Jinxin Zhou

Jiachen Jiang, Jinxin Zhou, Peng Wang et al. · deepmind

Neural collapse provides an elegant mathematical characterization of learned last layer representations (a.k.a. features) and classifier weights in deep classification models. Such results not only provide insights but also motivate new techniques for improving practical deep models. However, most of the existing empirical and theoretical studies in neural collapse focus on the case that the number of classes is small relative to the dimension of the feature space. This paper extends neural collapse to cases where the number of classes are much larger than the dimension of feature space, which broadly occur for language models, retrieval systems, and face recognition applications. We show that the features and classifier exhibit a generalized neural collapse phenomenon, where the minimum one-vs-rest margins is maximized.We provide empirical study to verify the occurrence of generalized neural collapse in practical deep neural networks. Moreover, we provide theoretical study to show that the generalized neural collapse provably occurs under unconstrained feature model with spherical constraint, under certain technical conditions on feature dimension and number of classes.

Jinxin Zhou, Tianyu Ding, Tianyi Chen et al.

We present DREAM, a novel training framework representing Diffusion Rectification and Estimation Adaptive Models, requiring minimal code changes (just three lines) yet significantly enhancing the alignment of training with sampling in diffusion models. DREAM features two components: diffusion rectification, which adjusts training to reflect the sampling process, and estimation adaptation, which balances perception against distortion. When applied to image super-resolution (SR), DREAM adeptly navigates the tradeoff between minimizing distortion and preserving high image quality. Experiments demonstrate DREAM's superiority over standard diffusion-based SR methods, showing a $2$ to $3\times $ faster training convergence and a $10$ to $20\times$ reduction in sampling steps to achieve comparable results. We hope DREAM will inspire a rethinking of diffusion model training paradigms.

Tianyu Ding, Jinxin Zhou, Tianyi Chen et al.

Existing angle-based contour descriptors suffer from lossy representation for non-starconvex shapes. By and large, this is the result of the shape being registered with a single global inner center and a set of radii corresponding to a polar coordinate parameterization. In this paper, we propose AdaContour, an adaptive contour descriptor that uses multiple local representations to desirably characterize complex shapes. After hierarchically encoding object shapes in a training set and constructing a contour matrix of all subdivided regions, we compute a robust low-rank robust subspace and approximate each local contour by linearly combining the shared basis vectors to represent an object. Experiments show that AdaContour is able to represent shapes more accurately and robustly than other descriptors while retaining effectiveness. We validate AdaContour by integrating it into off-the-shelf detectors to enable instance segmentation which demonstrates faithful performance. The code is available at https://github.com/tding1/AdaContour.

Jiachen Jiang, Yuxin Dong, Jinxin Zhou et al.

In-context learning (ICL) enables large language models (LLMs) to adapt to new tasks without weight updates by learning from demonstration sequences. While ICL shows strong empirical performance, its internal representational mechanisms are not yet well understood. In this work, we conduct a statistical geometric analysis of ICL representations to investigate how task-specific information is captured across layers. Our analysis reveals an intriguing phenomenon, which we term *Layerwise Compression-Expression*: early layers progressively produce compact and discriminative representations that encode task information from the input demonstrations, while later layers express these representations to incorporate the query and generate the prediction. This phenomenon is observed consistently across diverse tasks and a range of contemporary LLM architectures. We demonstrate that it has important implications for ICL performance -- improving with model size and the number of demonstrations -- and for robustness in the presence of noisy examples. To further understand the effect of the compact task representation, we propose a bias-variance decomposition and provide a theoretical analysis showing how attention mechanisms contribute to reducing both variance and bias, thereby enhancing performance as the number of demonstrations increases. Our findings reveal an intriguing layerwise dynamic in ICL, highlight how structured representations emerge within LLMs, and showcase that analyzing internal representations can facilitate a deeper understanding of model behavior.

Jiachen Jiang, Jinxin Zhou, Zhihui Zhu

Analyzing the similarity of internal representations has been an important technique for understanding the behavior of deep neural networks. Most existing methods for analyzing the similarity between representations of high dimensions, such as those based on Centered Kernel Alignment (CKA), rely on statistical properties of the representations for a set of data points. In this paper, we focus on transformer models and study the similarity of representations between the hidden layers of individual transformers. In this context, we show that a simple sample-wise cosine similarity metric is capable of capturing the similarity and aligns with the complicated CKA. Our experimental results on common transformers reveal that representations across layers are positively correlated, with similarity increasing when layers get closer. We provide a theoretical justification for this phenomenon under the geodesic curve assumption for the learned transformer. We then show that an increase in representation similarity implies an increase in predicted probability when directly applying the last-layer classifier to any hidden layer representation. We then propose an aligned training method to improve the effectiveness of shallow layer by enhancing the similarity between internal representations, with trained models that enjoy the following properties: (1) more early saturation events, (2) layer-wise accuracies monotonically increase and reveal the minimal depth needed for the given task, (3) when served as multi-exit models, they achieve on-par performance with standard multi-exit architectures which consist of additional classifiers designed for early exiting in shallow layers. To our knowledge, our work is the first to show that one common classifier is sufficient for multi-exit models. We conduct experiments on both vision and NLP tasks to demonstrate the performance of the proposed aligned training.

Zhihui Zhu, Tianyu Ding, Jinxin Zhou et al.

We provide the first global optimization landscape analysis of $Neural\;Collapse$ -- an intriguing empirical phenomenon that arises in the last-layer classifiers and features of neural networks during the terminal phase of training. As recently reported by Papyan et al., this phenomenon implies that ($i$) the class means and the last-layer classifiers all collapse to the vertices of a Simplex Equiangular Tight Frame (ETF) up to scaling, and ($ii$) cross-example within-class variability of last-layer activations collapses to zero. We study the problem based on a simplified $unconstrained\;feature\;model$, which isolates the topmost layers from the classifier of the neural network. In this context, we show that the classical cross-entropy loss with weight decay has a benign global landscape, in the sense that the only global minimizers are the Simplex ETFs while all other critical points are strict saddles whose Hessian exhibit negative curvature directions. In contrast to existing landscape analysis for deep neural networks which is often disconnected from practice, our analysis of the simplified model not only does it explain what kind of features are learned in the last layer, but it also shows why they can be efficiently optimized in the simplified settings, matching the empirical observations in practical deep network architectures. These findings could have profound implications for optimization, generalization, and robustness of broad interests. For example, our experiments demonstrate that one may set the feature dimension equal to the number of classes and fix the last-layer classifier to be a Simplex ETF for network training, which reduces memory cost by over $20\%$ on ResNet18 without sacrificing the generalization performance.