Neural Collapse refers to the remarkable structural properties characterizing the geometry of class embeddings and classifier weights, found by deep nets when trained beyond zero training error. However, this characterization only holds for balanced data. Here we thus ask whether it can be made invariant to class imbalances. Towards this end, we adopt the unconstrained feature model (UFM), a recent theoretical model for studying neural collapse, and introduce $\text{\emph{Simplex-Encoded-Labels Interpolation}}$ (SELI) as an invariant characterization of the neural collapse phenomenon. Specifically, we prove for the UFM with cross-entropy loss and vanishing regularization that, irrespective of class imbalances, the embeddings and classifiers always interpolate a simplex-encoded label matrix and that their individual geometries are determined by the SVD factors of this same label matrix. We then present extensive experiments on synthetic and real datasets that confirm convergence to the SELI geometry. However, we caution that convergence worsens with increasing imbalances. We theoretically support this finding by showing that unlike the balanced case, when minorities are present, ridge-regularization plays a critical role in tweaking the geometry. This defines new questions and motivates further investigations into the impact of class imbalances on the rates at which first-order methods converge to their asymptotically preferred solutions.

View missing remains a significant challenge in graph-based multi-view semi-supervised learning, hindering their real-world applications. To address this issue, traditional methods introduce a missing indicator matrix and focus on mining partial structure among existing samples in each view for label propagation (LP). However, we argue that these disregarded missing samples sometimes induce discontinuous local structures, i.e., sub-clusters, breaking the fundamental smoothness assumption in LP. Consequently, such a Sub-Cluster Problem (SCP) would distort graph fusion and degrade classification performance. To alleviate SCP, we propose a novel incomplete multi-view semi-supervised learning method, termed AGF-TI. Firstly, we design an adversarial graph fusion scheme to learn a robust consensus graph against the distorted local structure through a min-max framework. By stacking all similarity matrices into a tensor, we further recover the incomplete structure from the high-order consistency information based on the low-rank tensor learning. Additionally, the anchor-based strategy is incorporated to reduce the computational complexity. An efficient alternative optimization algorithm combining a reduced gradient descent method is developed to solve the formulated objective, with theoretical convergence. Extensive experimental results on various datasets validate the superiority of our proposed AGF-TI as compared to state-of-the-art methods. Code is available at https://github.com/ZhangqiJiang07/AGF_TI.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper addresses the problem of pairwise classification. The authors propose a two-step algorithm that estimates if two data points belong to the same class. Additional to the method, they provide a theoretical analysis giving a bound for the minimum number of labels for the quality of the estimated labels. The paper is well written.

Neural Information Processing Systems http://nips.cc/

In this work, we study the problem of transductive pairwise classification from pairwise similarities~\footnote{The pairwise similarities are usually derived from some side information instead of the underlying class labels.}. The goal of transductive pairwise classification from pairwise similarities is to infer the pairwise class relationships, to which we refer as pairwise labels, between all examples given a subset of class relationships for a small set of examples, to which we refer as labeled examples. We propose a very simple yet effective algorithm that consists of two simple steps: the first step is to complete the sub-matrix corresponding to the labeled examples and the second step is to reconstruct the label matrix from the completed sub-matrix and the provided similarity matrix. Our analysis exhibits that under several mild preconditions we can recover the label matrix with a small error, if the top eigen-space that corresponds to the largest eigenvalues of the similarity matrix covers well the column space of label matrix and is subject to a low coherence, and the number of observed pairwise labels is sufficiently enough. We demonstrate the effectiveness of the proposed algorithm by several experiments.

Partial Multi-Label Learning (PML) extends the multi-label learning paradigm to scenarios where each sample is associated with a candidate label set containing both ground-truth labels and noisy labels. Existing PML methods commonly rely on two assumptions: sparsity of the noise label matrix and low-rankness of the ground-truth label matrix. However, these assumptions are inherently conflicting and impractical for real-world scenarios, where the true label matrix is typically full-rank or close to full-rank. To address these limitations, we demonstrate that the sparsity constraint contributes to the high-rank property of the predicted label matrix. Based on this, we propose a novel method Schirn, which introduces a sparsity constraint on the noise label matrix while enforcing a high-rank property on the predicted label matrix. Extensive experiments demonstrate the superior performance of Schirn compared to state-of-the-art methods, validating its effectiveness in tackling real-world PML challenges.

Simultaneous or streaming machine translation generates translation while reading the input stream. These systems face a quality/latency trade-off, aiming to achieve high translation quality similar to non-streaming models with minimal latency. We propose an approach that efficiently manages this trade-off. By enhancing a pretrained non-streaming model, which was trained with a seq2seq mechanism and represents the upper bound in quality, we convert it into a streaming model by utilizing the alignment between source and target tokens. This alignment is used to learn a read/write decision boundary for reliable translation generation with minimal input. During training, the model learns the decision boundary through a read/write policy module, employing supervised learning on the alignment points (pseudo labels). The read/write policy module, a small binary classification unit, can control the quality/latency trade-off during inference. Experimental results show that our model outperforms several strong baselines and narrows the gap with the non-streaming baseline model.