Day 11 · When Your Chain of Thought Collapses (ProblemMap No.6)

[PSBigBig]

I’m PSbigbig. After watching hundreds of Python RAG and agent pipelines fail, I stopped believing bugs were random. Many failures repeat with the same fingerprints — they are math-shaped, not noise. Today’s focus is Logic Collapse & Recovery, also called No.6 in the Problem Map.

The story developers already know​

You’re running a multi-step reasoning chain:

1. Step 1 looks fine.
2. Step 2 repeats the question in slightly different words.
3. Step 3 outputs “intuitively, therefore…” and fills a paragraph with elegant but hollow prose.
4. Citations vanish. You’re left with filler and zero logical progress.

It feels like the model “kept talking” but the reasoning stalled.

You think: maybe my prompt wasn’t strong enough, maybe the model is weak at logic.
What actually happened: a collapse event — the model lost its reasoning state and invented a “fake bridge” to cover the gap.

Why it matters​

• Hidden errors: production logs look fluent, but correctness is gone.
• Eval mismatch: offline BLEU/ROUGE may pass, but logical depth is zero.
• User confusion: end-users see “answers” that sound confident yet skip the actual step.

How to catch collapse in 60 seconds​

1. Challenge test: ask a 3-hop reasoning task (conditional proof, small math puzzle).

• If the middle hop drifts into filler, collapse detected.

1. Paradox probe: add a self-referential clause.

• If the output smooths over it with generalities, you hit a fake bridge.

1. Rebirth operator: insert a self-repair instruction:

• “stop. identify last valid claim. restart reasoning from there.”
• If the model actually resets, you confirmed collapse was happening.

Minimal Fix Strategy​

Goal: Detect collapse early and re-anchor the chain.

• Rebirth operator: explicit reset to the last valid anchor (last cited span or equation).
• ΔS progression gate: measure semantic distance between steps; if ΔS < 0.15, block output.
• Citation guard: no step is valid without a snippet or equation id.
• Entropy clamp: if token entropy drops sharply, trigger recovery.

Diagnose Checklist​

• sudden entropy drop in generated tokens
• reasoning step grows in length but ΔS compared to prior step ≈ 0
• citations vanish mid-chain
• paraphrased queries produce diverging answers

If you see two or more, you are in No.6 Logic Collapse territory.

Code You Can Paste​

A tiny toy to detect step collapse by monitoring semantic distance:

import numpy as np
from sklearn.metrics.pairwise import cosine_similarity

def delta_s(vec_a, vec_b):
    return float(cosine_similarity([vec_a], [vec_b])[0][0])

def detect_collapse(step_vecs, threshold=0.15):
    # step_vecs: list of embeddings for each reasoning step
    for i in range(len(step_vecs)-1):
        if delta_s(step_vecs[i], step_vecs[i+1]) < threshold:
            return True
    return False

# usage: pass embeddings of reasoning steps
# returns True if a collapse event is likely

And a conceptual rebirth operator:

def rebirth(chain, last_valid_idx):
    """Truncate to last stable step and restart reasoning."""
    return chain[:last_valid_idx+1] + ["[RESTART reasoning here]"]

Harder Fixes​

• enforce citation-first schema: don’t allow synthesis without anchors
• run multiple parallel chains; drop collapsed ones
• retrain rerankers to favor progressive spans, not just semantic closeness
• add regression tests with paradox queries to flush out brittle logic

Acceptance Gates Before You Ship​

• ΔS progression ≥ 0.15 at every step
• each step carries a citation or anchor
• rebirth triggers visible resets, not silent filler
• answers converge across three paraphrases

TL;DR​

Logic collapse isn’t random. It’s a repeatable bug where reasoning halts and the model invents filler. Detect it by measuring semantic progression, suppress low-ΔS steps, and enforce rebirth operators. Once you do, chains can handle paradoxes and multi-hop logic without drifting into platitudes.

Full map of 16 reproducible failure modes (MIT, reproducible):
ProblemMap · Article Index

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