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arxiv: 2605.07990 · v1 · submitted 2026-05-08 · 💻 cs.CL · cs.AI· cs.LG· cs.SE

Recognition: 2 theorem links

· Lean Theorem

Tool Calling is Linearly Readable and Steerable in Language Models

Zekun Wu (1 , 2) , Ze Wang (1 , Seonglae Cho (2) , Yufei Yang (3) , Adriano Koshiyama (1 , Sahan Bulathwela (1) , Maria Perez-Ortiz (1) ((1) University College London
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(2) Holistic AI (3) Imperial College London)
Authors on Pith no claims yet

Pith reviewed 2026-05-11 03:04 UTC · model grok-4.3

classification 💻 cs.CL cs.AIcs.LGcs.SE
keywords tool callingactivation steeringlinear representationsmechanistic interpretabilitylanguage model agentserror detection
0
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The pith

The identity of the tool a language model chooses is linearly readable from its activations and can be switched by adding a mean difference vector.

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

Language models internally represent the tool they will call in a linear way that can be read directly from hidden states. Researchers calculate the average activation pattern for each tool across prompts and use the difference between two such patterns as a steering vector. Adding this vector during a forward pass causes the model to select the alternate tool at 77-100 percent accuracy on simple prompts, after which it generates JSON arguments that match the new tool's schema. The same averages also identify likely mistakes in advance because queries with small gaps between the top two tools produce far more errors. The pattern appears across model sizes from hundreds of millions to tens of billions of parameters and persists even in base models before instruction tuning.

Core claim

The identity of the chosen tool is linearly readable and steerable inside the model. Adding the mean-difference between two tools' average internal activations switches which tool the model selects at 77-100% accuracy on name-only single-turn prompts (93-100% at 4B+), and the JSON arguments that follow autoregressively match the new tool's schema. The causal effect concentrates along one direction, the row of the output layer that produces the target tool's first token. Activation patching localises this to a small set of mid- and late-layer attention heads, and a within-topic probe across 14 same-domain airline tools reaches 61-89% accuracy, ruling out a pure topic explanation. Even base 4B

What carries the argument

the mean-difference vector between average internal activations for each tool

Load-bearing premise

The vector difference between average activations for different tools specifically encodes tool identity rather than correlated features such as query topic or prompt syntax.

What would settle it

If adding the mean-difference vector between two tools no longer produces the new tool name and matching JSON schema at high rates on a fresh set of prompts outside the original calculation set, the linear steerability claim would fail.

Figures

Figures reproduced from arXiv: 2605.07990 by 2), (2) Holistic AI, (3) Imperial College London), Adriano Koshiyama (1, Maria Perez-Ortiz (1) ((1) University College London, Sahan Bulathwela (1), Seonglae Cho (2), Yufei Yang (3), Zekun Wu (1, Ze Wang (1.

Figure 1
Figure 1. Figure 1: Overview of the three-stage circuit and steering demonstration. Adding a mean-difference vector redirects [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Left: 3D PCA of 15-tool activations, one model per family. Right: cumulative variance converges to [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Mean steering accuracy vs model scale across [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Linearity of tool selection. Cosine similar [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Steering vectors align with unembedding di [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Steering accuracy across 12 models × 4 bench￾marks. 0 20 40 60 80 100 Switch accuracy (%) Finance (10t) Health (10t) Sports (10t) Science (10t) Music (10t) Travel (10t) 75% 75% 0% 80% 55% 95% Cross-domain: 100% ToolBench per-domain steering (Gemma 3 4B) [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: ToolBench per-domain steering (Gemma 3 4B). Sports fails due to near-synonymous tools. LAYER SAE FEATURE NEURONPEDIA LABEL 2 tc-262k 159677 “tool description” 9 tc-262k 73435 “tool selection” 9 res-16k 5625 “function calls” 16 tc-262k 177725 “tool calls” 17 res-16k 1645 “function calls” 17 res-16k 15177 “tools and their functions” 22 tc-262k 19924 “tool use invocation” 22 res-16k 3122 “function calls” 25 t… view at source ↗
Figure 9
Figure 9. Figure 9: k90 as the number of real ToolBench APIs grows from 5 to 2,000, across 12 instruction-tuned mod￾els from three families (Gemma 3, Qwen 3 / Qwen 2.5, Llama 3.1; stratified sampling across 49 domains, with descriptions). All models compress tool activations into k90 that grows far slower than K, but the absolute level depends more on architecture (attention heads) than parameter count: the Gemma 3 family (bl… view at source ↗
Figure 10
Figure 10. Figure 10: Phase transition at α≈0.7. 4B+ models jump to 95–100% with no collapse. 0 20 40 60 80 100 120 140 Number of tools (K) 60 70 80 90 100 Switch accuracy (%) 90% Gemma 3 Qwen 3 Llama 3.1 Qwen 2.5 [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: K-tool scaling. Larger models sustain accu￾racy better. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: Base vs IT. Left: 5-tool accuracy (base im [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Attribution patching peak layer. IT peaks at [PITH_FULL_IMAGE:figures/full_fig_p021_14.png] view at source ↗
Figure 12
Figure 12. Figure 12: SAE feature sharpening across layers. Spe [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 15
Figure 15. Figure 15: Cross-tool divergence by layer depth. Di [PITH_FULL_IMAGE:figures/full_fig_p022_15.png] view at source ↗
Figure 17
Figure 17. Figure 17: 3D PCA of 39 tools from 3 sources (15 syn [PITH_FULL_IMAGE:figures/full_fig_p022_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Linearity interpolation for all 4 tested tool [PITH_FULL_IMAGE:figures/full_fig_p022_18.png] view at source ↗
read the original abstract

When a tool-calling agent picks the wrong tool, the failure is invisible until execution: the email gets sent, the meeting gets missed. Probing 12 instruction-tuned models across Gemma 3, Qwen 3, Qwen 2.5, and Llama 3.1 (270M to 27B), we find the identity of the chosen tool is linearly readable and steerable inside the model. Adding the mean-difference between two tools' average internal activations switches which tool the model selects at 77-100% accuracy on name-only single-turn prompts (93-100% at 4B+), and the JSON arguments that follow autoregressively match the new tool's schema, so flipping the name is enough. The same per-tool means also flag likely errors before they happen: on Gemma 3 12B and 27B, queries where the gap between the top-1 and top-2 tool is smallest produce 14-21x more wrong calls than queries with the largest gap. The causal effect concentrates along one direction, the row of the output layer that produces the target tool's first token: a unit vector along it at matched magnitude already reaches 93-100%, while what is left over leaves the choice almost untouched. Activation patching localises this to a small set of mid- and late-layer attention heads, and a within-topic probe across 14 same-domain $\tau$-bench airline tools reaches top-1 61-89% across five 4B-14B models, ruling out the reading that we are just moving the model along a topic axis. Even base models encode the right tool before they can emit it: cosine readout from the internal state recovers 69-82% on BFCL while base generation reaches only 2-10%, suggesting pretraining forms the representation and instruction tuning later wires it to the output. We measure tool identity selection and JSON schema correctness in single-turn fixed-menu settings; multi-turn agentic transfer is more fragile and is discussed in Limitations.

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

2 major / 4 minor

Summary. The manuscript claims that tool identity in language models is linearly readable and steerable via internal activations. Across 12 instruction-tuned models (Gemma 3, Qwen 3/2.5, Llama 3.1; 270M–27B), mean-difference vectors between per-tool average activations steer tool selection at 77–100% accuracy on name-only single-turn prompts (93–100% for 4B+ models), with autoregressive JSON arguments matching the new tool's schema. The effect concentrates in the output-layer row for the tool's first token (unit vector along this direction reaches 93–100% while the orthogonal residual leaves choice nearly untouched), localizes to a small set of mid- and late-layer attention heads via patching, and is not reducible to topic (within-topic probe on 14 airline tools yields 61–89% top-1 across five 4B–14B models). Base models already encode the correct tool internally (69–82% cosine readout on BFCL) despite 2–10% generation accuracy, and activation gaps predict errors (14–21× higher error rate for smallest vs. largest top-1/top-2 gaps on Gemma 3 12B/27B). All measurements are in single-turn fixed-menu settings.

Significance. If the results hold under the reported controls, the work provides concrete mechanistic evidence that tool selection is mediated by linear directions in activation space, with the output-layer decomposition and within-topic probe addressing key alternative explanations (topic/syntax confounds and post-hoc fitting). The base-model readout result is particularly notable, indicating the representation forms during pretraining and is later wired to output by instruction tuning. The error-prediction finding via activation gaps has direct practical value for reliable tool use. These elements together strengthen the central claim beyond correlational probing and could inform interpretability, safety interventions, and steering of agentic systems.

major comments (2)
  1. [Experiments (within-topic probe)] The within-topic probe (14 airline tools, 61–89% top-1) is load-bearing for ruling out topic as the driver; however, the manuscript should explicitly report the number of queries per tool, the exact layer(s) used for the mean vectors, and whether the same held-out set was used for both mean computation and evaluation to confirm no data leakage.
  2. [Results (steering experiments)] The claim that 'flipping the name is enough' for JSON schema correctness relies on autoregressive continuation; the paper should quantify schema-match rates separately from name accuracy and report whether any residual JSON errors occur even when the steered name is accepted.
minor comments (4)
  1. [Abstract] The abstract reports ranges (77–100%, 93–100% at 4B+) without per-model breakdowns or trial counts; adding a table with exact accuracies, model sizes, and number of prompts per condition would improve reproducibility.
  2. [Localization results] Activation patching localization to 'a small set of mid- and late-layer attention heads' would benefit from a figure or table listing the specific head indices and layers across models.
  3. [Base model analysis] The base-model readout (69–82%) vs. generation (2–10%) is a strong point; clarify whether the cosine readout uses the same mean vectors as the steered models or a separate base-model probe.
  4. [Throughout] Minor typographical inconsistencies in model naming (e.g., 'Gemma 3' vs. 'Gemma-3') should be standardized throughout.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment and recommendation for minor revision. We appreciate the constructive comments on improving the clarity and reproducibility of the within-topic probe and steering results. We address each major comment below and will update the manuscript accordingly.

read point-by-point responses

  1. Referee: [Experiments (within-topic probe)] The within-topic probe (14 airline tools, 61–89% top-1) is load-bearing for ruling out topic as the driver; however, the manuscript should explicitly report the number of queries per tool, the exact layer(s) used for the mean vectors, and whether the same held-out set was used for both mean computation and evaluation to confirm no data leakage.

    Authors: We agree that these experimental details are necessary for full reproducibility and to confirm the absence of data leakage. We will revise the manuscript to explicitly report the number of queries per tool in the within-topic probe, the exact layer(s) from which the mean activation vectors were computed, and confirmation that the mean vectors were derived from a separate split with evaluation performed on a held-out set with no overlap. revision: yes

  2. Referee: [Results (steering experiments)] The claim that 'flipping the name is enough' for JSON schema correctness relies on autoregressive continuation; the paper should quantify schema-match rates separately from name accuracy and report whether any residual JSON errors occur even when the steered name is accepted.

    Authors: We agree that separating schema-match rates from name accuracy and reporting residual errors would strengthen the steering results. We will revise the relevant Results section to include explicit quantification of schema-match rates independent of name accuracy and to report the incidence of any residual JSON errors in cases where the steered tool name is accepted. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper derives its claims from direct empirical measurements of internal activations across multiple models, causal steering via mean-difference vector addition on held-out single-turn prompts, within-topic controls across 14 airline tools, activation patching to localize heads, and base-model readout comparisons. None of these steps reduce to their inputs by construction: the mean vectors are computed on separate data and tested causally, the within-topic probe explicitly addresses confounds, and the output-layer decomposition is an independent verification. No self-citation chains, ansatzes, or fitted predictions masquerading as results appear in the load-bearing sections. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the empirical computation of per-tool mean activation vectors from model forward passes on example prompts; these vectors are data-dependent and serve as the steering direction.

free parameters (1)
  • per-tool mean activation vectors
    Computed as averages of internal activations over prompts that elicit each tool; used to form the difference vector for steering.
axioms (1)
  • domain assumption Tool identity is represented as a linear direction in the model's residual stream or attention outputs.
    The entire steering and readout procedure assumes that adding a fixed vector can reliably alter tool choice without destroying other capabilities.

pith-pipeline@v0.9.0 · 5748 in / 1522 out tokens · 44401 ms · 2026-05-11T03:04:19.844351+00:00 · methodology

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Reference graph

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