explain the core technique

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I'll explain the core technique from the paper "Reasoning to Learn from Latent Thoughts" by Ruan et al.

Core Technique: Bootstrapping Latent Thoughts (BoLT)

The paper introduces a new approach to improve language model pretraining efficiency by modeling and inferring the "latent thoughts" that underlie the text generation process. The core idea is that human-written text is the compressed final outcome of a verbose human thought process, and explicitly modeling these latent thoughts can make learning more data-efficient.

Here's how the technique works:

1. Latent Variable Perspective: The authors approach language modeling from a latent variable perspective, where observed data X depends on underlying latent thoughts Z. They train the LM to learn from observed data X augmented with latents Z by modeling the joint distribution p(Z, X).
2. Bootstrapping Process: The key innovation is the "Bootstrapping Latent Thoughts" (BoLT) algorithm, which uses an Expectation-Maximization (EM) approach:
   • E-step: Generate multiple latent thought samples and select the best one using importance sampling (Monte Carlo)
   • M-step: Train the model on the data augmented with these latent thoughts
3. Implementation Details:
   • The latent thoughts are represented as natural language text
   • The authors use special tokens to separate latent thoughts from observed text
   • The same model is trained to both generate latent thoughts and use them for learning
   • The process is iterative, creating a self-improvement loop where better models generate better latent thoughts
4. Results: The technique showed significant improvements in data efficiency:
   • Models trained with synthetic latent thoughts achieved 25.4% accuracy on MATH benchmarks versus 5.74% for models trained on the same amount of raw data
   • Performance continued to improve across multiple bootstrap iterations
   • More Monte Carlo samples during latent thought generation led to better performance

This approach is novel because it leverages the model's own reasoning abilities to improve its learning efficiency, creating a virtuous cycle where better reasoning leads to better learning, which leads to better reasoning.

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YZ

can you explain in more detail and concretely?

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Reasoning to Learn from Latent Thoughts: A Concrete Explanation

Let me explain the BoLT technique more concretely with specific examples of how it works in practice.

The Problem: Data Inefficiency in LM Training

Current language models are trained on compressed text (like research papers) that represents the final output of human thought processes. This is inefficient because humans learn more efficiently from the same text by inferring the thinking process behind it.