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Toward Latent Language Model Skills Steering and Optimization: An Empirical Study
Xunyi Jiang, Junda Wu, Yuxin Xiong, Sheldon Yu, Tong Yu, David Arbour, Ritwik Sinha, Julian McAuley, Hongyi Wen
TL;DR
Existing approaches largely treat procedural skills as explicit or surface-level constructs, leaving open how they are represented and manipulated inside LLMs. This study extracts skill-conditioned activation directions and evaluates their steering, composition, personalization, and optimization. It finds that procedural skills exhibit a manipulable vector-space organization, including effective latent composition and non-monotonic optimization trajectories, within the evaluated scope.
Problem
Existing approaches primarily treat procedural skills as explicit or surface-level constructs, leaving their internal representation and latent manipulability unresolved.
Method
The study extracts skill-conditioned directions from hidden representations and evaluates them through inference-time intervention and gradient-based optimization on procedural benchmarks.
Results
Procedural skills admit vector-space organization: directions can steer behavior, compose into higher-level skills, personalize algorithmic strategies, and evolve non-monotonically.
Takeaways & Limitations
The findings support representation-level control of procedural LLM skills through direct manipulation of internal activation directions.
Takeaways & Limitations
Claims are bounded by controlled SKILLSET benchmarks and the evaluated Qwen3 models, while richer arithmetic over skill directions remains future work.
Abstract
from arXiv · showhide
Skills, as a useful abstraction for the procedural capabilities of large language models (LLMs), capture how models perform structured, multi-step reasoning and program execution. Existing approaches typically treat skills as explicit, surface-level constructs specified through prompts or programs, leaving open the question of how such procedural capabilities are represented inside the model and whether they can be manipulated as structured objects in latent space. In this empirical study, we investigate whether procedural LLM skills can be represented as directions in activation space and whether vector-space operations over these directions can express skill-level behaviors. We find that procedural skills admit a vector-space representation: individual skill directions can be activated to shift model behavior; independently extracted directions can compose to form higher-level skills. Contrastive directions yield context-conditioned algorithmic personalization and optimization trajectories over skill directions evolve non-monotonically, with intermediate states often surpassing fully optimized solutions. These results support a representation-level view of procedural LLM skills: they admit a latent vector-space organization that allows direct manipulation through internal interventions.
1 Introduction
The study tests whether procedural LLM skills are represented as manipulable activation-space directions rather than only explicit, surface-level constructs. It finds evidence for direct steering, latent composition, preference-conditioned personalization, and non-monotonic skill evolution.
- Procedural skills describe structured, multi-step LLM behaviors involving reasoning, program execution, and flexible problem solving.
- The study extracts skill-conditioned activation directions and evaluates their behavior under inference-time intervention and gradient-based optimization.The experiments use verifiable procedural targets rather than stylistic attributes.
- Skills can be activated directly through latent steering.
- Latent skill composition is effective and often outperforms prompting-based composition.
- Latent skills enable personalization, allowing different execution strategies under varying preferences.
- Skill evolution is non-monotonic, with intermediate latent states often outperforming fully optimized solutions.
- These findings support viewing procedural capabilities as structured latent objects manipulable through internal interventions.This perspective shifts control from surface-level prompting toward representation-level skill control.
2 Related Work
Prior work studies skills as learned, explicit, or executable constructs and activation steering as a way to control model behavior. The paper addresses the comparatively unexplored question of steering procedural capabilities directly.
- Prior skill research treats capabilities as atomic operations, composable chains, taxonomies, or structured training units.
- Agent research develops reusable executable skills through environmental interaction, feedback, and skill libraries.
- Activation steering manipulates hidden representations at inference time without modifying model parameters.
- Existing activation-steering work primarily targets style, persona, and factual attributes rather than procedural capabilities.
- This study examines skill-level steering across tasks and domains instead of proposing a new steering mechanism.
3 Problem Formulation
The paper formalizes latent skill directions as activation-space controls and evaluates four signatures: steerability, composition, personalization, and evolution. These directions can be intervened on, combined, and optimized as continuous objects.
- 3.1 Latent LLM Skill: Latent skill directions are vectors or layerwise interventions in activation space that capture procedural behavior without changing model parameters.A scalar activation strength controls the intervention during the forward pass.
- 3.1 Latent LLM Skill: A valid skill direction must induce a nontrivial first-order change in expected task behavior when activated.The validity criterion is defined over a task distribution and sample-level objective.
- 3.2 Latent LLM Skill Steering: Steerability means that some activation strength improves the expected task objective, measured empirically as accuracy improvement over the unsteered baseline.
- 3.2 Latent LLM Skill Steering: Vector-space composition jointly activates steerable directions and tests performance on composite tasks against unsteered and text-based composition baselines.
- 3.2 Latent LLM Skill Steering: Composition is interpreted through whether joint effects exceed the sum of individual effects, although the evaluation tests task performance rather than explicitly estimating Γ.
- 3.3 Latent LLM Skill Optimization: Latent skill optimization treats skill parameterizations as continuous objects updated by gradient-based optimization under downstream objectives and contextual preferences.
- 3.3 Latent LLM Skill Optimization: Personalization asks whether one latent skill can become multiple preference-aligned, task-effective variants, while evolution examines structure in optimization trajectories.
- 3.3 Latent LLM Skill Optimization: Non-monotonic evolution occurs when an earlier optimization state outperforms a later state under a downstream evaluation metric.
4 Empirical Study of Vector-Space Skill Representations
The study evaluates whether latent skill directions support steerability, composition, personalization, and optimization across controlled math and code benchmarks and real math benchmarks. It finds that latent directions shift behavior, compose effectively, enable preference control, and often peak before optimization converges.
- Experimental settings: The experiments probe four properties—steerability, composition, personalization, and evolution—across controlled and real-benchmark settings.Controlled evaluations use SKILLSET-MATH and SKILLSET-CODE; math directions are also transferred to GSM8K and MATH500.
- Benchmarks: SKILLSET-MATH separates atomic operations from composite skills, enabling tests of individual activation and recombination of independently extracted directions.SKILLSET-CODE instead uses paired algorithmic strategies to evaluate personalization and evolution.
- Steerability: 29 of 34 skills improve under PCA-extracted steering on Qwen3-0.6B, with an average gain of 19.1 percentage points.Largest reported gains include +86 points for algebraic_simplification and +58 points for solve_linear_equation.
- Composition: Vector composition achieves the highest accuracy on 13 of 18 composite skills, raising average accuracy from 51.9% to 77.1%.This +25.2-point improvement exceeds the reported gains for concise text composition (+23.8 points) and text-CoT composition (+22.3 points).
- Personalization: Contrastive skill directions improve approach match rates across categories and generalize to unseen task–situation instances.The directions represent differences between context-conditioned hidden-state expectations and select opposing activation directions according to situational context.
- Evolution: In 14 of 18 pair–model settings, the highest in-distribution approach match rate occurs before the final optimization step 200.On Qwen3-0.6B, 7 of 9 pairs peak strictly before step 200, showing non-monotonic optimization trajectories.
5 Conclusion
The study finds that procedural LLM skills exhibit a vector-space organization in model activations, supporting direct steering, composition, personalization, and trajectory-based analysis.
- PCA-extracted skill-conditioned directions directly activate procedural behaviors on SKILLSET-MATH and transfer to real math benchmarks.
- Independently extracted atomic directions compose in vector space to express composite skills, often outperforming text-based composition.
- Contrastive directions over paired algorithmic strategies enable context-conditioned control of the model’s preferred execution approach.
- Optimization trajectories over skill directions evolve non-monotonically, with intermediate states frequently outperforming fully converged solutions.
- Overall, the findings support viewing procedural skills as latent vector-space objects that complement surface-level prompting control.
6 Limitations
The study’s claims are bounded by controlled SKILLSET benchmarks and evaluated Qwen3 models, while its composition analysis is limited to equal-weighted additive combinations.
- The empirical claims are bounded by the controlled SKILLSET benchmarks and the Qwen3 models evaluated.
- Composition is restricted to equal-weighted additive combinations, leaving richer arithmetic over skill directions for future work.
- SKILLSET covers math and code, providing controlled evaluation of latent skill properties across two domains.
- SKILLSET-MATH contains 16 atomic skills and 18 composite skills, with each skill represented by 1000 questions split 8:1:1 across training, validation, and testing.
- The composition study uses independently extracted atomic vectors and tests composite performance without composite-skill training.
A.2 LLM-Based Data Generation.
The data-generation pipeline creates and verifies paired algorithmic solutions, then exports them into formats supporting personalization and skill-evolution experiments.
- GPT-4o generates coding problems in batches, while candidate solutions are executed in a sandbox and repaired using error traces.
- Accepted solution pairs pass execution, cross-check agreement, and approach-authenticity verification before dataset inclusion.
- The pipeline uses an adaptive top-up loop for up to five rounds to reach a default target of 200 verified pairs per approach pair.
- Nine contrastive approach pairs receive steering vectors computed as the mean positive hidden state minus the mean negative hidden state.
- The accepted data are exported as approach groups for personalization and contrastive triplets for progressively shifting default approach preferences.
B Experiments Details
The experiment prompts require step-by-step reasoning and boxed final answers, with MATH500 following the EasySteer prompt format.
- Inference prompts require the model to place its final answer within \boxed{} for evaluation.
- MATH500 follows the prompt used in EasySteer.
- The general prompt explicitly requests step-by-step reasoning before the boxed final answer.
- The SkillSet inference prompt combines a skill instruction, an example, a problem, and the boxed-answer requirement.
B.2 Compositionality
The compositionality setup uses text-based prompts as baselines for combining procedural skills, with concise and chain-of-thought-style decompositions illustrated on algebraic simplification.
- Baselines: Two text-based composition baselines, Txt-C and Txt-CoT, augment composite-skill prompts with concise or longer procedural decompositions.Worked examples are provided for both baselines.
- Prompt structure: The baseline prompt specifies combining like terms, a coefficient*x + constant format, string output, and a three-step procedure.The steps are to identify like terms, add their coefficients, and combine constants.
- Worked example: The example task asks the model to simplify 1x+4x by identifying like terms, adding coefficients, and producing 5x.The illustrated decomposition uses compare_values and add_multiple_numbers skills.
- Evaluation setup: SKILLSET-CODE evaluation presents two alternative solution methods across two situational contexts, each favoring one method.This dataset structure supports comparisons between algorithmic approaches.
B.3 Personalization Experimental Details
The personalization study evaluates algorithmic approach control on SKILLSET-CODE using paired solution data, extracted steering vectors, inference-time interventions, and an LLM judge.
- Dataset: SKILLSET-CODE contains 18 LeetCode-style problems, two approach-favoring situational descriptions per problem, and 72 evaluation records.Vector extraction uses 200 model-generated solutions per approach.
- Inference intervention: Steering directions are injected into the last 50% of layers at the last prefill token and every generated token.The reported activation strength is α = 1.0, with greedy decoding and a maximum of 4096 tokens.
- Evaluation: An LLM judge receives the problem, target approach, and generated code, then returns whether the implementation follows the intended approach.The approach match rate measures procedural controllability rather than functional correctness.
- Judge criteria: The judging prompts classify outputs as positive, negative, or none based on actual algorithmic structure, explicit approach descriptions, or ambiguity.The evolution prompt requires exactly one of these labels.
Approach Match Rate Over Training
The approach match rate for RePS-optimized steering directions changes non-monotonically during training, often peaking at early or intermediate steps before declining.
- Training trajectory: Performance is consistently non-monotonic over training for RePS-optimized steering directions on Qwen3-0.6B and Qwen3-1.7B.Figure 4 plots one curve per approach pair and marks peak values.
- Training trajectory: Many approach pairs reach their maximum match rate at early or intermediate training steps before performance declines.The reported pattern indicates that the best direction can emerge before convergence.
- Representation assumption: The study models skill-conditioned activations as concentrated near a low-dimensional manifold along a procedural-execution axis.The assumed decomposition includes a per-example procedure-engagement scalar and an instance-specific residual.
- Extraction procedure: Single-class PCA extracts one normalized per-layer direction from centered skill-conditioned activations for atomic and composite math skills.Up to 500 examples are collected per skill from prompts containing the instruction, problem, and answer text.
- Scope caveat: For RQ1 and RQ2, PCA directions are extracted from prompts that include correct answers, so they reflect answer-conditioned rather than autonomous-generation hidden states.The PCA sign is uncorrected, while evaluation fixes the sign of α across skills.
- Extraction design: The two extraction schemes are matched to skill structure: PCA for atomic or composite math skills and mean-difference for paired algorithmic strategies.The paper does not claim PCA is the only or best extractor for the math setting.
E Cross-Family Results on Llama-2-7B-chat
Experiments on Llama-2-7B-chat extend the composition, transfer, and intervention-strength findings beyond Qwen3, while showing model- and skill-dependent performance patterns.
- Cross-family scope: The cross-family evaluation covers all 18 composite skills, transfer to GSM8K and MATH500, and intervention-strength sweeps on representative skills.Llama-2-7B-chat differs from Qwen3 in tokenizer, training corpus, and instruction-tuning procedure.
- Skill Composition: Vector composition outperforms text baselines on 13 of 18 composite skills and reaches 31.5 average accuracy, versus 21.6 for Txt-C and 20.7 for Txt-CoT.The same 13-of-18 ratio observed on Qwen3-0.6B is reproduced on Llama-2-7B-chat.
- Transfer to Real Benchmarks: Skill directions improve Llama-2-7B-chat by 3.26 GSM8K points and 2.80 MATH500 points over zero-shot decoding.The gains exceed those observed on the stronger Qwen3 models, alongside lower Llama-2-7B-chat baselines.
- Sensitivity to Intervention Strength: Useful intervention strength is skill-dependent: inequality_solving responds only at α=2.0, solve_linear_equation varies little, and large α can over-steer.The study therefore reports a consistent α within each dataset and extraction regime rather than one global value.