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arxiv: 2605.14358 · v1 · pith:CCAUQ6O4new · submitted 2026-05-14 · 💻 cs.AI · cs.LG

Uncovering the Representation Geometry of Minimal Cores in Overcomplete Reasoning Traces

Sanjoy Chowdhury , Dinesh Manocha This is my paper

Pith reviewed 2026-06-30 21:01 UTC · model grok-4.3

classification 💻 cs.AI cs.LG
keywords minimal coreovercomplete reasoning traceschain-of-thoughtlanguage modelsreasoning compressionpredictive necessitytrace geometry
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The pith

Minimal cores isolate the necessary steps in language model reasoning traces by removing nearly half while preserving answers.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper defines minimal cores as the smallest subsets of steps in a generated chain-of-thought trace that still preserve either the final answer or the full predictive distribution. It reports that across six benchmarks in arithmetic, math, science, and QA, greedy extraction removes 46 percent of steps on average while keeping the original answer in 86 percent of cases. Necessity concentrates so that the top three steps carry 65 percent of the measured mass, and the resulting minimal cores show 11-point better separation of correct versus incorrect traces, 34 percent lower intrinsic dimensionality, and 85 percent answer retention when transferred across model families. Readers would care because the work supplies both a practical compression method and theoretical certificates for overcompleteness and sparse support.

Core claim

We define the minimal core as the smallest subset of steps that preserves either the final answer or predictive distribution. Across six deliberative reasoning benchmarks spanning arithmetic, competition mathematics, expert scientific reasoning, and commonsense multi-hop QA, we find substantial overcompleteness: on average, 46% of steps are removable under greedy minimal-core extraction while preserving the original answer in 86% of cases. We also find that predictive support is concentrated: the top three steps account for 65% of measured necessity mass on average. Beyond compression, minimal cores expose a cleaner geometry of reasoning: compared with full traces, they improve correct-incor

What carries the argument

The minimal core, defined as the smallest subset of reasoning steps that preserves the final answer or predictive distribution under greedy elimination.

If this is right

  • Greedy extraction yields an average compression ratio of 46 percent of steps while retaining the answer in 86 percent of cases.
  • Necessity mass concentrates so the top three steps account for 65 percent on average.
  • Minimal cores improve correct-incorrect trace separation by 11 points over full traces.
  • Estimated intrinsic dimensionality drops 34 percent in minimal cores.
  • Minimal cores retain answers at 85 percent when transferred across model families.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If minimal cores capture effective support, then generation-time pruning of non-core steps could reduce token usage with little accuracy loss.
  • The observed concentration of necessity suggests step-level importance scores could be computed directly from extraction runs for interpretability.
  • The geometric improvements imply minimal cores may align more closely with the model's internal decision geometry than full traces do.
  • The existence and irreducibility certificates could be turned into practical audits that flag overcomplete traces in deployed systems.

Load-bearing premise

Removing steps while preserving the final answer or predictive distribution means those steps were unnecessary for the model's internal computation.

What would settle it

Running the same model on held-out problems using only the extracted minimal-core steps and observing whether the answer distribution matches the full-trace distribution.

Figures

Figures reproduced from arXiv: 2605.14358 by Dinesh Manocha, Sanjoy Chowdhury.

Figure 1
Figure 1. Figure 1: LLM reasoning traces are substantially overcomplete. Generated traces contain a sparse predictive core surrounded by removable reasoning mass. Minimal-core extraction separates answer￾supporting steps from redundant elaboration and exposes a compact, transferable representation geometry of reasoning. We study this problem through the lens of overcomplete reasoning traces. A trace is overcomplete if it cont… view at source ↗
Figure 2
Figure 2. Figure 2: Compact diagnostics for overcomplete reasoning traces. The panels show: (a) greedy deletion degrades more gracefully than necessity-guided or random pruning beyond the matched budgets in Tab. 2; (b) redundancy mass concentrates at moderate-to-high values for both math and non-math tasks; (c) necessity mass is concentrated in a few steps, above a uniform baseline; (d) minimal-core length grows sublinearly w… view at source ↗
Figure 3
Figure 3. Figure 3: Expanded diagnostics for overcomplete reasoning traces. Shaded bands show cross-model [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Transfer analysis. Minimal cores transfer strongly off-diagonal and preserve most of [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Extraction-method tradeoffs. Greedy deletion lies at the high-fidelity end of the frontier, [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Robustness diagnostics across sufficiency criteria, prompting styles, difficulty levels, and [PITH_FULL_IMAGE:figures/full_fig_p025_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Additional representation diagnostics. Minimal cores improve correctness predictiveness [PITH_FULL_IMAGE:figures/full_fig_p026_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Qualitative examples of overcomplete reasoning traces, part I. Green steps are retained in the extracted minimal core; red steps are removed by sufficiency-preserving deletion. Removed steps often include verification, caveats, alternative paths, or explanatory scaffolding, while minimal cores retain the decisive operations or factual links needed for the prediction. Takeaway. Tab. 12 and [PITH_FULL_IMAGE… view at source ↗
Figure 9
Figure 9. Figure 9: Qualitative examples of overcomplete reasoning traces, part II. Minimal cores retain the decisive factual links needed for the answer, while removable steps often contain setup, caveats, or explanatory context that does not change the prediction. 28 [PITH_FULL_IMAGE:figures/full_fig_p028_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Qualitative examples of overcomplete reasoning traces, part III. Even short correct traces can contain removable setup or optional checking. The extracted minimal core keeps the operations needed to preserve the answer while deleting behaviorally redundant steps. 1 2 3 4 5 0.2 0.4 0.6 0.8 Top-k steps Cumulative mass (a) Cumulative necessity mass All avg. ± range All avg. Math avg. Non-math avg. GSM8K MATH… view at source ↗
Figure 11
Figure 11. Figure 11: Additional necessity diagnostics. Panel (a) shows cumulative top- [PITH_FULL_IMAGE:figures/full_fig_p029_11.png] view at source ↗
read the original abstract

Language models often generate long chain-of-thought traces, but it remains unclear how much of this reasoning is necessary for preserving the final prediction. We study this through the lens of overcomplete reasoning traces: generated traces that contain more intermediate steps than are needed to support the model's answer. We define the minimal core as the smallest subset of steps that preserves either the final answer or predictive distribution, and introduce metrics for compression ratio, redundancy mass, step necessity, and necessity concentration. Across six deliberative reasoning benchmarks spanning arithmetic, competition mathematics, expert scientific reasoning, and commonsense multi-hop QA, we find substantial overcompleteness: on average, 46% of steps are removable under greedy minimal-core extraction while preserving the original answer in 86% of cases. We also find that predictive support is concentrated: the top three steps account for 65% of measured necessity mass on average. Beyond compression, minimal cores expose a cleaner geometry of reasoning: compared with full traces, they improve correct-incorrect trace separation by 11 points, reduce estimated intrinsic dimensionality by 34%, and transfer across model families with 85% off-diagonal answer retention. Theoretically, we establish existence of minimal sufficient subsets, local irreducibility guarantees for greedy elimination, and certificates of overcompleteness and sparse necessity. Together, these results suggest that full reasoning traces are often verbose and overcomplete, while minimal cores isolate the effective support underlying language-model predictions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript claims that language model reasoning traces are often overcomplete, defining minimal cores as the smallest subsets of steps preserving the final answer or predictive distribution under greedy extraction. Across six benchmarks it reports 46% average step removability while preserving answers in 86% of cases, with necessity concentrated (top-3 steps account for 65% of necessity mass), plus geometric gains (11-point improvement in correct-incorrect separation, 34% reduction in intrinsic dimensionality) and 85% cross-model transfer. Theoretical results establish existence of minimal sufficient subsets and local irreducibility of the extraction procedure.

Significance. If the interpretation linking output preservation to internal effective support were substantiated, the work would supply concrete compression metrics and geometric diagnostics for reasoning traces, with implications for interpretability and efficiency. The scale of the empirical survey and the existence/irreducibility theorems would constitute a useful contribution to the study of verbose CoT traces.

major comments (1)
  1. [Abstract] Abstract: The claim that minimal cores 'isolate the effective support underlying language-model predictions' and expose a 'cleaner geometry of reasoning' is not supported by evidence that removed steps are irrelevant to the model's internal forward pass. All metrics (necessity mass, necessity concentration, separation, dimensionality) are computed solely from output invariance under greedy elimination; the manuscript describes no causal interventions on hidden states, attention ablation, or logit-lens probes on intermediate tokens that would confirm internal routing through the retained steps. This gap is load-bearing for the representation-geometry claims in the title and abstract.
minor comments (2)
  1. The abstract states results across six benchmarks without reporting per-benchmark breakdowns, sample sizes, or confidence intervals on the headline percentages (46%, 86%, 65%, 11 points, 34%, 85%), making it difficult to assess robustness or variability.
  2. Notation for the necessity-mass and necessity-concentration metrics is introduced in the abstract but not connected to the precise definition of the greedy extraction procedure or to the theoretical certificates mentioned later.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback. The major comment correctly identifies that our claims about isolating effective support and representation geometry rest on output-based metrics rather than internal causal evidence. We address this below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that minimal cores 'isolate the effective support underlying language-model predictions' and expose a 'cleaner geometry of reasoning' is not supported by evidence that removed steps are irrelevant to the model's internal forward pass. All metrics (necessity mass, necessity concentration, separation, dimensionality) are computed solely from output invariance under greedy elimination; the manuscript describes no causal interventions on hidden states, attention ablation, or logit-lens probes on intermediate tokens that would confirm internal routing through the retained steps. This gap is load-bearing for the representation-geometry claims in the title and abstract.

    Authors: We agree that the manuscript provides no causal interventions, hidden-state ablations, or logit-lens analyses to establish that removed steps are irrelevant to the internal forward pass. All reported metrics (necessity mass, concentration, separation, and dimensionality reduction) are defined strictly in terms of output invariance under greedy step elimination. The interpretation that minimal cores isolate 'effective support underlying language-model predictions' is therefore an inference from behavioral necessity rather than direct internal evidence. To correct this, we will revise the abstract, title, and introduction to frame the contribution in terms of output-preserving minimal cores and their observable geometric properties in the space of reasoning traces. We will also add an explicit limitations paragraph stating that the work does not claim to identify internal routing or causal support within the model. These changes will be made in the next revision. revision: yes

Circularity Check

0 steps flagged

No circularity: operational definitions and empirical measurements are independent of target claims

full rationale

The paper defines the minimal core explicitly as the smallest subset preserving final answer or predictive distribution under greedy extraction, then computes compression ratio, necessity mass, and geometric metrics directly from that procedure and model outputs. Theoretical results establish existence and local irreducibility via standard set-theoretic arguments without self-referential equations or fitted parameters. No load-bearing step reduces to a self-citation, ansatz smuggled via prior work, or renaming of known results; all quantities are measured from the defined extraction process itself. The interpretation linking output preservation to internal necessity is interpretive rather than a derivation that collapses by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no information on free parameters, background axioms, or new postulated entities; all claims are stated at the level of definitions and aggregate statistics.

pith-pipeline@v0.9.1-grok · 5789 in / 1108 out tokens · 38546 ms · 2026-06-30T21:01:55.434583+00:00 · methodology

discussion (0)

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