Sparse Internal Control of Language Models
Abstract
Language models are increasingly used in text generation, decision support, and automated interaction, creating a need for localized, reversible, and selective control of their behavior. Activation steering demonstrates that internal interventions can alter the behavior of frozen models, but how to select and evaluate compact, multi-site control interfaces remains an open question. I introduce sparse internal control, a framework for steering target behavior by applying inference-time interventions to a small set of internal model nodes. A local target-controllability formulation characterizes candidate site--direction pairs by their behavioral effects and specifies constraints on target recovery, off-target preservation, and intervention energy. Two complementary selectors instantiate this formulation: Driver-OMP selects nodes for sparse reconstruction of a desired behavioral displacement, while Coverage-Driver favors stable coverage across prompts. I propose a six-axis control-evaluation protocol measuring reachability, signed reversal, dose response, feedback controllability, off-target preservation, and held-out reuse. Exploratory experiments on indirect object identification, MMLU multiple-choice question answering, sentiment steering, and refusal steering provide evidence for the feasibility of steering task-defined behavior through sparse internal interventions. The six-axis evaluation characterizes these interventions beyond target movement, revealing distinct control properties that depend on the task and available direction information. Together, the formulation, reference algorithms, and evaluation protocol provide a foundation for the systematic study and development of internal control methods for language models.
Figures & tables
| Axis | Evaluation objective | Quantitative readout |
|---|---|---|
| Reachability | Proximity to the target | |
| Signed reversal | Return toward source under the opposite patch | |
| Dose response | Target progress across intervention doses | Progress and signed |
| Feedback controllability | Tracking targets through feedback-adjusted doses | Error, hit rate, evaluations |
| Off-target preservation | Output changes on non-target prompts | |
| Held-out reuse | Reuse of sites or interventions on unseen prompts | Held-out residual or recovery |
| Method | IOI (10 seeds) | Humanities (3 seeds) | STEM (3 seeds) |
|---|---|---|---|
| Driver-OMP | |||
| Coverage-Driver | |||
| Top- | |||
| Random | |||
| Nonlinear greedy |
| Task | Mode | Driver-OMP | Coverage-Driver | Top- |
|---|---|---|---|---|
| IOI | Evaluation-pair (P) | 24/24 | — | — |
| Humanities | Evaluation-pair (P) | 38/48 | 46/48 | 45/48 |
| Humanities | Training-mean (F) | 8/48 | 8/48 | 8/48 |
| STEM | Evaluation-pair (P) | 39/48 | 47/48 | 47/48 |
| STEM | Training-mean (F) | 8/48 | 7/48 | 7/48 |
| Refusal | Evaluation-pair (P) | 12/40 | 21/40 | 21/40 |
Appendix figures & tables15 assets
Supplementary material from the paper’s appendix.
Appendix
| Setting type | Component | Setting |
|---|---|---|
| Reference | Refit and certificate | Ridge and preservation weights ; activation-energy bound ; target criterion ; preservation bound . |
| Reference | Sparse selection | Driver-OMP residual tolerance and improvement tolerance ; Coverage-Driver coverage . Denominator stabilizers ; normalized marginal-gain threshold . Uniform row weights for give ; Algorithm C.4 normalizes coverage by . Target normalization guard . |
| Executed | IOI recurrence | Five seeds and five budgets give 25 seed–budget configurations; consensus threshold . |
| Series | Readout and panel | Repetitions and reporting unit |
|---|---|---|
| IOI nominal | IO–S margin; 64 pairs, same panel | 10 seeds; stacked and |
| MCQA nominal | Four option logits; 8 questions/category, same panel | 3 seeds/category; stacked and |
| MCQA control | Scalar mean-wrong margin; 24 questions/category, 12/12; head library; P/F | 8 seeds; feedback endpoints/selector/mode; 8 reversal ratios; 8 nominal-dose values/selector/mode |
| Refusal control | Lexical margin; 20 pairs, 10/10; head library; P/F | 8 seeds; feedback endpoints/selector/mode; 8 reversal ratios; 8 nominal-dose values/selector/mode |
| IOI reversal | Saved nominal interventions; same 64 pairs; P | 10 seed-level ratios/selector |
| Sentiment reversal | Saved paired interventions; 16 pairs, 8/8; P/F | 8 seed-level ratios/selector/mode; 8 nominal-dose values/selector/mode |
| Method | IOI (10 seeds) | Humanities (3 seeds) | STEM (3 seeds) |
|---|---|---|---|
| Driver-OMP | (10/10) | (3/3) | (3/3) |
| Coverage-Driver | (10/10) | (3/3) | (3/3) |
| Top- | (10/10) | (2/3) | (3/3) |
| Random | (1/10) | (0/3) | (0/3) |
| Nonlinear greedy | (10/10) | (3/3) | (3/3) |
| Task | Method | P: mean SD (pass) | F: mean SD (pass) |
|---|---|---|---|
| Humanities | Driver-OMP | (6/8) | (0/8) |
| Coverage-Driver | (8/8) | (0/8) | |
| Top- | (8/8) | (0/8) | |
| STEM | Driver-OMP | (6/8) | (0/8) |
| Coverage-Driver | (8/8) | (0/8) | |
| Top- | (8/8) | (0/8) |
| Method | IOI (10 seeds) | Humanities (3 seeds) | STEM (3 seeds) |
|---|---|---|---|
| Driver-OMP | |||
| Coverage-Driver | |||
| Top- | |||
| Random | |||
| Nonlinear greedy |
| Task | Mode | Selector | Pass/seeds | Ratio mean SD |
|---|---|---|---|---|
| IOI | P | Driver-OMP | 10/10 | |
| IOI | P | Coverage-Driver | 10/10 | |
| IOI | P | Top- | 10/10 | |
| Sentiment | P | Driver-OMP | 4/8 | |
| Sentiment | F | Driver-OMP | 0/8 | |
| Sentiment | P | Coverage-Driver | 8/8 |
| Task | Mode | Selector | Mean | SD | ||
|---|---|---|---|---|---|---|
| Humanities | P | Driver-OMP | 3/8 | 0/8 | 0.5970 | 0.6005 |
| Humanities | P | Coverage-Driver | 5/8 | 0/8 | 0.9394 | 0.0987 |
| Humanities | P | Top- | 2/8 | 0/8 | 0.8939 | 0.0727 |
| Humanities | F | Driver-OMP | 4/8 | 3/8 | 0.2303 | 1.0202 |
| Humanities | F | Coverage-Driver | 5/8 | 3/8 | 0.2500 | 1.0351 |
| Humanities | F | Top- | 5/8 | 3/8 | 0.2500 | 1.0351 |
| Task | Selector | Mode | Hits | MAE | Evals | Initial |
|---|---|---|---|---|---|---|
| IOI | Driver-OMP | P | 24/24 | 0.1351 | 3.958 | 2/24 |
| Humanities | Driver-OMP | P | 38/48 | 1.0026 | 6.125 | 6/48 |
| Humanities | Driver-OMP | F | 8/48 | 2.2641 | 11.479 | 6/48 |
| Humanities | Coverage-Driver | P | 46/48 | 0.2378 | 4.417 | 6/48 |
| Humanities | Coverage-Driver | F | 8/48 | 1.9239 | 11.479 | 6/48 |
| Humanities | Top- | P | 45/48 | 0.2679 | 4.583 | 6/48 |
| Task | Selector | Mean KL | Median | P95 | Max | Mean-pass | All-pass |
|---|---|---|---|---|---|---|---|
| Sentiment | Driver-OMP | 0.005527 | 0.004959 | 0.011119 | 0.0286 | 0/8 | 0/8 |
| Sentiment | Coverage-Driver | 0.011015 | 0.009627 | 0.024779 | 0.0381 | 0/8 | 0/8 |
| Sentiment | Top- | 0.011567 | 0.010322 | 0.024746 | 0.0387 | 0/8 | 0/8 |
| Humanities | Driver-OMP | 0.496530 | 0.050394 | 2.349920 | 15.5523 | 0/8 | 0/8 |
| Humanities | Coverage-Driver | 0.109692 | 0.050405 | 0.392607 | 1.0154 | 0/8 | 0/8 |
| Humanities | Top- | 0.115396 | 0.056724 | 0.478003 | 0.6963 | 0/8 | 0/8 |
| Task | Method | Seeds | Refit- | Fully frozen |
|---|---|---|---|---|
| Humanities | Driver-OMP | 4 | ||
| Humanities | Coverage-Driver | 4 | ||
| Humanities | Top- | 4 | ||
| Humanities | Random | 4 | ||
| STEM | Driver-OMP | 4 | ||
| STEM | Coverage-Driver | 4 |
| Method | Refit rec. | Fixed- rec. | Refit fail frac. | Fixed- fail frac. |
|---|---|---|---|---|
| Driver-OMP | 0.583 | 0.661 | ||
| Coverage-Driver | 0.667 | 0.833 | ||
| Top- | 0.464 | 0.734 | ||
| Random | 0.984 | 0.984 |
| Selector | Mode | Mean | SD | Seeds | |
|---|---|---|---|---|---|
| Driver-OMP | 3 | P | 0.3602 | 0.1887 | 8 |
| Driver-OMP | 3 | F | 0.3536 | 0.1723 | 8 |
| Coverage-Driver | 3 | P | 0.7687 | 0.1038 | 8 |
| Coverage-Driver | 3 | F | 0.8137 | 0.4851 | 8 |
| Top- | 3 | P | 0.7804 | 0.1173 | 8 |
| Top- | 3 | F | 0.8127 | 0.4852 | 8 |
| Task | Selector | Mode | 0.10 | 0.20 | 0.30 | 0.40 | 0.50 |
|---|---|---|---|---|---|---|---|
| Humanities | Coverage-Driver | F | 1/48 | 2/48 | 8/48 | 9/48 | 10/48 |
| Humanities | Coverage-Driver | P | 11/48 | 24/48 | 46/48 | 46/48 | 46/48 |
| Humanities | Driver-OMP | F | 1/48 | 2/48 | 8/48 | 8/48 | 10/48 |
| Humanities | Driver-OMP | P | 6/48 | 17/48 | 38/48 | 38/48 | 38/48 |
| Humanities | Top- | F | 1/48 | 2/48 | 8/48 | 10/48 | 10/48 |
| Humanities | Top- | P | 10/48 | 29/48 | 45/48 | 45/48 | 45/48 |
| Model | Seeds | Driver-OMP | Coverage- Driver | Top- | Random |
|---|---|---|---|---|---|
| Qwen3-4B | 3 | ||||
| Qwen3-8B | 5 | ||||
| Mistral-7B | 3 |