concretely explain the core technique, illustrating with examples

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The core technique of "Reasoning to Learn from Latent Thoughts" is a data-efficient approach to language model pretraining that augments observed data with inferred latent thoughts. Let me explain this concretely:

Core Concept

The key insight is that human-written text is "compressed" - it's the final outcome of an underlying thought process that includes reasoning steps, background knowledge, and contextual information. The authors propose that explicitly modeling and inferring these latent thoughts can significantly improve learning efficiency.

The Technique

1. Latent Thought Models

The approach models the text generation process as:

• Latent Z: The underlying thoughts (background knowledge, reasoning steps)
• Observed X: The actual written text
• Joint distribution p(Z, X): How thoughts and text relate

2. Training Process (Illustrated in Figure 2b)

For each document:

1. Chunk the text into segments (e.g., ~8 sentences each)
2. Generate latent thoughts for each chunk using either:
   • A powerful model like GPT-4o-mini (initially)
   • The model itself (during bootstrapping)
3. Train on augmented data by randomly placing latents either:
   • Before the text chunk (to learn p(Z, X))
   • After the text chunk (to learn q(Z|X))

Concrete Examples

Example 1: Math Derivation (PCA)

Raw text: "The second step is to find the new most marked axis. How do we find the best most standard axis to achieve principal component analysis?"

Inferred latent thought: