---
title: "UC Santa Barbara's LoRi Closes the Silent Reasoning Gap by 12%"
subtitle: "LoRi teaches LLMs to reason silently by compressing a teacher's chain-of-thought into a low-rank latent subspace, cutting inference latency up to 6.9x while nearly matching explicit CoT accuracy."
url: "https://alphasignal.ai/news/uc-santa-barbara-s-lori-closes-the-silent-reasoning-gap-by-12"
author: "AlphaSignal Newsroom"
author_url: "https://alphasignal.ai/editorial-team"
company: "AlphaSignal"
company_url: "https://alphasignal.ai/company/alphasignal"
published: "2026-06-03T00:00:00.000Z"
updated: "2026-06-15T01:19:42.737Z"
type: "Paper"
topics:
  - "Post Training"
  - "Reasoning"
subtopics:
  - "Distillation"
  - "Math Reasoning"
  - "Test Time Compute"
upvotes: 17
source_url: "https://arxiv.org/abs/2606.05315"
comments: 0
truncated: true
---

# UC Santa Barbara's LoRi Closes the Silent Reasoning Gap by 12%

> LoRi teaches LLMs to reason silently by compressing a teacher's chain-of-thought into a low-rank latent subspace, cutting inference latency up to 6.9x while nearly matching explicit CoT accuracy.

Chain-of-thought prompting made LLMs dramatically better at reasoning, but it came with a tax: every answer now requires generating hundreds of intermediate tokens before the model can commit to a final response. Explicit CoT is computationally expensive, can encourage reliance on non-robust patterns, and is sensitive to inference procedures. The field has been chasing a cleaner solution: can a model reason just as well without writing its work out loud?

Implicit Chain-of-Thought (CoT) models are a class of neural reasoning frameworks for LLMs in which the multi-step reasoning process occurs within the model's high-dimensional latent or hidden-state space, rather than being externalized via explicit, human-readable intermediate tokens. The idea is compelling, but in practice, recent iCoT distillation approaches transfer explicit rationales into latent reasoning states, but still underperform explicit CoT on difficult mathematical reasoning tasks. A team from UC Santa Barbara thinks they know why, and they have a fix.

## The gap nobody could close

The core problem with existing iCoT methods is architectural, not just a matter of training harder. A key challenge is that explicit reasoning steps lack a clear correspondence to latent dynamics, making token-to-latent transfer inherently ill-posed. Existing methods rely on local supervision or sampled intermediate states, which may not fully capture the global reasoning trajectory. Methods like CODI align representations at a single boundary token, KAVA distills KV-cache trajectories step-by-step, and SIM-CoT applies step-level supervision through an auxiliary decoder. All of them are trying to match the teacher token-by-token, which is a fundamentally mismatched problem.

The UC Santa Barbara team made an empirical observation that reframes the whole challenge: hidden-state reasoning trajectories exhibit low-rank structure. In other words, when you stack all the hidden states across layers and CoT tokens into a matrix and run SVD on it, the singular values decay rapidly. Despite a model like LLaMA-3.2-1B having a hidden dimension of 2048, the reasoning trajectory lives in a much smaller subspace. You don't need to match every step; you just need to match the shape of that subspace.

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## Sources

- [LoRi: Low-Rank Distillation for Implicit Reasoning (arXiv)](https://arxiv.org/abs/2606.05315)
- [LoRi HTML Paper (arXiv)](https://arxiv.org/html/2606.05315)
- [CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation](https://arxiv.org/html/2502.21074v1)
- [Implicit Chain of Thought Reasoning via Knowledge Distillation (OpenReview)](https://openreview.net/forum?id=9cumTvvlHG)
- [Implicit Chain-of-Thought Model (Emergent Mind)](https://www.emergentmind.com/topics/implicit-chain-of-thought-cot-model)