Lei Wu

Yuhao Mo, Chu Han, Yu Liu et al. · pku

Ultrasonography is an important routine examination for breast cancer diagnosis, due to its non-invasive, radiation-free and low-cost properties. However, the diagnostic accuracy of breast cancer is still limited due to its inherent limitations. It would be a tremendous success if we can precisely diagnose breast cancer by breast ultrasound images (BUS). Many learning-based computer-aided diagnostic methods have been proposed to achieve breast cancer diagnosis/lesion classification. However, most of them require a pre-define ROI and then classify the lesion inside the ROI. Conventional classification backbones, such as VGG16 and ResNet50, can achieve promising classification results with no ROI requirement. But these models lack interpretability, thus restricting their use in clinical practice. In this study, we propose a novel ROI-free model for breast cancer diagnosis in ultrasound images with interpretable feature representations. We leverage the anatomical prior knowledge that malignant and benign tumors have different spatial relationships between different tissue layers, and propose a HoVer-Transformer to formulate this prior knowledge. The proposed HoVer-Trans block extracts the inter- and intra-layer spatial information horizontally and vertically. We conduct and release an open dataset GDPH&SYSUCC for breast cancer diagnosis in BUS. The proposed model is evaluated in three datasets by comparing with four CNN-based models and two vision transformer models via five-fold cross validation. It achieves state-of-the-art classification performance with the best model interpretability. In the meanwhile, our proposed model outperforms two senior sonographers on the breast cancer diagnosis when only one BUS image is given.

Yiqi Zhong, Lei Wu, Xianming Liu et al.

Robustness of deep neural networks (DNNs) to malicious perturbations is a hot topic in trustworthy AI. Existing techniques obtain robust models given fixed datasets, either by modifying model structures, or by optimizing the process of inference or training. While significant improvements have been made, the possibility of constructing a high-quality dataset for model robustness remain unexplored. Follow the campaign of data-centric AI launched by Andrew Ng, we propose a novel algorithm for dataset enhancement that works well for many existing DNN models to improve robustness. Transferable adversarial examples and 14 kinds of common corruptions are included in our optimized dataset. In the data-centric robust learning competition hosted by Alibaba Group and Tsinghua University, our algorithm came third out of more than 3000 competitors in the first stage while we ranked fourth in the second stage. Our code is available at \url{https://github.com/hncszyq/tianchi_challenge}.

Chao Ma, Daniel Kunin, Lei Wu et al.

A quadratic approximation of neural network loss landscapes has been extensively used to study the optimization process of these networks. Though, it usually holds in a very small neighborhood of the minimum, it cannot explain many phenomena observed during the optimization process. In this work, we study the structure of neural network loss functions and its implication on optimization in a region beyond the reach of a good quadratic approximation. Numerically, we observe that neural network loss functions possesses a multiscale structure, manifested in two ways: (1) in a neighborhood of minima, the loss mixes a continuum of scales and grows subquadratically, and (2) in a larger region, the loss shows several separate scales clearly. Using the subquadratic growth, we are able to explain the Edge of Stability phenomenon [5] observed for the gradient descent (GD) method. Using the separate scales, we explain the working mechanism of learning rate decay by simple examples. Finally, we study the origin of the multiscale structure and propose that the non-convexity of the models and the non-uniformity of training data is one of the causes. By constructing a two-layer neural network problem we show that training data with different magnitudes give rise to different scales of the loss function, producing subquadratic growth and multiple separate scales.

Lei Wu, Mingze Wang, Weijie Su

The phenomenon that stochastic gradient descent (SGD) favors flat minima has played a critical role in understanding the implicit regularization of SGD. In this paper, we provide an explanation of this striking phenomenon by relating the particular noise structure of SGD to its \emph{linear stability} (Wu et al., 2018). Specifically, we consider training over-parameterized models with square loss. We prove that if a global minimum $θ^*$ is linearly stable for SGD, then it must satisfy $\|H(θ^*)\|_F\leq O(\sqrt{B}/η)$, where $\|H(θ^*)\|_F, B,η$ denote the Frobenius norm of Hessian at $θ^*$, batch size, and learning rate, respectively. Otherwise, SGD will escape from that minimum \emph{exponentially} fast. Hence, for minima accessible to SGD, the sharpness -- as measured by the Frobenius norm of the Hessian -- is bounded \emph{independently} of the model size and sample size. The key to obtaining these results is exploiting the particular structure of SGD noise: The noise concentrates in sharp directions of local landscape and the magnitude is proportional to loss value. This alignment property of SGD noise provably holds for linear networks and random feature models (RFMs), and is empirically verified for nonlinear networks. Moreover, the validity and practical relevance of our theoretical findings are also justified by extensive experiments on CIFAR-10 dataset.

Alex Fedorov, Eloy Geenjaar, Lei Wu et al.

Recent neuroimaging studies that focus on predicting brain disorders via modern machine learning approaches commonly include a single modality and rely on supervised over-parameterized models.However, a single modality provides only a limited view of the highly complex brain. Critically, supervised models in clinical settings lack accurate diagnostic labels for training. Coarse labels do not capture the long-tailed spectrum of brain disorder phenotypes, which leads to a loss of generalizability of the model that makes them less useful in diagnostic settings. This work presents a novel multi-scale coordinated framework for learning multiple representations from multimodal neuroimaging data. We propose a general taxonomy of informative inductive biases to capture unique and joint information in multimodal self-supervised fusion. The taxonomy forms a family of decoder-free models with reduced computational complexity and a propensity to capture multi-scale relationships between local and global representations of the multimodal inputs. We conduct a comprehensive evaluation of the taxonomy using functional and structural magnetic resonance imaging (MRI) data across a spectrum of Alzheimer's disease phenotypes and show that self-supervised models reveal disorder-relevant brain regions and multimodal links without access to the labels during pre-training. The proposed multimodal self-supervised learning yields representations with improved classification performance for both modalities. The concomitant rich and flexible unsupervised deep learning framework captures complex multimodal relationships and provides predictive performance that meets or exceeds that of a more narrow supervised classification analysis. We present elaborate quantitative evidence of how this framework can significantly advance our search for missing links in complex brain disorders.

Xiaolei Diao, Daqian Shi, Hao Tang et al.

The long-tail effect is a common issue that limits the performance of deep learning models on real-world datasets. Character image datasets are also affected by such unbalanced data distribution due to differences in character usage frequency. Thus, current character recognition methods are limited when applied in the real world, especially for the categories in the tail that lack training samples, e.g., uncommon characters. In this paper, we propose a zero-shot character recognition framework via radical-based reasoning, called RZCR, to improve the recognition performance of few-sample character categories in the tail. Specifically, we exploit radicals, the graphical units of characters, by decomposing and reconstructing characters according to orthography. RZCR consists of a visual semantic fusion-based radical information extractor (RIE) and a knowledge graph character reasoner (KGR). RIE aims to recognize candidate radicals and their possible structural relations from character images in parallel. The results are then fed into KGR to recognize the target character by reasoning with a knowledge graph. We validate our method on multiple datasets, and RZCR shows promising experimental results, especially on few-sample character datasets.

Zhanran Lin, Puheng Li, Lei Wu

One of the most intriguing findings in the structure of neural network landscape is the phenomenon of mode connectivity: For two typical global minima, there exists a path connecting them without barrier. This concept of mode connectivity has played a crucial role in understanding important phenomena in deep learning. In this paper, we conduct a fine-grained analysis of this connectivity phenomenon. First, we demonstrate that in the overparameterized case, the connecting path can be as simple as a two-piece linear path, and the path length can be nearly equal to the Euclidean distance. This finding suggests that the landscape should be nearly convex in a certain sense. Second, we uncover a surprising star-shaped connectivity: For a finite number of typical minima, there exists a center on minima manifold that connects all of them simultaneously via linear paths. These results are provably valid for linear networks and two-layer ReLU networks under a teacher-student setup, and are empirically supported by models trained on MNIST and CIFAR-10.

Ke Ma, Jiaqi Tang, Bin Guo et al.

Despite the growing integration of deep models into mobile terminals, the accuracy of these models declines significantly due to various deployment interferences. Test-time adaptation (TTA) has emerged to improve the performance of deep models by adapting them to unlabeled target data online. Yet, the significant memory cost, particularly in resource-constrained terminals, impedes the effective deployment of most backward-propagation-based TTA methods. To tackle memory constraints, we introduce SURGEON, a method that substantially reduces memory cost while preserving comparable accuracy improvements during fully test-time adaptation (FTTA) without relying on specific network architectures or modifications to the original training procedure. Specifically, we propose a novel dynamic activation sparsity strategy that directly prunes activations at layer-specific dynamic ratios during adaptation, allowing for flexible control of learning ability and memory cost in a data-sensitive manner. Among this, two metrics, Gradient Importance and Layer Activation Memory, are considered to determine the layer-wise pruning ratios, reflecting accuracy contribution and memory efficiency, respectively. Experimentally, our method surpasses the baselines by not only reducing memory usage but also achieving superior accuracy, delivering SOTA performance across diverse datasets, architectures, and tasks.

Lei Wu

An important problem in machine learning theory is to understand the approximation and generalization properties of two-layer neural networks in high dimensions. To this end, researchers have introduced the Barron space $\mathcal{B}_s(Ω)$ and the spectral Barron space $\mathcal{F}_s(Ω)$, where the index $s\in [0,\infty)$ indicates the smoothness of functions within these spaces and $Ω\subset\mathbb{R}^d$ denotes the input domain. However, the precise relationship between the two types of Barron spaces remains unclear. In this paper, we establish a continuous embedding between them as implied by the following inequality: for any $δ\in (0,1), s\in \mathbb{N}^{+}$ and $f: Ω\mapsto\mathbb{R}$, it holds that \[ δ\|f\|_{\mathcal{F}_{s-δ}(Ω)}\lesssim_s \|f\|_{\mathcal{B}_s(Ω)}\lesssim_s \|f\|_{\mathcal{F}_{s+1}(Ω)}. \] Importantly, the constants do not depend on the input dimension $d$, suggesting that the embedding is effective in high dimensions. Moreover, we also show that the lower and upper bound are both tight.

Lei Wu, Weijie J. Su

In this paper, we study the implicit regularization of stochastic gradient descent (SGD) through the lens of {\em dynamical stability} (Wu et al., 2018). We start by revising existing stability analyses of SGD, showing how the Frobenius norm and trace of Hessian relate to different notions of stability. Notably, if a global minimum is linearly stable for SGD, then the trace of Hessian must be less than or equal to $2/η$, where $η$ denotes the learning rate. By contrast, for gradient descent (GD), the stability imposes a similar constraint but only on the largest eigenvalue of Hessian. We then turn to analyze the generalization properties of these stable minima, focusing specifically on two-layer ReLU networks and diagonal linear networks. Notably, we establish the {\em equivalence} between these metrics of sharpness and certain parameter norms for the two models, which allows us to show that the stable minima of SGD provably generalize well. By contrast, the stability-induced regularization of GD is provably too weak to ensure satisfactory generalization. This discrepancy provides an explanation of why SGD often generalizes better than GD. Note that the learning rate (LR) plays a pivotal role in the strength of stability-induced regularization. As the LR increases, the regularization effect becomes more pronounced, elucidating why SGD with a larger LR consistently demonstrates superior generalization capabilities. Additionally, numerical experiments are provided to support our theoretical findings.

Lei Wu

We study the problem of learning a single neuron $\mathbf{x}\mapsto σ(\mathbf{w}^T\mathbf{x})$ with gradient descent (GD). All the existing positive results are limited to the case where $σ$ is monotonic. However, it is recently observed that non-monotonic activation functions outperform the traditional monotonic ones in many applications. To fill this gap, we establish learnability without assuming monotonicity. Specifically, when the input distribution is the standard Gaussian, we show that mild conditions on $σ$ (e.g., $σ$ has a dominating linear part) are sufficient to guarantee the learnability in polynomial time and polynomial samples. Moreover, with a stronger assumption on the activation function, the condition of input distribution can be relaxed to a non-degeneracy of the marginal distribution. We remark that our conditions on $σ$ are satisfied by practical non-monotonic activation functions, such as SiLU/Swish and GELU. We also discuss how our positive results are related to existing negative results on training two-layer neural networks.

Yongxin Liu, Jian Wang, Yingjie Chen et al.

The integration of air and ground smart vehicles is becoming a new paradigm of future transportation. A decent number of smart unmanned vehicles or UAS will be sharing the national airspace for various purposes, such as express delivery, surveillance, etc. However, the proliferation of UAS also brings challenges considering the safe integration of them into the current Air Traffic Management (ATM) systems. Especially when the current Automatic Dependent Surveillance Broadcasting (ADS-B) systems do not have message authentication mechanisms, it can not distinguish whether an authorized UAS is using the corresponding airspace. In this paper, we aim to address these practical challenges in two folds. We first use blockchain to provide a secure authentication platform for flight plan approval and sharing between the existing ATM facilities. We then use the fountain code to encode the authentication payloads and adapt them into the de facto communication protocol of ATM. This maintains backward compatibility and ensures the verification success rate under the noisy broadcasting channel. We simulate the realistic wireless communication scenarios and theoretically prove that our proposed authentication framework is with low latency and highly compatible with existing ATM communication protocols.

Lei Wu, Jihao Long

We propose a spectral-based approach to analyze how two-layer neural networks separate from linear methods in terms of approximating high-dimensional functions. We show that quantifying this separation can be reduced to estimating the Kolmogorov width of two-layer neural networks, and the latter can be further characterized by using the spectrum of an associated kernel. Different from previous work, our approach allows obtaining upper bounds, lower bounds, and identifying explicit hard functions in a united manner. We provide a systematic study of how the choice of activation functions affects the separation, in particular the dependence on the input dimension. Specifically, for nonsmooth activation functions, we extend known results to more activation functions with sharper bounds. As concrete examples, we prove that any single neuron can instantiate the separation between neural networks and random feature models. For smooth activation functions, one surprising finding is that the separation is negligible unless the norms of inner-layer weights are polynomially large with respect to the input dimension. By contrast, the separation for nonsmooth activation functions is independent of the norms of inner-layer weights.

Alex Fedorov, Tristan Sylvain, Eloy Geenjaar et al.

Sensory input from multiple sources is crucial for robust and coherent human perception. Different sources contribute complementary explanatory factors. Similarly, research studies often collect multimodal imaging data, each of which can provide shared and unique information. This observation motivated the design of powerful multimodal self-supervised representation-learning algorithms. In this paper, we unify recent work on multimodal self-supervised learning under a single framework. Observing that most self-supervised methods optimize similarity metrics between a set of model components, we propose a taxonomy of all reasonable ways to organize this process. We first evaluate models on toy multimodal MNIST datasets and then apply them to a multimodal neuroimaging dataset with Alzheimer's disease patients. We find that (1) multimodal contrastive learning has significant benefits over its unimodal counterpart, (2) the specific composition of multiple contrastive objectives is critical to performance on a downstream task, (3) maximization of the similarity between representations has a regularizing effect on a neural network, which can sometimes lead to reduced downstream performance but still reveal multimodal relations. Results show that the proposed approach outperforms previous self-supervised encoder-decoder methods based on canonical correlation analysis (CCA) or the mixture-of-experts multimodal variational autoEncoder (MMVAE) on various datasets with a linear evaluation protocol. Importantly, we find a promising solution to uncover connections between modalities through a jointly shared subspace that can help advance work in our search for neuroimaging biomarkers.

Alex Fedorov, Lei Wu, Tristan Sylvain et al.

Introspection of deep supervised predictive models trained on functional and structural brain imaging may uncover novel markers of Alzheimer's disease (AD). However, supervised training is prone to learning from spurious features (shortcut learning) impairing its value in the discovery process. Deep unsupervised and, recently, contrastive self-supervised approaches, not biased to classification, are better candidates for the task. Their multimodal options specifically offer additional regularization via modality interactions. In this paper, we introduce a way to exhaustively consider multimodal architectures for contrastive self-supervised fusion of fMRI and MRI of AD patients and controls. We show that this multimodal fusion results in representations that improve the results of the downstream classification for both modalities. We investigate the fused self-supervised features projected into the brain space and introduce a numerically stable way to do so.

Han He, Lei Wu, Xiaokun Yang et al.

Characters have commonly been regarded as the minimal processing unit in Natural Language Processing (NLP). But many non-latin languages have hieroglyphic writing systems, involving a big alphabet with thousands or millions of characters. Each character is composed of even smaller parts, which are often ignored by the previous work. In this paper, we propose a novel architecture employing two stacked Long Short-Term Memory Networks (LSTMs) to learn sub-character level representation and capture deeper level of semantic meanings. To build a concrete study and substantiate the efficiency of our neural architecture, we take Chinese Word Segmentation as a research case example. Among those languages, Chinese is a typical case, for which every character contains several components called radicals. Our networks employ a shared radical level embedding to solve both Simplified and Traditional Chinese Word Segmentation, without extra Traditional to Simplified Chinese conversion, in such a highly end-to-end way the word segmentation can be significantly simplified compared to the previous work. Radical level embeddings can also capture deeper semantic meaning below character level and improve the system performance of learning. By tying radical and character embeddings together, the parameter count is reduced whereas semantic knowledge is shared and transferred between two levels, boosting the performance largely. On 3 out of 4 Bakeoff 2005 datasets, our method surpassed state-of-the-art results by up to 0.4%. Our results are reproducible, source codes and corpora are available on GitHub.

Han He, Lei Wu, Hua Yan et al.

We present a simple yet elegant solution to train a single joint model on multi-criteria corpora for Chinese Word Segmentation (CWS). Our novel design requires no private layers in model architecture, instead, introduces two artificial tokens at the beginning and ending of input sentence to specify the required target criteria. The rest of the model including Long Short-Term Memory (LSTM) layer and Conditional Random Fields (CRFs) layer remains unchanged and is shared across all datasets, keeping the size of parameter collection minimal and constant. On Bakeoff 2005 and Bakeoff 2008 datasets, our innovative design has surpassed both single-criterion and multi-criteria state-of-the-art learning results. To the best knowledge, our design is the first one that has achieved the latest high performance on such large scale datasets. Source codes and corpora of this paper are available on GitHub.