What properties must a thought state have?
Beyond expressiveness: can it expose progress, separate correct from incorrect trajectories, support verification, and remain steerable?
A research map beyond chain-of-thought
How should thoughts flow through a model?
Flow of Thoughts traces how reasoning can move through a model—not only along token-by-token chains, but through recurrent depth, latent states, flow-based refinement, adaptive allocation, and recurrent memory. The goal is not necessarily more computation, but better-structured computation.
Living research notes
Notes last updated
Revised as new papers and evidence arrive.
Core idea
reasoning = only generate more tokens
→
reasoning = structure and route computation
How to read this site
Four layers, four different jobs
You do not need to read the page from top to bottom. Choose the layer that matches what you want to know.
01 · Vocabulary
Map
Six overlapping mechanisms for organizing the field. A single paper can belong to several.
Use this to learn the landscape → 02 · ConclusionsFindings
Cross-paper conclusions that separate direct results from our synthesis and hypotheses.
Use this for the main scientific takeaways → 03 · Audit trailPaper evidence
Structured records of what each core paper actually establishes, limits, and leaves open.
Use this to verify a claim → 04 · IndexLibrary
The complete searchable bibliography, including roots, core papers, and adjacent work.
Use this to find a specific paper →New to the topic? Read Map → Findings → one or two Paper evidence cards. Use the Library only when you need breadth.
Conceptual map
Six overlapping mechanisms
Unifying lens
Four questions for every method
State: what carries the intermediate computation? Update: how does it change? Compute policy: where and how long does the model iterate? Outcome: what improves?
01
problem
x
task + context
initialize
02
iterative thought
t = 0, 1, …
state
zt
update rule
Fθ
Compute policy
continue ↻ or stop →
read out
03
solution
y
measured outcome
Evidence-backed synthesis
Cross-paper findings
Each synthesis separates direct paper evidence from our cross-paper inference, then ends with a concrete unresolved gap and falsifiable hypotheses.
DIRECT explicitly reported by the paper
FOLLOW-UP later work testing the claim
SYNTHESIS inference supported across papers
HYPOTHESIS testable, not established
Read the full evidence ledger →
Paper dossiers
What each core paper establishes
Each dossier records the paper's research question, state, update rule, compute policy, direct findings, and scoped limitations. This is the audit trail behind the higher-level synthesis.
Paper explorer
Search the full bibliography
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Research programs
Open problems derived from the evidence
These are downstream of the evidence synthesis above: each should be traceable to concrete results, limitations, or future-work statements.
What makes another loop useful?
Can training guarantee progress under self-application rather than instability, saturation, or spurious fixed points?
When is convergence trustworthy?
Can we distinguish solution-aligned convergence from confidently wrong convergence before an external checker is available?
Where should the next FLOP go?
Depth, breadth, whole-state refinement, or token-wise pondering: which allocation has the highest marginal value?
Can reasoning dynamics be steered?
Can weak-to-strong or verifier-derived directions reshape trajectories without damaging their convergence or general capability?
Is there a coupled scaling law for thinking?
When should a system buy parameters, data, recurrent depth, state capacity, breadth, or wall-clock time?
Reading paths
Enter from the question you care about
Recurrent depth
Universal Transformers → Recurrent Depth → Ouro → LoopFormer → Parcae → Loop, Think, & Generalize
Lens: Why should another loop help?Latent reasoning
Coconut → PonderLM-2 → PonderLM-3 → Latent Recurrent Transformer
Lens: What can hidden thought do that token thought cannot?Flows & dynamics
RIN → Flow Reasoning Models → Attractor Models → Thinking with Looped Flows → Parcae
Lens: Is reasoning progress a form of convergence?Contribute
Help make the map sharper, not just larger.
Suggest a paper, challenge a category, or add a missing failure mode. Every entry should explain its state, update rule, compute policy, and scientific contribution.