# MIC: Maximizing Informational Capacity in Adaptive Representations via Isotropic Subspace Alignment

arXiv: https://arxiv.org/abs/2605.29987 · HTML: https://mlsanity.com/paper/2605.29987/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 23 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 14 of 14)

- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [TweetEval: Unified Benchmark and Comparative Evaluation for Tweet Classification](https://mlsanity.com/paper/2010.12421/) (2020)
- [LLM2Vec: Large Language Models Are Secretly Powerful Text Encoders](https://mlsanity.com/paper/2404.05961/) (2024)
- [WiC: the Word-in-Context Dataset for Evaluating Context-Sensitive Meaning Representations](https://mlsanity.com/paper/1808.09121/) (2018)
- [SentEval: An Evaluation Toolkit for Universal Sentence Representations](https://mlsanity.com/paper/1803.05449/) (2018)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [EASE: Entity-Aware Contrastive Learning of Sentence Embedding](https://mlsanity.com/paper/2205.04260/) (2022)
- [Refining Sentence Embedding Model through Ranking Sentences Generation with Large Language Models](https://mlsanity.com/paper/2502.13656/) (2025)

## Built on by (most cited first, 1 of 1)

- [Adaptive Latent Capacity for World Models](https://mlsanity.com/paper/2609.32921/) (2026)

## Abstract (arXiv)

Although multi-scales representation learning enables elastic-dimension embeddings, nested subspaces often suffer from dimensional redundancy and spectral collapse. To address this, we introduce MIC, a framework that optimizes the geometric landscape of multi-granular embeddings through isotropic subspace alignment. MIC employs Soft Collapse Regularization (SCR) to mitigate redundancy between prefix and residual subspaces via cross-correlation penalties, alongside Spectral Isotropy Regularization (SIR) to ensure hyper-spherical uniformity in low-dimensional prefixes. By unifying these strategies through a self-distillation objective, MIC generates semantically dense representations that maintain high discriminative power. Our experiments demonstrate that MIC significantly outperforms standard baselines, particularly in high-compression scenarios where maintaining informational capacity is most critical.