Jianfeng Yao

Xuran Meng, Jianfeng Yao, Yuan Cao

Recent works have demonstrated a double descent phenomenon in over-parameterized learning. Although this phenomenon has been investigated by recent works, it has not been fully understood in theory. In this paper, we investigate the multiple descent phenomenon in a class of multi-component prediction models. We first consider a ''double random feature model'' (DRFM) concatenating two types of random features, and study the excess risk achieved by the DRFM in ridge regression. We calculate the precise limit of the excess risk under the high dimensional framework where the training sample size, the dimension of data, and the dimension of random features tend to infinity proportionally. Based on the calculation, we further theoretically demonstrate that the risk curves of DRFMs can exhibit triple descent. We then provide a thorough experimental study to verify our theory. At last, we extend our study to the ''multiple random feature model'' (MRFM), and show that MRFMs ensembling $K$ types of random features may exhibit $(K+1)$-fold descent. Our analysis points out that risk curves with a specific number of descent generally exist in learning multi-component prediction models.

Mengda Li, Zeng Li, Jianfeng Yao

Removing noise is difficult, but adding noise is easy. In this work, we show how to eliminate mean-shift noisy components from PCA by deliberately introducing knockoff mean-shift perturbation. Standard PCA is highly sensitive to shifts in the sample mean: a small fraction of samples from a shifted distribution can cause large deviations in the leading principal components. In high-dimensional regimes, existing Robust PCA approaches cannot handle the mean-shift contamination structure inherent in the mixture model. Using tools from Random Matrix Theory, we prove that the mean-shift spikes are spectrally separable from the stable eigenvalues of the original covariance. Furthermore, the original eigenspace remains asymptotically invariant to the contamination, independent of the mixture weight. Exploiting this spectral stability, we propose a simple, two-stage PCA algorithm by adding knockoff mean that identifies and removes the mean-shift component using only standard PCA operations.

Zhaorui Dong, Yushun Zhang, Jianfeng Yao et al.

Empirical studies reported that the Hessian matrix of neural networks (NNs) exhibits a near-block-diagonal structure, yet its theoretical foundation remains unclear. In this work, we reveal that the reported Hessian structure comes from a mixture of two forces: a ``static force'' rooted in the architecture design, and a ''dynamic force'' arisen from training. We then provide a rigorous theoretical analysis of ''static force'' at random initialization. We study linear models and 1-hidden-layer networks for classification tasks with $C$ classes. By leveraging random matrix theory, we compare the limit distributions of the diagonal and off-diagonal Hessian blocks and find that the block-diagonal structure arises as $C$ becomes large. Our findings reveal that $C$ is one primary driver of the near-block-diagonal structure. These results may shed new light on the Hessian structure of large language models (LLMs), which typically operate with a large $C$ exceeding $10^4$.

Xiaofei Zhu, Jiawei Cheng, Zhou Yang et al.

Multimodal emotion recognition in conversation (MER) aims to accurately identify emotions in conversational utterances by integrating multimodal information. Previous methods usually treat multimodal information as equal quality and employ symmetric architectures to conduct multimodal fusion. However, in reality, the quality of different modalities usually varies considerably, and utilizing a symmetric architecture is difficult to accurately recognize conversational emotions when dealing with uneven modal information. Furthermore, fusing multi-modality information in a single granularity may fail to adequately integrate modal information, exacerbating the inaccuracy in emotion recognition. In this paper, we propose a novel Cross-Modality Augmented Transformer with Hierarchical Variational Distillation, called CMATH, which consists of two major components, i.e., Multimodal Interaction Fusion and Hierarchical Variational Distillation. The former is comprised of two submodules, including Modality Reconstruction and Cross-Modality Augmented Transformer (CMA-Transformer), where Modality Reconstruction focuses on obtaining high-quality compressed representation of each modality, and CMA-Transformer adopts an asymmetric fusion strategy which treats one modality as the central modality and takes others as auxiliary modalities. The latter first designs a variational fusion network to fuse the fine-grained representations learned by CMA- Transformer into a coarse-grained representations. Then, it introduces a hierarchical distillation framework to maintain the consistency between modality representations with different granularities. Experiments on the IEMOCAP and MELD datasets demonstrate that our proposed model outperforms previous state-of-the-art baselines. Implementation codes can be available at https://github.com/ cjw-MER/CMATH.

Xuran Meng, Jianfeng Yao

Much research effort has been devoted to explaining the success of deep learning. Random Matrix Theory (RMT) provides an emerging way to this end: spectral analysis of large random matrices involved in a trained deep neural network (DNN) such as weight matrices or Hessian matrices with respect to the stochastic gradient descent algorithm. To have more comprehensive understanding of weight matrices spectra, we conduct extensive experiments on weight matrices in different modules, e.g., layers, networks and data sets. Following the previous work of \cite{martin2018implicit}, we classify the spectra in the terminal stage into three main types: Light Tail (LT), Bulk Transition period (BT) and Heavy Tail(HT). These different types, especially HT, implicitly indicate some regularization in the DNNs. A main contribution from the paper is that we identify the difficulty of the classification problem as a driving factor for the appearance of heavy tail in weight matrices spectra. Higher the classification difficulty, higher the chance for HT to appear. Moreover, the classification difficulty can be affected by the signal-to-noise ratio of the dataset, or by the complexity of the classification problem (complex features, large number of classes) as well. Leveraging on this finding, we further propose a spectral criterion to detect the appearance of heavy tails and use it to early stop the training process without testing data. Such early stopped DNNs have the merit of avoiding overfitting and unnecessary extra training while preserving a much comparable generalization ability. These findings from the paper are validated in several NNs, using Gaussian synthetic data and real data sets (MNIST and CIFAR10).