GCN-DevLSTM: Path Development for Skeleton-Based Action Recognition

Skeleton-based action recognition (SAR) in videos is an important but challenging task in computer vision. The recent state-of-the-art models for SAR are primarily based on graph convolutional neural networks (GCNs), which are powerful in extracting the spatial information of skeleton data. However, it is yet clear that such GCN-based models can effectively capture the temporal dynamics of human action sequences. To this end, we propose the DevLSTM module, which exploits the path development -- a principled and parsimonious representation for sequential data by leveraging the Lie group structure. The path development, originated from Rough path theory, can effectively capture the order of events in high-dimensional stream data with massive dimension reduction and consequently enhance the LSTM module substantially. Our proposed G-DevLSTM module can be conveniently plugged into the temporal graph, complementing existing advanced GCN-based models. Our empirical studies on the NTU60, NTU120 and Chalearn2013 datasets demonstrate that our proposed hybrid model significantly outperforms the current best-performing methods in SAR tasks. The code is available at https://github.com/DeepIntoStreams/GCN-DevLSTM.

Part-Aware Transformer for Generalizable Person Re-identification

Domain generalization person re-identification (DG-ReID) aims to train a model on source domains and generalize well on unseen domains. Vision Transformer usually yields better generalization ability than common CNN networks under distribution shifts. However, Transformer-based ReID models inevitably over-fit to domain-specific biases due to the supervised learning strategy on the source domain. We observe that while the global images of different IDs should have different features, their similar local parts (e.g., black backpack) are not bounded by this constraint. Motivated by this, we propose a pure Transformer model (termed Part-aware Transformer) for DG-ReID by designing a proxy task, named Cross-ID Similarity Learning (CSL), to mine local visual information shared by different IDs. This proxy task allows the model to learn generic features because it only cares about the visual similarity of the parts regardless of the ID labels, thus alleviating the side effect of domain-specific biases. Based on the local similarity obtained in CSL, a Part-guided Self-Distillation (PSD) is proposed to further improve the generalization of global features. Our method achieves state-of-the-art performance under most DG ReID settings. Under the Market$\to$Duke setting, our method exceeds state-of-the-art by 10.9% and 12.8% in Rank1 and mAP, respectively. The code is available at https://github.com/liyuke65535/Part-Aware-Transformer.

Generative Modelling of Lévy Area for High Order SDE Simulation

It is well known that, when numerically simulating solutions to SDEs, achieving a strong convergence rate better than O(\sqrt{h}) (where h is the step size) requires the use of certain iterated integrals of Brownian motion, commonly referred to as its "L\'{e}vy areas". However, these stochastic integrals are difficult to simulate due to their non-Gaussian nature and for a d-dimensional Brownian motion with d > 2, no fast almost-exact sampling algorithm is known. In this paper, we propose L\'{e}vyGAN, a deep-learning-based model for generating approximate samples of L\'{e}vy area conditional on a Brownian increment. Due to our "Bridge-flipping" operation, the output samples match all joint and conditional odd moments exactly. Our generator employs a tailored GNN-inspired architecture, which enforces the correct dependency structure between the output distribution and the conditioning variable. Furthermore, we incorporate a mathematically principled characteristic-function based discriminator. Lastly, we introduce a novel training mechanism termed "Chen-training", which circumvents the need for expensive-to-generate training data-sets. This new training procedure is underpinned by our two main theoretical results. For 4-dimensional Brownian motion, we show that L\'{e}vyGAN exhibits state-of-the-art performance across several metrics which measure both the joint and marginal distributions. We conclude with a numerical experiment on the log-Heston model, a popular SDE in mathematical finance, demonstrating that high-quality synthetic L\'{e}vy area can lead to high order weak convergence and variance reduction when using multilevel Monte Carlo (MLMC).

Minimally-Supervised Speech Synthesis with Conditional Diffusion Model and Language Model: A Comparative Study of Semantic Coding

Recently, there has been a growing interest in text-to-speech (TTS) methods that can be trained with minimal supervision by combining two types of discrete speech representations and using two sequence-to-sequence tasks to decouple TTS. To address the challenges associated with high dimensionality and waveform distortion in discrete representations, we propose Diff-LM-Speech, which models semantic embeddings into mel-spectrogram based on diffusion models and introduces a prompt encoder structure based on variational autoencoders and prosody bottlenecks to improve prompt representation capabilities. Autoregressive language models often suffer from missing and repeated words, while non-autoregressive frameworks face expression averaging problems due to duration prediction models. To address these issues, we propose Tetra-Diff-Speech, which designs a duration diffusion model to achieve diverse prosodic expressions. While we expect the information content of semantic coding to be between that of text and acoustic coding, existing models extract semantic coding with a lot of redundant information and dimensionality explosion. To verify that semantic coding is not necessary, we propose Tri-Diff-Speech. Experimental results show that our proposed methods outperform baseline methods. We provide a website with audio samples.

A Neural RDE-based model for solving path-dependent PDEs

The concept of the path-dependent partial differential equation (PPDE) was first introduced in the context of path-dependent derivatives in financial markets. Its semilinear form was later identified as a non-Markovian backward stochastic differential equation (BSDE). Compared to the classical PDE, the solution of a PPDE involves an infinite-dimensional spatial variable, making it challenging to approximate, if not impossible. In this paper, we propose a neural rough differential equation (NRDE)-based model to learn PPDEs, which effectively encodes the path information through the log-signature feature while capturing the fundamental dynamics. The proposed continuous-time model for the PPDE solution offers the benefits of efficient memory usage and the ability to scale with dimensionality. Several numerical experiments, provided to validate the performance of the proposed model in comparison to the strong baseline in the literature, are used to demonstrate its effectiveness.

PCF-GAN: generating sequential data via the characteristic function of measures on the path space

Generating high-fidelity time series data using generative adversarial networks (GANs) remains a challenging task, as it is difficult to capture the temporal dependence of joint probability distributions induced by time-series data. Towards this goal, a key step is the development of an effective discriminator to distinguish between time series distributions. We propose the so-called PCF-GAN, a novel GAN that incorporates the path characteristic function (PCF) as the principled representation of time series distribution into the discriminator to enhance its generative performance. On the one hand, we establish theoretical foundations of the PCF distance by proving its characteristicity, boundedness, differentiability with respect to generator parameters, and weak continuity, which ensure the stability and feasibility of training the PCF-GAN. On the other hand, we design efficient initialisation and optimisation schemes for PCFs to strengthen the discriminative power and accelerate training efficiency. To further boost the capabilities of complex time series generation, we integrate the auto-encoder structure via sequential embedding into the PCF-GAN, which provides additional reconstruction functionality. Extensive numerical experiments on various datasets demonstrate the consistently superior performance of PCF-GAN over state-of-the-art baselines, in both generation and reconstruction quality. Code is available at https://github.com/DeepIntoStreams/PCF-GAN.

NODE-ImgNet: a PDE-informed effective and robust model for image denoising

Inspired by the traditional partial differential equation (PDE) approach for image denoising, we propose a novel neural network architecture, referred as NODE-ImgNet, that combines neural ordinary differential equations (NODEs) with convolutional neural network (CNN) blocks. NODE-ImgNet is intrinsically a PDE model, where the dynamic system is learned implicitly without the explicit specification of the PDE. This naturally circumvents the typical issues associated with introducing artifacts during the learning process. By invoking such a NODE structure, which can also be viewed as a continuous variant of a residual network (ResNet) and inherits its advantage in image denoising, our model achieves enhanced accuracy and parameter efficiency. In particular, our model exhibits consistent effectiveness in different scenarios, including denoising gray and color images perturbed by Gaussian noise, as well as real-noisy images, and demonstrates superiority in learning from small image datasets.

Beating the Best: Improving on AlphaFold2 at Protein Structure Prediction

The goal of Protein Structure Prediction (PSP) problem is to predict a protein's 3D structure (confirmation) from its amino acid sequence. The problem has been a 'holy grail' of science since the Noble prize-winning work of Anfinsen demonstrated that protein conformation was determined by sequence. A recent and important step towards this goal was the development of AlphaFold2, currently the best PSP method. AlphaFold2 is probably the highest profile application of AI to science. Both AlphaFold2 and RoseTTAFold (another impressive PSP method) have been published and placed in the public domain (code & models). Stacking is a form of ensemble machine learning ML in which multiple baseline models are first learnt, then a meta-model is learnt using the outputs of the baseline level model to form a model that outperforms the base models. Stacking has been successful in many applications. We developed the ARStack PSP method by stacking AlphaFold2 and RoseTTAFold. ARStack significantly outperforms AlphaFold2. We rigorously demonstrate this using two sets of non-homologous proteins, and a test set of protein structures published after that of AlphaFold2 and RoseTTAFold. As more high quality prediction methods are published it is likely that ensemble methods will increasingly outperform any single method.

Parameter-Efficient Conformers via Sharing Sparsely-Gated Experts for End-to-End Speech Recognition

While transformers and their variant conformers show promising performance in speech recognition, the parameterized property leads to much memory cost during training and inference. Some works use cross-layer weight-sharing to reduce the parameters of the model. However, the inevitable loss of capacity harms the model performance. To address this issue, this paper proposes a parameter-efficient conformer via sharing sparsely-gated experts. Specifically, we use sparsely-gated mixture-of-experts (MoE) to extend the capacity of a conformer block without increasing computation. Then, the parameters of the grouped conformer blocks are shared so that the number of parameters is reduced. Next, to ensure the shared blocks with the flexibility of adapting representations at different levels, we design the MoE routers and normalization individually. Moreover, we use knowledge distillation to further improve the performance. Experimental results show that the proposed model achieves competitive performance with 1/3 of the parameters of the encoder, compared with the full-parameter model.

Path Development Network with Finite-dimensional Lie Group Representation

The path signature, a mathematically principled and universal feature of sequential data, leads to a performance boost of deep learning-based models in various sequential data tasks as a complimentary feature. However, it suffers from the curse of dimensionality when the path dimension is high. To tackle this problem, we propose a novel, trainable path development layer, which exploits representations of sequential data with the help of finite-dimensional matrix Lie groups. We also design the backpropagation algorithm of the development layer via an optimisation method on manifolds known as trivialisation. Numerical experiments demonstrate that the path development consistently and significantly outperforms, in terms of accuracy and dimensionality, signature features on several empirical datasets. Moreover, stacking the LSTM with the development layer with a suitable matrix Lie group is empirically proven to alleviate the gradient issues of LSTMs and the resulting hybrid model achieves the state-of-the-art performance.