Understanding the Expressive Power and Mechanisms of Transformer for Sequence Modeling

We conduct a systematic study of the approximation properties of Transformer for sequence modeling with long, sparse and complicated memory. We investigate the mechanisms through which different components of Transformer, such as the dot-product self-attention, positional encoding and feed-forward layer, affect its expressive power, and we study their combined effects through establishing explicit approximation rates. Our study reveals the roles of critical parameters in the Transformer, such as the number of layers and the number of attention heads, and these insights also provide natural suggestions for alternative architectures.

Anchor function: a type of benchmark functions for studying language models

Understanding transformer-based language models is becoming increasingly crucial, particularly as they play pivotal roles in advancing towards artificial general intelligence. However, language model research faces significant challenges, especially for academic research groups with constrained resources. These challenges include complex data structures, unknown target functions, high computational costs and memory requirements, and a lack of interpretability in the inference process, etc. Drawing a parallel to the use of simple models in scientific research, we propose the concept of an anchor function. This is a type of benchmark function designed for studying language models in learning tasks that follow an "anchor-key" pattern. By utilizing the concept of an anchor function, we can construct a series of functions to simulate various language tasks. The anchor function plays a role analogous to that of mice in diabetes research, particularly suitable for academic research. We demonstrate the utility of the anchor function with an example, revealing two basic operations by attention structures in language models: shifting tokens and broadcasting one token from one position to many positions. These operations are also commonly observed in large language models. The anchor function framework, therefore, opens up a series of valuable and accessible research questions for further exploration, especially for theoretical study.

Learning Free Terminal Time Optimal Closed-loop Control of Manipulators

This paper presents a novel approach to learning free terminal time closed-loop control for robotic manipulation tasks, enabling dynamic adjustment of task duration and control inputs to enhance performance. We extend the supervised learning approach, namely solving selected optimal open-loop problems and utilizing them as training data for a policy network, to the free terminal time scenario. Three main challenges are addressed in this extension. First, we introduce a marching scheme that enhances the solution quality and increases the success rate of the open-loop solver by gradually refining time discretization. Second, we extend the QRnet in Nakamura-Zimmerer et al. (2021b) to the free terminal time setting to address discontinuity and improve stability at the terminal state. Third, we present a more automated version of the initial value problem (IVP) enhanced sampling method from previous work (Zhang et al., 2022) to adaptively update the training dataset, significantly improving its quality. By integrating these techniques, we develop a closed-loop policy that operates effectively over a broad domain with varying optimal time durations, achieving near globally optimal total costs.

Machine-Learned Invertible Coarse Graining for Multiscale Molecular Modeling

Multiscale molecular modeling is widely applied in scientific research of molecular properties over large time and length scales. Two specific challenges are commonly present in multiscale modeling, provided that information between the coarse and fine representations of molecules needs to be properly exchanged: One is to construct coarse grained (CG) models by passing information from the fine to coarse levels; the other is to restore finer molecular details given CG configurations. Although these two problems are commonly addressed independently, in this work, we present a theory connecting them, and develop a methodology called Cycle Coarse Graining (CCG) to solve both problems in a unified manner. In CCG, reconstruction can be achieved via a tractable optimization process, leading to a general method to retrieve fine details from CG simulations, which in turn, delivers a new solution to the CG problem, yielding an efficient way to calculate free energies in a rare-event-free manner. CCG thus provides a systematic way for multiscale molecular modeling, where the finer details of CG simulations can be efficiently retrieved, and the CG models can be improved consistently.

MAC: A unified framework boosting low resource automatic speech recognition

We propose a unified framework for low resource automatic speech recognition tasks named meta audio concatenation (MAC). It is easy to implement and can be carried out in extremely low resource environments. Mathematically, we give a clear description of MAC framework from the perspective of bayesian sampling. In this framework, we leverage a novel concatenative synthesis text-to-speech system to boost the low resource ASR task. By the concatenative synthesis text-to-speech system, we can integrate language pronunciation rules and adjust the TTS process. Furthermore, we propose a broad notion of meta audio set to meet the modeling needs of different languages and different scenes when using the system. Extensive experiments have demonstrated the great effectiveness of MAC on low resource ASR tasks. For CTC greedy search, CTC prefix, attention, and attention rescoring decode mode in Cantonese ASR task, Taiwanese ASR task, and Japanese ASR task the MAC method can reduce the CER by more than 15\%. Furthermore, in the ASR task, MAC beats wav2vec2 (with fine-tuning) on common voice datasets of Cantonese and gets really competitive results on common voice datasets of Taiwanese and Japanese. Among them, it is worth mentioning that we achieve a \textbf{10.9\%} character error rate (CER) on the common voice Cantonese ASR task, bringing about \textbf{30\%} relative improvement compared to the wav2vec2 (with fine-tuning).

PAMP: A unified framework boosting low resource automatic speech recognition

We propose a novel text-to-speech (TTS) data augmentation framework for low resource automatic speech recognition (ASR) tasks, named phoneme audio mix up (PAMP). The PAMP method is highly interpretable and can incorporate prior knowledge of pronunciation rules. Furthermore, PAMP can be easily deployed in almost any language, extremely for low resource ASR tasks. Extensive experiments have demonstrated the great effectiveness of PAMP on low resource ASR tasks: we achieve a \textbf{10.84\%} character error rate (CER) on the common voice Cantonese ASR task, bringing a great relative improvement of about \textbf{30\%} compared to the previous state-of-the-art which was achieved by fine-tuning the wav2vec2 pretrained model.

A multi-scale sampling method for accurate and robust deep neural network to predict combustion chemical kinetics

Machine learning has long been considered as a black box for predicting combustion chemical kinetics due to the extremely large number of parameters and the lack of evaluation standards and reproducibility. The current work aims to understand two basic questions regarding the deep neural network (DNN) method: what data the DNN needs and how general the DNN method can be. Sampling and preprocessing determine the DNN training dataset, further affect DNN prediction ability. The current work proposes using Box-Cox transformation (BCT) to preprocess the combustion data. In addition, this work compares different sampling methods with or without preprocessing, including the Monte Carlo method, manifold sampling, generative neural network method (cycle-GAN), and newly-proposed multi-scale sampling. Our results reveal that the DNN trained by the manifold data can capture the chemical kinetics in limited configurations but cannot remain robust toward perturbation, which is inevitable for the DNN coupled with the flow field. The Monte Carlo and cycle-GAN samplings can cover a wider phase space but fail to capture small-scale intermediate species, producing poor prediction results. A three-hidden-layer DNN, based on the multi-scale method without specific flame simulation data, allows predicting chemical kinetics in various scenarios and being stable during the temporal evolutions. This single DNN is readily implemented with several CFD codes and validated in various combustors, including (1). zero-dimensional autoignition, (2). one-dimensional freely propagating flame, (3). two-dimensional jet flame with triple-flame structure, and (4). three-dimensional turbulent lifted flames. The results demonstrate the satisfying accuracy and generalization ability of the pre-trained DNN. The Fortran and Python versions of DNN and example code are attached in the supplementary for reproducibility.

A deep learning-based model reduction (DeePMR) method for simplifying chemical kinetics

A deep learning-based model reduction (DeePMR) method for simplifying chemical kinetics is proposed and validated using high-temperature auto-ignitions, perfectly stirred reactors (PSR), and one-dimensional freely propagating flames of n-heptane/air mixtures. The mechanism reduction is modeled as an optimization problem on Boolean space, where a Boolean vector, each entry corresponding to a species, represents a reduced mechanism. The optimization goal is to minimize the reduced mechanism size given the error tolerance of a group of pre-selected benchmark quantities. The key idea of the DeePMR is to employ a deep neural network (DNN) to formulate the objective function in the optimization problem. In order to explore high dimensional Boolean space efficiently, an iterative DNN-assisted data sampling and DNN training procedure are implemented. The results show that DNN-assistance improves sampling efficiency significantly, selecting only $10^5$ samples out of $10^{34}$ possible samples for DNN to achieve sufficient accuracy. The results demonstrate the capability of the DNN to recognize key species and reasonably predict reduced mechanism performance. The well-trained DNN guarantees the optimal reduced mechanism by solving an inverse optimization problem. By comparing ignition delay times, laminar flame speeds, temperatures in PSRs, the resulting skeletal mechanism has fewer species (45 species) but the same level of accuracy as the skeletal mechanism (56 species) obtained by the Path Flux Analysis (PFA) method. In addition, the skeletal mechanism can be further reduced to 28 species if only considering atmospheric, near-stoichiometric conditions (equivalence ratio between 0.6 and 1.2). The DeePMR provides an innovative way to perform model reduction and demonstrates the great potential of data-driven methods in the combustion area.

DeePN$^2$: A deep learning-based non-Newtonian hydrodynamic model

A long standing problem in the modeling of non-Newtonian hydrodynamics is the availability of reliable and interpretable hydrodynamic models that faithfully encode the underlying micro-scale polymer dynamics. The main complication arises from the long polymer relaxation time, the complex molecular structure, and heterogeneous interaction. DeePN$^2$, a deep learning-based non-Newtonian hydrodynamic model, has been proposed and has shown some success in systematically passing the micro-scale structural mechanics information to the macro-scale hydrodynamics for suspensions with simple polymer conformation and bond potential. The model retains a multi-scaled nature by mapping the polymer configurations into a set of symmetry-preserving macro-scale features. The extended constitutive laws for these macro-scale features can be directly learned from the kinetics of their micro-scale counterparts. In this paper, we carry out further study of DeePN$^2$ using more complex micro-structural models. We show that DeePN$^2$ can faithfully capture the broadly overlooked viscoelastic differences arising from the specific molecular structural mechanics without human intervention.