The explosion in the amount of data available for analysis often necessitates a transition from batch to incremental clustering methods, which process one element at a time and typically store only a small subset of the data. In this paper, we initiate the formal analysis of incremental clustering methods focusing on the types of cluster structure that they are able to detect. We find that the incremental setting is strictly weaker than the batch model, proving that a fundamental class of cluster structures that can readily be detected in the batch setting is impossible to identify using any incremental method. Furthermore, we show how the limitations of incremental clustering can be overcome by allowing additional clusters.

An approach to improve neural network interpretability is via clusterability, i.e., splitting a model into disjoint clusters that can be studied independently. We define a measure for clusterability and show that pre-trained models form highly enmeshed clusters via spectral graph clustering. We thus train models to be more modular using a "clusterability loss" function that encourages the formation of non-interacting clusters. Using automated interpretability techniques, we show that our method can help train models that are more modular and learn different, disjoint, and smaller circuits. We investigate CNNs trained on MNIST and CIFAR, small transformers trained on modular addition, and language models. Our approach provides a promising direction for training neural networks that learn simpler functions and are easier to interpret.

An approach to improve network interpretability is via clusterability, i.e., splitting a model into disjoint clusters that can be studied independently. We find pretrained models to be highly unclusterable and thus train models to be more modular using an ``enmeshment loss'' function that encourages the formation of non-interacting clusters. Using automated interpretability measures, we show that our method finds clusters that learn different, disjoint, and smaller circuits for CIFAR-10 labels. Our approach provides a promising direction for making neural networks easier to interpret.

In semi-supervised learning, methods that rely on confidence learning to generate pseudo-labels have been widely proposed. However, increasing research finds that when faced with noisy and biased data, the model's representation network is more reliable than the classification network. Additionally, label generation methods based on model predictions often show poor adaptability across different datasets, necessitating customization of the classification network. Therefore, we propose a Hierarchical Dynamic Labeling (HDL) algorithm that does not depend on model predictions and utilizes image embeddings to generate sample labels. We also introduce an adaptive method for selecting hyperparameters in HDL, enhancing its versatility. Moreover, HDL can be combined with general image encoders (e.g., CLIP) to serve as a fundamental data processing module. We extract embeddings from datasets with class-balanced and long-tailed distributions using pre-trained semi-supervised models. Subsequently, samples are re-labeled using HDL, and the re-labeled samples are used to further train the semi-supervised models. Experiments demonstrate improved model performance, validating the motivation that representation networks are more reliable than classifiers or predictors. Our approach has the potential to change the paradigm of pseudo-label generation in semi-supervised learning.

The explosion in the amount of data available for analysis often necessitates a transition from batch to incremental clustering methods, which process one element at a time and typically store only a small subset of the data. In this paper, we initiate the formal analysis of incremental clustering methods focusing on the types of cluster structure that they are able to detect. We find that the incremental setting is strictly weaker than the batch model, proving that a fundamental class of cluster structures that can readily be detected in the batch setting is impossible to identify using any incremental method. Furthermore, we show how the limitations of incremental clustering can be overcome by allowing additional clusters.

In the burgeoning field of natural language processing (NLP), Neural Topic Models (NTMs) , Large Language Models (LLMs) and Diffusion model have emerged as areas of significant research interest. Despite this, NTMs primarily utilize contextual embeddings from LLMs, which are not optimal for clustering or capable for topic based text generation. NTMs have never been combined with diffusion model for text generation. Our study addresses these gaps by introducing a novel framework named Diffusion-Enhanced Topic Modeling using Encoder-Decoder-based LLMs (DeTiME). DeTiME leverages Encoder-Decoder-based LLMs to produce highly clusterable embeddings that could generate topics that exhibit both superior clusterability and enhanced semantic coherence compared to existing methods. Additionally, by exploiting the power of diffusion model, our framework also provides the capability to do topic based text generation. This dual functionality allows users to efficiently produce highly clustered topics and topic based text generation simultaneously. DeTiME's potential extends to generating clustered embeddings as well. Notably, our proposed framework(both encoder-decoder based LLM and diffusion model) proves to be efficient to train and exhibits high adaptability to other LLMs and diffusion model, demonstrating its potential for a wide array of applications.

The objective of clusterability evaluation is to check whether a clustering structure exists within the data set. As a crucial yet often-overlooked issue in cluster analysis, it is essential to conduct such a test before applying any clustering algorithm. If a data set is unclusterable, any subsequent clustering analysis would not yield valid results. Despite its importance, the majority of existing studies focus on numerical data, leaving the clusterability evaluation issue for categorical data as an open problem. Here we present TestCat, a testing-based approach to assess the clusterability of categorical data in terms of an analytical $p$-value. The key idea underlying TestCat is that clusterable categorical data possess many strongly correlated attribute pairs and hence the sum of chi-squared statistics of all attribute pairs is employed as the test statistic for $p$-value calculation. We apply our method to a set of benchmark categorical data sets, showing that TestCat outperforms those solutions based on existing clusterability evaluation methods for numeric data. To the best of our knowledge, our work provides the first way to effectively recognize the clusterability of categorical data in a statistically sound manner.

We present Sauron, a filter pruning method that eliminates redundant feature maps by discarding the corresponding filters with automatically-adjusted layer-specific thresholds. Furthermore, Sauron minimizes a regularization term that, as we show with various metrics, promotes the formation of feature maps clusters. In contrast to most filter pruning methods, Sauron is single-phase, similarly to typical neural network optimization, requiring fewer hyperparameters and design decisions. Additionally, unlike other cluster-based approaches, our method does not require pre-selecting the number of clusters, which is non-trivial to determine and varies across layers. We evaluated Sauron and three state-of-the-art filter pruning methods on three medical image segmentation tasks. This is an area where filter pruning has received little attention and where it can help building efficient models for medical grade computers that cannot use cloud services due to privacy considerations. Sauron achieved models with higher performance and pruning rate than the competing pruning methods. Additionally, since Sauron removes filters during training, its optimization accelerated over time. Finally, we show that the feature maps of a Sauron-pruned model were highly interpretable. The Sauron code is publicly available at https://github.com/jmlipman/SauronUNet.

The knowledge of the label noise transition matrix, characterizing the probabilities of a training instance being wrongly annotated, is crucial to designing popular solutions to learning with noisy labels, including loss correction and loss reweighting approaches. Existing works heavily rely on the existence of "anchor points" or their approximates, defined as instances that belong to a particular class almost surely. Nonetheless, finding anchor points remains a non-trivial task, and the estimation accuracy is also often throttled by the number of available anchor points. In this paper, we propose an alternative option to the above task. Our main contribution is the discovery of an efficient estimation procedure based on a clusterability condition. We prove that with clusterable representations of features, using up to third-order consensuses of noisy labels among neighbor representations is sufficient to estimate a unique transition matrix. Compared with methods using anchor points, our approach uses substantially more instances and benefits from a much better sample complexity. We demonstrate the estimation accuracy and advantages of our estimates using both synthetic noisy labels (on CIFAR-10/100) and real human-level noisy labels (on Clothing1M and our self-collected human-annotated CIFAR-10).

Clustering is the prototypical unsupervised learning activity which consists in identifying cohesive and well-differentiated groups of records in data. A data set is clusterable if such groups exist; however, due to the variety in data distributions and the inadequate formalization of certain basic notions of clustering, determining data clusterability before applying specific clustering algorithms is a difficult task. Evaluating data clusterability before the application of clustering algorithms can be very helpful because clustering algorithms are expensive. However, many such evaluations are impractical because they are NPhard, as shown in [4]. Other notions define data as clusterable when the minimum between-cluster separation is greater than the maximum intra-cluster distance [13], or when each element is closer to all elements in its cluster than to all other data [7].