# Cluster Validation Indices as Self-Supervised Objectives for Text Representation Learning

arXiv: https://arxiv.org/abs/2610.04830 · HTML: https://mlsanity.com/paper/2610.04830/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Builds on (most cited first, 12 of 12)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [DiffCSE: Difference-based Contrastive Learning for Sentence Embeddings](https://mlsanity.com/paper/2204.10298/) (2022)
- [ESimCSE: Enhanced Sample Building Method for Contrastive Learning of Unsupervised Sentence Embedding](https://mlsanity.com/paper/2109.04380/) (2021)
- [SCD: Self-Contrastive Decorrelation for Sentence Embeddings](https://mlsanity.com/paper/2203.07847/) (2022)
- [CARL-G: Clustering-Accelerated Representation Learning on Graphs](https://mlsanity.com/paper/2306.06936/) (2023)

## Abstract (arXiv)

Self-supervised fine-tuning refines the embedding space of a pretrained language encoder without labels. However, the commonly used approaches are computationally expensive. Specifically, contrastive learning-based methods need multiview data and in-batch negative examples, while negative-free approaches require auxiliary graphs/networks. An interesting question arises: can self-supervised fine-tuning be done without relying on either additional negatives or graph data? To answer this question, we introduce SilK (Silhouette-guided K-means), which trains on a Cluster Validation Index, an internal measure of cluster quality without using labels. SilK clusters the corpus and then regresses a simplified silhouette toward a target value. Each document is compared only against the k cluster centroids, never against other documents, so the method needs no augmentation, no negative pairs and one view per document. On BERT-base, SilK trains 1.46x faster per epoch than the fastest baseline we evaluate and uses 45.4% less peak GPU memory than the leanest one. Under frozen-encoder linear probing, SilK stays competitive with the best baselines on three downstream tasks.