{"id":"05b097de-1750-43ec-9b7b-373ddbb9fb8f","arxiv_id":"2602.04843","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"During long reasoning traces, QwQ-32B progressively refines action and predicate representations toward naming-invariant 'symbolic' vectors, and steering with these vectors modestly improves obfuscated planning accuracy.","lead":"This paper studies how a reasoning LLM (QwQ-32B) changes its internal representations of actions and predicates while solving obfuscated BlocksWorld puzzles, finding that semantically equivalent actions converge toward shared 'symbolic' vectors over the course of long reasoning traces. The authors use activation steering and patching to argue these refined representations causally improve puzzle-solving accuracy, with modest but statistically suggestive gains.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Cross-naming average in Eq. (3) includes each naming, so convergence and steering may be inflated; leave-one-out control is needed.","rationale":"The reader's weakest_assumption identifies exactly the self-referential estimator in Eq. (3), and this is the most load-bearing concern because it threatens the primary descriptive evidence (Fig. 4a) and the cross-naming steering/patching vectors. The paper does include independent checks (Fig. 2 pairwise, Fig. 4b clean BlocksWorld), which keep the work from being rejected, but those checks do not validate the cross-naming average used in the main narrative and causal interventions. The reader's verdict of CONDITIONAL is appropriate: the concern is real and requires a concrete control, but the existing independent support and the overall plausibility of the mechanism mean a conditional accept with a required reanalysis is the right call. I agree with the reader's assessment; no change to the verdict is needed, but the concern should be explicitly addressed in revision.","tokens_in":19182,"tokens_out":3020,"duration_ms":35418,"concrete_test":"Recompute the Fig. 4a analysis with leave-one-out cross-naming representations: for each naming N, compute the cross-naming average Excl(N) = (1/(|N|-1)) * sum_{M != N} r_tilde_M, and plot similarity of r_tilde_N to Excl(N) over timestamps. Additionally, repeat the positive steering experiment (Section 4.1, layer 20 and 40) using cross-naming vectors built without the target naming, comparing accuracy gains to the full-average condition. If the convergence plateau and the significant steering improvements (p<0.05) disappear under leave-one-out, the self-inclusive average is responsible for the observed effects.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central convergence evidence (Fig. 4a) measures similarity of each naming's centered representations to the cross-naming average defined in Eq. (3) over all namings, including the very naming being compared. Since every naming contributes to the average, part of the observed convergence is mechanical: as representations shift, they move toward a target that contains themselves. This inflates the 'same action' similarity and can also affect the increasingly negative 'different actions' similarity, which is computed against the same self-inclusive average. The concern is not merely statistical: the same cross-naming representations are used as steering vectors in Section 4.1 and as 'symbolic' replacements in Section 4.2. If the average encodes naming-specific surface features (or generic trace-position/syntax directions) rather than a clean invariant semantic core, then the causal experiments may be injecting the model's own naming-specific statistics rather than abstract structure. The paper does provide non-self-referential comparisons in Fig. 2 (pairwise naming 1 vs. others) and Fig. 4b (clean BlocksWorld vs. mystery namings), which partially support convergence, but those analyses are secondary and do not directly validate the cross-naming average that underpins the symbolic abstraction and steering claims. A leave-one-out variant—where each naming is compared to an average computed over all other namings—would directly test whether the convergence and steering benefits persist when the target naming is excluded. If convergence disappears or steering gains vanish, the central claim that representations converge to a naming-invariant symbolic code is not supported; if they persist, the self-inclusion concern is resolved. This is the most load-bearing weakness because it affects both the descriptive and causal pillars of the paper.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces 'Fluid Reasoning Representations' (FRRs) and studies QwQ-32B on Mystery BlocksWorld, a semantically obfuscated planning domain. The authors extract centered action/predicate representations from hidden states at different reasoning timestamps and define cross-naming representations as averages over 15 namings. They report that (i) same-action representations across different namings become more similar over the reasoning trace and move toward clean BlocksWorld representations; (ii) positive steering with refined in-naming and cross-naming vectors improves held-out accuracy, with cross-naming vectors most effective; (iii) symbolic patching with cross-naming vectors outperforms shuffled controls; and (iv) subtracting refined directions degrades accuracy. They conclude that extended reasoning dynamically constructs context-specific, naming-invariant representational spaces, and that this is a key mechanism behind reasoning models' performance on abstract tasks. The paper includes open-source code, multiple naming variants, and a base-model comparison.","tokens_in":19505,"tokens_out":5627,"duration_ms":62193,"significance":"If the findings hold, this is a valuable mechanistic contribution to interpretability of reasoning LLMs: it identifies a concrete representational process—dynamic refinement toward shared symbolic encodings—that could explain part of the reasoning model advantage on obfuscated tasks. The paper has notable strengths: it provides a codebase, uses 15 naming variants, includes leave-one-out pairwise evidence in Fig. 2, compares against clean BlocksWorld in Fig. 4b, and attempts causal validation through steering and patching with controls. However, the central convergence metric and the causal vectors both rely on a cross-naming average that includes the query naming (Eq. 3), and the statistical support for the causal claims is thin once multiple testing is considered. The core idea is plausible and testable, but the current evidence requires additional analyses before the claims are fully supported.","major_comments":[{"comment":"The main convergence plot measures each naming's centered representation against the cross-naming average defined in Eq. (3), which is computed over all namings including the query naming itself. Since each naming contributes to the average, the similarity at the extraction timestamp has a mechanical self-inclusion component; similarly, the 'different actions' similarity is computed against an average that contains the query action. This inflates the observed convergence and separation. The same cross-naming representations are used as steering vectors in Section 4.1 and as the basis for symbolic patching in Section 4.2, so if the average encodes naming-common surface statistics or trace-position/syntax directions rather than a clean invariant semantic core, the causal conclusions are also affected. Please provide a leave-one-out version of Fig. 4a (and, where feasible, leave-one-out ste","section":"Section 3.2, Eq. (3), Fig. 4a"},{"comment":"The statistical evidence for steering improvements is not robust to multiple testing. Table 5 reports 10 one-sided t-tests at alpha=0.05; 3 are significant, but the smallest p-value is 0.021, which is above a Bonferroni threshold of 0.005. Under 10 independent tests, about 0.5 false positives are expected by chance. The claim in Fig. 6 that 'cross-naming > in-naming >> random' is also not supported by Table 5: at layer 30 cross-naming has p=0.139, and at layer 40 in-naming has p=0.274. Moreover, Figs. 2, 4, and 5 show no confidence intervals or significance tests. Please report adjusted p-values (e.g., Benjamini-Hochberg), provide confidence intervals for the mean improvements, and consider pre-registering or limiting the primary comparisons to avoid selection effects from the reported layer/condition search.","section":"Section L, Table 5"},{"comment":"The symbolic patching experiment inherits the self-inclusion issue: the 'symbolic' vectors are constructed from the same cross-naming averages of Eq. (3), which include the naming being patched. This makes it difficult to attribute the observed advantage over shuffled control to naming-invariant abstraction rather than to shared naming-specific statistics. In addition, Fig. 7 provides no statistical test; the error bars (s.e. across namings) are descriptive. A leave-one-out variant of the symbolic vectors (excluding the target naming from the average) would directly address the abstraction claim. The paper's existing non-self-referential evidence (Fig. 2 and Fig. 4b) partially supports convergence, but it does not validate the specific vectors used in the causal experiments.","section":"Section 4.2, Eq. (6), Fig. 7"}],"minor_comments":[{"comment":"The statement that 'some version of Mystery BlocksWorld was present in QwQ-32B's training data' is an inference from shorter traces and manual analysis. This is an important exclusion criterion (naming 3 is dropped), but it is not directly verified. Please soften the claim or provide additional evidence, and discuss how residual partial recognition of other namings could affect the results.","section":"Section 2.2"},{"comment":"The base-model comparison feeds QwQ-generated traces to the base model. Differences in adaptation speed may reflect distribution shift (base model processing unnatural traces) rather than fundamental model capability. A cleaner comparison would use base-model-generated traces (or at least control for trace difficulty), or the claim should be limited to 'base models can adapt in-context when given a long context'.","section":"Section 3.3"},{"comment":"The main text says the window size is w=100, while Appendix F.1 states '200 is selected to contain at least 10 action mentions.' Please reconcile this inconsistency.","section":"Section 2.3 vs. Appendix F.1"},{"comment":"Minor typo: 'preformed' should be 'performed'.","section":"Appendix F.1"},{"comment":"The notation v_type[a] is introduced without a formal definition; it refers to the three vector types (in-naming, cross-naming, random). Please define it explicitly.","section":"Section 4.1"}],"recommendation":"major_revision","confidential_remarks":"The paper's central hypothesis is interesting and the open-source code is a plus. However, the main convergence and causal evidence depend on a self-inclusive average, and the statistical support is fragile under multiple-testing corrections. These are fixable with additional analysis (leave-one-out, adjusted p-values), not fundamental errors. I recommend major revision and encourage the authors to strengthen the evidence before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a well-designed descriptive study with a plausible mechanism story, but the headline convergence metric in Fig 4a is inflated by a self-inclusive average, and the causal effects are small enough that the strong framing in the abstract outruns the evidence. Still, it deserves a serious referee; the authors have done enough independent checks that the central direction likely holds.\n\nWhat's actually new: applying the in-context representation learning methodology from Park et al. to 15–20k-token reasoning traces in Mystery BlocksWorld with 15 namings, and showing that action/predicate representations converge across wordings as reasoning proceeds. That is a new phenomenon and the paper documents it carefully: Fig 2 gives a leave-one-out pairwise analysis for naming 1, Fig 4b compares mystery representations against clean BlocksWorld, and the appendix includes several other models plus base-model comparisons. The paper is honest about its limitations and discloses exploratory controls. Code is open-sourced; that's real.\n\nWhere the soft spots are: the central convergence plot, Fig 4a, measures each naming's similarity to a cross-naming average that includes that naming (Eq. 3). That mechanically inflates the same-action similarity and can also create the increasingly negative different-action similarity. The concern lands. The same average is then used as steering vectors, so the causal experiments inherit the potential contamination. The paper does provide non-self-referential support—Fig 2's leave-one-out and the clean BlocksWorld comparison—so this is not fatal, but the authors should redo the analysis with leave-one-out averaging and report confidence intervals and significance tests for the similarity curves.\n\nThe steering statistics are fragile: Table 5 runs one t-test per layer and condition; only three are nominally significant at p<0.05, and no multiple-comparison correction is applied. The effect sizes (1.4–1.8% accuracy on top of a ~30% baseline) are modest, and some early-layer improvements appear even with random vectors. The layer/scale/window choices are post hoc. These concerns are real, but proportionate: the pattern across layers and controls suggests something is there.\n\nWho should read it: people working on mechanistic interpretability of reasoning models, and anyone using steering as evidence for representation-level claims. It is not a home run, and the abstract overstates the strength of the evidence, but it is a genuine empirical contribution.\n\nRecommendation: send to peer review, with both the leave-one-out control and the multiple-comparison issue as mandatory revision points. If the authors fix those faithfully, the paper would be a solid contribution.","headline":"A credible descriptive result about representational convergence during extended reasoning, but the key metric is partly self-referential and the causal evidence is statistically fragile; still worth refereeing.","tokens_in":20048,"tokens_out":2557,"would_cite":true,"duration_ms":26307,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"During extended reasoning, QwQ-32B's internal representations of actions converge to abstract, naming-independent encodings, and steering those encodings measurably changes problem-solving accuracy.","keywords":["Fluid Reasoning Representations","mechanistic interpretability","reasoning language models","Mystery BlocksWorld","activation steering","symbolic abstraction","representation convergence","chain-of-thought"],"falsifier":"Compute the convergence metric with a leave-one-out cross-naming average (exclude the target naming from the mean) and check whether similarity still rises during reasoning; if it does not, the observed convergence is an artifact of the estimator. A second check: steer with cross-naming vectors built from namings never used in the steering set; if held-out accuracy does not improve, the vectors are not naming-invariant.","tokens_in":19056,"feed_emoji":"🧠","tokens_out":4062,"duration_ms":40477,"temperature":0.7,"pith_summary":"This paper tries to establish why reasoning language models outperform ordinary LLMs on abstract tasks whose vocabulary has been deliberately scrambled: not merely because they search longer, but because their internal vector representations of actions and predicates are progressively rebuilt during the reasoning trace. Using Mystery BlocksWorld, where 'pick up' becomes 'attack' and 'on top of' becomes 'craves', the authors show that QwQ-32B's hidden states for the same logical action grow more similar across different wordings as reasoning proceeds, and move toward the representations the model uses on the unobfuscated task. They then show these changes matter: injecting the refined representations into early reasoning improves held-out accuracy beyond random controls, while subtracting or scrambling them degrades accuracy. The paper names this phenomenon Fluid Reasoning Representations and argues it is a general capability present in base models too, with extended thinking supplying the context needed to activate it. A sympathetic reader would care because it offers a concrete, testable mechanism for what 'thinking longer' does inside a model, with implications for both interpretability and intervention.","feed_headline":"Thinking longer makes a model's action codes abstract","feed_subtitle":"In obfuscated planning puzzles, QwQ-32B's hidden states for the same action converge across wordings, and steering them improves accuracy.","key_machinery":"The load-bearing object is the cross-naming representation, defined as the average of centered in-naming representations across all namings (Eq. 3): for each action, one subtracts the mean over actions within a naming, then averages the resulting directions across 14 obfuscated wordings to cancel naming-specific surface features and expose an invariant semantic core. This averaged vector serves both as the target for measuring representational convergence and as the steering/patching vector in the causal experiments. The steering rule itself — a norm-preserving convex combination of the token's hidden state with the target vector — is the mechanism by which the paper injects or subtracts the","core_discovery":"On the paper's own terms, the central discovery is that QwQ-32B dynamically constructs context-specific representational spaces during extended reasoning. Over the course of a 15–20k-token chain of thought on semantically obfuscated BlocksWorld puzzles, hidden-state representations of the same action or predicate across different namings become more similar to each other, more similar to the clean BlocksWorld representations, and more separated from representations of different actions. The paper introduces Fluid Reasoning Representations (FRRs) to name this progressive refinement, and reports causal evidence: positive steering with refined representations, especially cross-naming averages,","pith_inferences":["I infer that the same convergence dynamic should appear in other fixed-action-space planning domains (e.g., Towers of Hanoi) and in mathematical reasoning with redefined notation, though the paper only tests BlocksWorld.","A sharper test than the paper's would use leave-one-out cross-naming averages to confirm the convergence is not an artifact of measuring similarity to a mean that includes the measured point.","If the shared direction in late-layer action vectors (seen in shuffled-control gains) is a generic 'action-ness' component, then part of the steering effect may come from injecting task-generic structure rather than naming-invariant semantics; the paper flags but does not resolve this.","One could test transfer by computing cross-naming vectors from one set of namings and steering on a held-out naming; the paper's Table 4 hints at heterogeneous per-naming responsiveness that such a design would quantify."],"forward_implications":["If correct, accuracy gains on obfuscated tasks are partly attributable to in-context representational refinement, not just extended search or memorized shortcuts.","Cross-naming steering transfers task knowledge across wordings, implying learned abstraction is portable across surface forms.","Base and instruction-tuned models already exhibit the refinement dynamic, so reasoning-model training may mainly supply the long context that lets the dynamic unfold.","Steering and patching offer a practical handle: model behavior on abstract tasks can be improved or disrupted by editing these refined directions."],"fun_headline_variants":["Longer reasoning makes LLM action codes more abstract","Abstract codes emerge as LLMs think longer","Deep thinking refines action representations in LLMs","Reasoning length drives abstraction of action concepts","LLM action codes converge with extended thought"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The cross-naming representation is an average of centered representations that includes the very naming being compared, and the paper assumes this average cancels surface features while preserving semantic content; if instead that average captures shared syntax, trace position, or a generic action-token direction, the convergence and steering results would not demonstrate symbolic abstraction.","fun_headline_variants_meta":{"raw":{"variants":["Longer reasoning makes LLM action codes more abstract","Abstract codes emerge as LLMs think longer","Deep thinking refines action representations in LLMs","Reasoning length drives abstraction of action concepts","LLM action codes converge with extended thought"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000175,"raw_usage":{"total_tokens":1111,"prompt_tokens":724,"completion_tokens":387,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":468,"completion_tokens_details":{"reasoning_tokens":328}},"tokens_in":468,"tokens_out":387,"duration_ms":5196,"temperature":1.0,"reasoning_tokens":328,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T04:24:38.894246+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the convergence metric with a leave-one-out cross-naming average (exclude the target naming from the mean) and check whether similarity still rises during reasoning; if it does not, the observed convergence is an artifact of the estimator. A second check: steer with cross-naming vectors built from namings never used in the steering set; if held-out accuracy does not improve, the vectors are not naming-invariant.","supporting_citations":[],"review_version":1}