Why Struggle with Continuous Latents? proposes Discrete Latent Reasoning:

• TL;DR:

  • Replace explicit CoT with a short sequence of non-verbal tokens via image tokeniser
  • Kinda insane, unprincipled idea (patches may not even cover full words!), but decent performance

• Constructs these by compressing real CoTs:

  • take written CoT, render as image ("screenshot"), tokenise with DeepEncoder V2
  • reduces 1024 × 1024 image into 256 tokens, leading to up to 20× compression

• Codebook trained so that latent tokens can be (approximately) decoded:

  • is a code from a learned compression scheme over actual CoTs
  • has an approximate textual interpretation via the decoder
  • can be supervised with ordinary token-level losses

• Training the LM is then fairly clean:

  1. Align the new latent tokens to the LM: learn projectors from codebook to LM space
  2. SFT on sequences like problem -> <latent> compressed-CoT tokens </latent> -> answer
  3. RL the model's latent-token policy: correctness, formatting and/or process-level via decode

Abstract-CoT has similar goals, with discrete latents whose embeddings are learned, but differs in the implementation:

• Abstract-CoT: learns (reserved) latent language from scratch during training
• DLR: token IDs precomputed from compressed images

Results are broadly positive:

• DLR beats latent-reasoning baselines, but still a step below standard CoT
• It uses much shorter traces than explicit CoT - perhaps 20x shorter
• RL helps, and ablations suggest alignment stage, SFT stage and process reward all matter