Fluid Reasoning Representations

AI summary

Overview

Research area: Mechanistic interpretability of large language models, specifically the internal representation dynamics of extended test-time thinking (long reasoning traces).

Technical level: Advanced. The paper assumes familiarity with activation-space analysis, hidden-state representations, linear probing, and causal interventions such as activation steering and patching.

One-sentence scope: The paper introduces Fluid Reasoning Representations (FRRs) and shows that LLMs' internal representations of actions and predicates become more consistent across obfuscated wordings and drift toward their unobfuscated counterparts over the course of a self-generated reasoning trace, with causal evidence that these representations affect downstream behavior.

What This Paper Is About

Frontier LLMs increasingly solve hard tasks by thinking for a long time at inference, but there is little mechanistic understanding of what extended thinking actually changes inside the model. This paper asks whether test-time thinking merely allocates more search computation, or whether it reshapes the internal representations the model later reasons with. To answer this, the authors study "obfuscated" tasks where task-relevant words are systematically replaced while the underlying problem structure is preserved, and they track how representations of the same operation converge across wordings and align with the corresponding clean concepts.

Key Contributions

1. Defines Fluid Reasoning Representations (FRRs). A representation-level account in which representations of the same action or predicate become more similar across different surface namings and move toward the corresponding unobfuscated concept as reasoning proceeds. FRRs are formalized as three criteria (C1 cross-naming alignment, C2 clean-domain similarity, C3 causal contribution).

2. Provides a measurement pipeline for obfuscated traces. The authors extract action and predicate vectors from LLM activations during BlocksWorld and Mystery BlocksWorld reasoning, center them per naming, and average across namings to isolate shared role information.

3. Establishes causal evidence that these representations matter. Using positive steering, symbolic patching, negative steering, and clean-centroid replacement on controlled planning domains, the paper shows that injecting refined directions improves held-out accuracy relative to Gaussian and shuffled controls, and that subtracting them degrades accuracy.

4. Shows the dynamic predates extended-thinking post-training. Base and instruction-tuned Qwen2.5 models exhibit the same convergence at lower magnitude when fed the same QwQ-generated traces, suggesting extended thinking amplifies and operationally exploits a pre-existing representational substrate rather than creating it.

Main Findings

Representations converge across obfuscated namings. In QwQ-32B, in-naming representations extracted from Mystery naming 1 at 2k, 4k, 7k, and 10k tokens become more similar to their counterparts averaged across other namings as the trace proceeds, plateauing around 7k tokens, while different-action similarities stay lower. The residual similarity among different actions is mainly driven by "stack" and "unstack" being closer to each other than to "pick up" or "put down".

Convergence is the expensive part of reasoning. QwQ-32B solves Standard BlocksWorld with roughly 3.6k tokens, but successful Mystery solutions require 15–20k tokens. The first ~7k tokens align with the convergence phase, suggesting representational alignment rather than raw token count alone is the relevant cost.

Clean-domain representations drift toward the same cross-naming vectors. Clean BlocksWorld representations move toward the cross-naming averages over time, linking obfuscated-trace adaptation to the model's representation of the unobfuscated task. In the clean-domain panel, predicates are omitted because their tokens are harder to identify in clean traces.

Baseline accuracy collapses under obfuscation. On 300 puzzles, QwQ-32B is the strongest open-weight model evaluated, solving regular BlocksWorld at 96% and Mystery BlocksWorld at 35% (36% accuracy preserved). GPT-4.1 (step-by-step) drops from 0.92 to 0.18 (20% preserved), Qwen2.5-32B-base from 0.21 to 0.00, Qwen2.5-32B-instruct from 0.38 to 0.00, Llama-3.3-70B-instruct from 0.40 to 0.02 (5% preserved), DeepSeek-R1-Distill-Qwen-32B from 0.81 to 0.08 (10%), DeepSeek-R1-Distill-Llama-70B from 0.66 to 0.10 (15%), and Nemotron-49B-instruct from 0.48 (marked unparsable formatting) to 0.19 (40% preserved).

Performance depends strongly on the naming. QwQ-32B accuracy varies across namings from 0.05 to 0.47. Coherent alternative domains and reversible-sounding operations are hardest, while abstract or mismatched replacements are easier. Mystery naming 3 uses random strings, and QwQ-32B often recognizes BlocksWorld and maps symbols quickly there (about 2k tokens versus 15–20k elsewhere), so it is excluded from representational analyses.

Positive steering works, and the structured/random asymmetry is the key signal. Random Gaussian steering gains are confined to early layers (L ≤ 10). From layer 20 onward random noise stops helping (layer 20 random Gaussian: −0.36%, p = 0.627), while structured injections continue to yield significant gains (layer 40 cross-naming: +1.43%, p = 0.021). Mean improvements at significant cells are 1.4–1.8%, with per-naming maxima reaching +10% on coherent-domain namings. The ordering is cross-naming >> in-naming ≫ random.

Symbolic patching beats shuffled patching. Replacing residual stream activations for action and predicate tokens with cross-naming "symbolic" representations (constructed as the mean cross-naming vector plus a scaled centered cross-naming representation) consistently outperforms shuffled patching across all tested mixing scales and end layers, with patching over token window [2000, 4000].

Subtracting refined directions selectively degrades accuracy. Negative steering over token window [2000, 4000] using representations extracted at the 4k timestamp degrades held-out accuracy by 2.9% ± 1.06% (start layer 10, end layer 30) relative to a shuffled control of equal magnitude, and by 2.3% ± 0.99% at end layer 20.

Geometric alignment does not guarantee functional interchangeability. Clean-centroid replacement is less disruptive than zeroing for coherent Mystery BlocksWorld namings on Nemotron-49B-instruct, but the advantage disappears for random-letter naming and does not appear in Logistics. Re-run on Qwen2.5-32B-instruct, Qwen2.5-32B-base, and the two highest-C1 LLMs outside QwQ-32B, clean-centroid replacement is consistently more disruptive than zeroing on BlocksWorld, while the two probes are statistically indistinguishable on Logistics.

The dynamic transfers beyond BlocksWorld, but rankings are domain dependent. Cross-naming cosine alignment (C1) is positive in every (LLM, family) cell tested on Mystery Logistics (PDDL Logistics with action and predicate vocabulary obfuscated under five surface variants) and GSM8K-Renamed (math word problems with nouns and operation verbs replaced under four variants, numerals and person names preserved). QwQ-32B gives the clearest BlocksWorld alignment (C1 actions 0.94, predicates 0.93 with 14 namings), while Seed-OSS-36B-instruct leads on GSM8K (0.86 actions) and Qwen2.5-32B-base leads on Logistics (0.84 actions).

Base and instruction-tuned models show a weaker form of the same dynamic. Fed the same QwQ-generated traces, both Qwen2.5-32B-instruct and Qwen2.5-32B-base show qualitatively similar but weaker convergence, with the base model adapting more slowly.

Layer-wise structure emerges with depth. PCA of action representations shows clean action-type clustering at 7k tokens that sharpens with depth, with clear separation between action types emerging around layers 20–30.

Behavioral phases were identified by manual trace inspection. In DeepSeek-R1-Distill-Qwen-32B and QwQ-32B traces, the authors describe comparative analysis of initial and goal states, alternation between recursive search and exploration (occupying the first half of traces), then plan formulation with iterative rebuilding, and finally plan verification.

Alignment holds across many namings. Across 20 namings spanning coherent alternative domains (gardening, legal, cooking), mystical framings, and nonsense strings, baseline accuracy ranges 0.05–0.65 with naming, but C1 holds for every non-degenerate naming, and the cross-naming construction generalizes to namings withheld from steering-vector construction.

Methodology in Plain English

The task setup. The researchers start from BlocksWorld, a classic planning domain where an agent uses pick-up, put-down, stack, and unstack under simple physical constraints. Puzzles were generated and verified with PlanBench. They then create "Mystery BlocksWorld" by replacing every action and predicate with a semantically unrelated word under a complete naming, preserving the logical structure while breaking familiar surface cues. They generated 14 variants beyond the original, yielding 15 obfuscations of the same domain. A puzzle is a unique initial-goal state pair, and the analysis uses 300 four-block puzzles mapped across all 15 namings.

Extracting representations. Following Park et al. (2025), the authors scan the 100-token window before a given timestamp, collect token spans encoding an action or predicate plus one preceding token, average hidden states within each span and then across spans, and repeat every 200 tokens at all layers. Following Venhoff et al. (2025), they center each vector by subtracting the mean over the action or predicate set within a naming, which removes the per-naming common-mode component. They then average the centered vectors across namings to isolate what is shared across surface forms.

Defining the three criteria. An LLM exhibits FRRs if, for some layer, three things hold as the timestamp increases: in-naming vectors align more with their own cross-naming average than with other actions' averages (C1); the cross-naming vector approaches the centered representation of the same concept computed on the unobfuscated domain despite zero token overlap (C2); and injecting the cross-naming vector early improves held-out accuracy more than Gaussian noise, shuffled assignments, or in-naming vectors, while subtracting it degrades accuracy more than a shuffled control (C3).

Testing causality. Steering vectors are collected from 40 correctly solved puzzles and evaluated on a hold-out set of 100 different four-block problem rollouts. The norm-preserving intervention blends the original hidden state with the steering vector at a chosen scale and rescales to the original magnitude. The scale s = 2/3 was selected after a sweep on layer 20 using in-naming representations, and the steering window is [1500, 2500]. Negative steering and symbolic/shuffled patching operate over [2000, 4000]. Replacement steering installs a forward hook that substitutes the clean-naming centroid at obfuscated phrase positions, scored by per-token log-likelihood of each obfuscated trace's own continuation tokens over 30 traces per cell.

Cross-domain replication. The pipeline is also run on Mystery Logistics and GSM8K-Renamed, collecting 200 traces per cell at each LLM's default steering layer (47 for QwQ-32B, 60 for Nemotron-49B-instruct). All experiments are inference-only; no training or fine-tuning is performed. The stack is vLLM v0.7.3 with PyTorch forward hooks.

Why This Matters

Impact on research. The paper reframes extended test-time thinking as something more than longer search: it argues that thinking constructs task-specific symbol meanings in activation space. It also places FRRs on an in-context representational adaptation substrate that already exists in base and instruction-tuned models, which gives interpretability researchers a measurable dynamic, three explicit criteria, and a reusable probing toolkit that extends beyond the single BlocksWorld setting to Logistics and GSM8K-style renaming.

Real-world applications (potential, derived from the paper's framing):

• Diagnosing why reasoning models fail when domain terminology is unfamiliar or arbitrary, such as internal code names, unfamiliar jargon, or renamed business objects.
• Evaluating whether a model's reasoning is grounded in task structure or in memorized surface cues, by measuring cross-naming convergence.
• Guiding training or prompting choices for reasoning models by treating representational alignment (not token count

Authors’ abstract

Frontier large language models increasingly solve complex tasks involving abstract concepts through extended test-time thinking. Yet we lack a mechanistic account of how extended thinking changes hidden-state representations over the course of a reasoning trace. We introduce \textit{Fluid Reasoning Representations} (FRRs), a representation-level account of how LLMs organize action and predicate concepts during self-generated reasoning, and test them on obfuscated planning, symbolic, and mathematical tasks where task-relevant words are replaced while problem structure is preserved. Across open-weight base, instruction-tuned, and extended-thinking LLMs, representations of the same action or predicate become more similar across wordings and move toward the corresponding unobfuscated concepts over the reasoning trace. Causal probes show that these representations affect behavior: cross-naming steering improves held-out accuracy beyond Gaussian and shuffled controls, symbolic patching retains more action information than shuffled patching, and subtracting refined directions degrades accuracy; together, these results suggest that extended thinking strengthens a representation dynamic already present at lower magnitude in base and instruction-tuned LLMs. Our codebase is open-sourced \href{https://github.com/AI4Collaboration/Fluid-Reasoning-Representation}{here}.