) is an entropy-regularized optimal transport problem that has received increasing attention in deep generative modeling for its mathematical flexibility compared to the Scored-based Generative Model (SGM). In this work, we present a novel computational framework for likelihood training of SB models grounded on Forward-Backward Stochastic Differential Equations Theory.

In this work, I collaborate with Guan (who is co-author of this paper) closely to pressure the ICLR in around four months. Accomplishing this work in such a short time is not an easy task, so I have to learn to communicate and collaborate efficiently.

Our findings provide new theoretical insights by generalizing previous theoretical results for Score-based Generative Model and facilitate applications of modern generative training for SB. We validate our method on various image generative tasks, e.g. MNIST, CelebA, and CIFAR10, showing encouraging results in synthesizing high-fidelity samples while retaining the rigorous mathematical framework.

Life can only be understood going backward, but it must be lived going forward.

My paper is about how to use deep learning to learn algorithms for solving sparse estimation problems. It falls into the category of learning to learn. What’s new in the paper includes a more generic method that can be applied to more general settings and novel theoretical guarantees for such methods.

This is interdisciplinary research that covers topics in both statistics, optimization, and deep learning. It allows me to learn more about optimization theory and learning theory as we derived the theoretical results in this work.

• How to learn algorithms for solving various sparse estimation problems?
• How to understand the behaviors of these learning-based algorithms?
• How are the generalization and representation abilities of these learning-based algorithms related to their algorithmic properties such as convergence rate?”

What is the biggest regret?

Our paper focuses on integrating cognitive k-level hierarchy theory — which is how humans deeply reason about decisions in real-world settings — into multi-agent reinforcement learning. We mathematically show that our k-level algorithm, InfoPG, encourages collaboration between agents, and empirically, we demonstrate this leads to better performance relative to standard baselines.

This work helped me grow my collaboration skills because in order to communicate my mathematical formulations or algorithmic ideas, I had to learn how to dissect content and present the main ideas. This skill developed during weekly meetings with my advisor Professor Gombolay and Ph.D. student, Esmaeil Seraj.

Our work provides a key connection between two independently researched ideas in Multi-Agent RL: Mutual Information Maximization and K-Level Cognitive Hierarchy Theory. We mathematically show that by equipping each agent with a k-level policy, we can implicitly increase mutual information with other agents’ policies, which is something that previous works could only perform explicitly.

I would want advice on whether industry or academia is the best place to continue researching.

Most Adagrad/Adam variants struggle to achieve provable benefits in nonconvex settings, despite the fact that they demonstrate superior performances compared to SGD especially for learning quality embedding vectors in modern NLP/recommendation systems. It seems that the fancy updates of these adaptive methods create nontrivial challenges in terms of algorithmic analysis.

The FA-SGD we propose can be viewed as a simplified variant of these adaptive methods. It comes with great empirical performances – with almost no memory overhead compared to Adagrad/Adam – while achieving on par or even better model performance. Better yet, it is the first method that shows provable benefits over SGD to date.

From the development process of FA-SGD, the biggest personal takeaway as a junior researcher is to approach the current understanding/development/status of the current ML methods with not only appreciation, but more importantly, with a critical mindset. By doing so, I often find new understandings/perspectives can arise which sometimes leads to new methods.

The simple intuition behind FA-SGD — adjusting the learning rate of each token depending on their occurrence frequency — is something we would really like to highlight. When proposing new optimization methods for representation learning, one might consider exploiting the problem structure first, which can lead to methods with algorithmic simplicity, intuitive updates, and favorable theoretical properties.

I am still working on developing my career as a junior researcher 🙂

Recent research has shown the existence of significant redundancy in large Transformer models. One can prune the redundant parameters without significantly sacrificing the generalization performance. However, we question whether the redundant parameters could have contributed more if they were properly trained. To answer this question, we propose a novel training strategy that encourages all parameters to be trained sufficiently. Specifically, we adaptively adjust the learning rate for each parameter according to its sensitivity, a robust gradient-based measure reflecting this parameter’s contribution to the model performance. A parameter with low sensitivity is redundant, and we improve its fitting by increasing its learning rate. In contrast, a parameter with high sensitivity is well-trained, and we regularize it by decreasing its learning rate to prevent further overfitting.

I worked on developing parameter-efficient large neural models from a novel perspective. Instead of pruning redundant parameters, we train them sufficiently so that they also contribute to the model performance. Such a new perspective gives me inspiration for future research.

• There exists a significant number of redundant parameters in large Transformer models, which can hurt the model generalization performance.
• We propose a novel training strategy, SAGE, which encourages all parameters to receive sufficient training and become useful ultimately.
• SAGE adaptively adjusts the learning rate for each parameter based on its sensitivity, a gradient-based measure reflecting this parameter’s contribution to the model performance.
• A parameter with low sensitivity is redundant and we improve its fitting by increasing its learning rate. A parameter with high sensitivity is well-trained and we regularize it by decreasing its learning rate.
• SAGE significantly improves model generalization for both NLP and CV tasks and in both fine-tuning and training-from-scratch settings.

Career advice: What is the best decision you have made in the workplace?
Personal advice: How to better manage work-life balance?

A prediction set is a promising way to quantify the uncertainty of predictions with some correctness guarantee; under the i.i.d. assumption, a prediction set can be constructed with the probably approximately correct (PAC) guarantee, but the guarantee violates under covariate shift. We provide an algorithm that returns a prediction set with PAC guarantee even in covariate shift under some smoothness conditions on distributions.

This work forces me to understand and correctly use rigorous mathematical tools to provides the end-to-end correctness guarantee.

You can construct a prediction set with correctness guarantee even under covariate shift if you’re using our tool (for sure it works under some assumption).

Fill out this form carefully to sell your work!

We study the generalization of overparameterized deep feedforward neural network with ReLU activation under non-parametric statistical setting wherein the labels are generated using a ground truth function, which is assumed to be in the RKHS associated with the NTK, perturbed with noise. We find out that gradient-descent based training without early stopping fails whereas L2-regularized gradient descent achieves minimax optimal convergence rate of L2 prediction risk.

While working on this project, I read many papers on deep learning from the statistical viewpoint. This helps me to deepen my understandings both on theoretical analysis on deep neural network and on non-parametric regression problem in statistics.

The linearized deep feedforward neural network via over-parametrization behaves similarly with kernel regression method in terms of generalization, and the adoption of early-stopping or regularization can help the generalization.

Keep up the hard work!

Our paper studies the effect of large learning rate on solving matrix factorization problem that helps gradient descent find the minimum with better curvature. Especially when the learning rate is larger than the typical upper bound 2/L (can be at most approximately 4/L), gradient descent is proved to converge to a flatter global minimum.

Instead of abstract mathematical theories, this work is a demonstration of a novel phenomenon that draws much attention in real world applications. It’s inspiring to at least partly bridge the gap between rigorous math and the practice.

Large learning rate is theoretically proven to help search for better minimum.

• Be 100 percent sure that you believe in what you will be doing before proceeding.
• Don’t judge. Just calculate.

We present Path Integral Sampler~(PIS), a novel algorithm to draw samples from unnormalized probability density functions. The PIS is built on the Schrödinger bridge problem which aims to recover the most likely evolution of a diffusion process given its initial distribution and terminal distribution.

Sometimes thinking out of the box and good ideas just work.

A non-MCMC sampling algorithm with guaranteed performance.

Multidisciplinary has lots of opportunities.

Self- and mutually-exciting point processes are popular models in machine learning and statistics for dependent discrete event data. In this paper, we devise a non-stationary influence kernel in the point process model to capture more complex spatio-temporal dependence while providing theoretical performance guarantees.

In this study, we collaborate with researchers and students extensively and bring their expertise together to make things happen.

In this work, the kernel function is represented by a spectral decomposition of the influence kernel with a finite-rank truncation in practice. Such a kernel representation will enable us to capture the most general non-stationary process as well as high-dimensional marks. The model also allows the distribution of marks to depend on time, which is drastically different from the separable kernels considered in the existing literature.

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