Georgia Tech’s experts and larger research community are invested in a future where artificial intelligence (AI) solutions can benefit individuals and communities across our planet. Meet the four industrial and systems engineers among other maestros on their work at the International Conference on Machine Learning — July 23-29, 2023, in Honolulu — and learn about their work.

### Yao Xie

Sequential Predictive Conformal Inference for Time Series | Chen Xu, Yao Xie

We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the \textit{sequential predictive conformal inference} (\texttt{SPCI}). We specifically account for the nature that time series data are non-exchangeable, and thus many existing conformal prediction algorithms are not applicable. The main idea is to adaptively re-estimate the conditional quantile of non-conformity scores (e.g., prediction residuals), upon exploiting the temporal dependence among them. More precisely, we cast the problem of conformal prediction interval as predicting the quantile of a future residual, given a user-specified point prediction algorithm. Theoretically, we establish asymptotic valid conditional coverage upon extending consistency analyses in quantile regression. Using simulation and real-data experiments, we demonstrate a significant reduction in interval width of \texttt{SPCI} compared to other existing methods under the desired empirical coverage.

### Xiaoming Huo

Conformalization of Sparse Generalized Linear Models | Etash Guha, Eugene Ndiaye, Xiaoming Huo

Given a sequence of observable variables $(x_1, y_1), \ldots, (x_n, y_n)$, the conformal prediction method estimates a confidence set for $y_{n+1}$ given $x_{n+1}$ that is valid for any finite sample size by merely assuming that the distribution is permutation invariant. Although attractive, computing such a set is infeasible in most regression problems. Indeed, in these cases, the unknown variable $y_{n+1}$ can take an infinite number of possible values, and generating conformal sets requires retraining a predictive model for each of them. In this paper, we focus on a sparse model with only a subset of variables for prediction, and we leverage numerical continuation techniques to efficiently approximate the solution path. The key property we exploit is that the set of selected variables is invariant under a small perturbation of the input data. Therefore, it is sufficient to enumerate and refit the model only at the change points of the set of active features and smoothly interpolate the rest of the solution via a predictor-corrector mechanism. We show how our path-following algorithm accurately approximates conformal prediction sets and illustrate its performance using synthetic and real data examples.

### Tuo Zhao

Effective Minkowski Dimension of Deep Nonparametric Regression: Function Approximation and Statistical Theories | Zixuan Zhang, Minshuo Chen, Mengdi Wang, Wenjing Liao, Tuo Zhao

Existing theories on deep nonparametric regression have shown that when the input data lie on a low-dimensional manifold, deep neural networks can adapt to the intrinsic data structures. In real world applications, such an assumption of data lying exactly on a low dimensional manifold is stringent. This paper introduces a relaxed assumption that the input data are concentrated around a subset of $\RR^d$ denoted by $\cS$, and the intrinsic dimension of $\cS$ can be characterized by a new complexity notation — effective Minkowski dimension. We prove that, the sample complexity of deep nonparametric regression only depends on the effective Minkowski dimension of $\cS$ denoted by $p$. We further illustrate our theoretical findings by considering nonparametric regression with an anisotropic Gaussian random design $N(0,\Sigma)$, where $\Sigma$ is full rank. When the eigenvalues of $\Sigma$ have an exponential or polynomial decay, the effective Minkowski dimension of such an Gaussian random design is $p=\cO(\sqrt{\log n})$ or $p=\cO(n^\gamma)$, respectively, where $n$ is the sample size and $\gamma\in(0,1)$ is a small constant depending on the polynomial decay rate. Our theory shows that, when the manifold assumption does not hold, deep neural networks can still adapt to the effective Minkowski dimension of the data, and circumvent the curse of the ambient dimensionality for moderate sample sizes.

Less is More: Task-aware Layer-wise Distillation for Language Model Compression | Chen Liang, Simiao Zuo, Qingru Zhang, Pengcheng He, Weizhu Chen, Tuo Zhao

Layer-wise distillation is a powerful tool to compress large models (i.e. teacher models) into small ones (i.e., student models). The student distills knowledge from the teacher by mimicking the hidden representations of the teacher at every intermediate layer. However, layer-wise distillation is difficult. Since the student has a smaller model capacity than the teacher, it is often under-fitted. Furthermore, the hidden representations of the teacher contain redundant information that the student does not necessarily need for the target task’s learning. To address these challenges, we propose a novel Task-aware layEr-wise Distillation (TED). TED designs task-aware filters to align the hidden representations of the student and the teacher at each layer. The filters select the knowledge that is useful for the target task from the hidden representations. As such, TED reduces the knowledge gap between the two models and helps the student to fit better on the target task. We evaluate TED in two scenarios: continual pre-training and fine-tuning. TED demonstrates significant and consistent improvements over existing distillation methods in both scenarios.

LoSparse: Structured Compression of Large Language Models based on Low-Rank and Sparse Approximation | Yixiao Li, Yifan Yu, Qingru Zhang, Chen Liang, Pengcheng He, Weizhu Chen, Tuo Zhao

Transformer models have achieved remarkable results in various natural language tasks, but they are often prohibitively large, requiring massive memories and computational resources. To re- duce the size and complexity of these models, we propose LoSparse (Low-Rank and Sparse ap- proximation), a novel model compression tech- nique that approximates a weight matrix by the sum of a low-rank matrix and a sparse matrix. Our method combines the advantages of both low- rank approximations and pruning, while avoid- ing their limitations. Low-rank approximation compresses the coherent and expressive parts in neurons, while pruning removes the incoherent and non-expressive parts in neurons. Pruning enhances the diversity of low-rank approxima- tions, and low-rank approximation prevents prun- ing from losing too many expressive neurons. We evaluate our method on natural language under- standing, question answering, and natural lan- guage generation tasks. We show that it signif- icantly outperforms existing compression meth- ods. Our code is publicly available at https: //github.com/yxli2123/LoSparse

Machine Learning Force Fields with Data Cost-Aware Training | Alexander Bukharin, Tianyi Liu, Shengjie Wang, Simiao Zuo, Weihao Gao, Wen Yan, Tuo Zhao

Machine learning force fields (MLFF) have been proposed to accelerate molecular dynamics (MD) simulation, which finds widespread applications in chemistry and biomedical research. Even for the most data-efficient MLFFs, reaching chemical accuracy can require hundreds of frames of force and energy labels generated by expensive quantum mechanical algorithms, which may scale as $O(n^3)$ to $O(n^7)$, with $n$ proportional to the number of basis functions.To address this issue, we propose a multi-stage computational framework — ASTEROID, which lowers the data cost of MLFFs by leveraging a combination of cheap inaccurate data and expensive accurate data. The motivation behind ASTEROID is that inaccurate data, though incurring large bias, can help capture the sophisticated structures of the underlying force field. Therefore, we first train a MLFF model on a large amount of inaccurate training data, employing a bias-aware loss function to prevent the model from overfitting the potential bias of this data. We then fine-tune the obtained model using a small amount of accurate training data, which preserves the knowledge learned from the inaccurate training data while significantly improving the model’s accuracy. Moreover, we propose a variant of ASTEROID based on score matching for the setting where the inaccurate training data are unlabeled. Extensive experiments on MD datasets and downstream tasks validate the efficacy of ASTEROID.Our code and data are available at \url{https://github.com/abukharin3/asteroid}.

Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data | Minshuo Chen, Kaixuan Huang, Tuo Zhao, Mengdi Wang

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Further, the generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution. The convergence rate depends on subspace dimension, implying that diffusion models can circumvent the curse of data ambient dimensionality.

SMURF-THP: Score Matching-based UnceRtainty quantiFication for Transformer Hawkes Process | Zichong Li, Yanbo Xu, Simiao Zuo, Haoming Jiang, Chao Zhang, Tuo Zhao, Hongyuan Zha

Transformer Hawkes process models have shown to be successful in modeling event sequence data. However, most of the existing training methods rely on maximizing the likelihood of event sequences, which involves calculating some intractable integral. Moreover, the existing methods fail to provide uncertainty quantification for model predictions, e.g., confidence interval for the predicted event’s arrival time. To address these issues, we propose SMURF-THP, a score-based method for learning Transformer Hawkes process and quantifying prediction uncertainty. Specifically, SMURF-THP learns the score function of the event’s arrival time based on a score-matching objective that avoids the intractable computation. With such a learnt score function, we can sample the arrival time of events from the predictive distribution. This naturally allows for the quantification of uncertainty by computing confidence intervals over the generated samples. We conduct extensive experiments in both event type prediction and uncertainty quantification on time of arrival. In all the experiments, SMURF-THP outperforms existing likelihood-based methods in confidence calibration while exhibiting comparable prediction accuracy.

### Juba Ziani

Sequential Strategic Screening | Lee Cohen, Saeed Sharifi-Malvajerdi, Kevin Stangl, Ali Vakilian, Juba Ziani

We initiate the study of strategic behavior in screening processes with multiple classifiers. We focus on two contrasting settings: a “conjunctive” setting in which an individual must satisfy all classifiers simultaneously, and a sequential setting in which an individual to succeed must satisfy classifiers one at a time. In other words, we introduce the combination of strategic classification}with screening processes. We show that sequential screening pipelines exhibit new and surprising behavior where individuals can exploit the sequential ordering of the tests to “zig-zag” between classifiers without having to simultaneously satisfy all of them. We demonstrate an individual can obtain a positive outcome using a limited manipulation budget even when far from the intersection of the positive regions of every classifier. Finally, we consider a learner whose goal is to design a sequential screening process that is robust to such manipulations and provide a construction for the learner that optimizes a natural objective.

ICML - ISyE Faculty