DV-Lens: Revealing the Functional Organization of Language Model Parameters

Chenhang Cui; Jian Yu; Shuyi Miao; Xiaohao Liu; Rui Huang; Fei Shen; An Zhang; Tat-Seng Chua

cs.CLOct 3, 2026

DV-Lens: Revealing the Functional Organization of Language Model Parameters

Authors: Chenhang Cui, Jian Yu, Shuyi Miao, Xiaohao Liu, Rui Huang, Fei Shen, An Zhang, Tat-Seng Chua

Organizations: National University of Singapore · Nanjing University of Science and Technology · Beihang University · University of Hong Kong ·

Abstract

Understanding parameter functions helps elucidate the internal mechanisms of large language models (LLMs). However, how to connect parameters from different modules to verifiable output effects and further characterize the relationship between their functional organization and model capability remains to be explored. To this end, we introduce the downstream vocabulary lens (DV-Lens), a parameter-level interpretability framework that links native parameter directions to their downstream vocabulary responses. Specifically, we first estimate module-specific downstream Jacobians over a reference prompt set for attention query, key, value, and output (Q/K/V/O) projections and feed-forward networks (FFNs). Second, we use these mappings to project native parameter columns into the final vocabulary space, obtaining signed readouts that characterize their average local output responses. Third, we group parameter columns by their vocabulary readouts and introduce downstream vocabulary complexity (DV-Complexity), which quantifies within-group structural variation using normalized reconstruction residuals of the original weights. At the parameter level, randomized controls and finite-difference tests show that DV-Lens readouts capture non-random vocabulary structure and predict local logit changes with 98.0% coordinate-orientation agreement across 720 cases from nine models. These readouts further guide parameter ablation, steering, and swapping across 21 models, shifting target-token probabilities in the predicted directions under controlled conditions. At the model level, the joint-parameter score of DV-Complexity achieves a Spearman correlation of 0.904 with benchmark-based capability rankings across 48 language models. Together, these results provide intervention-based evidence for DV-Lens interpretations and reveal an association between DV-Complexity and model capability.

Figures & tables

Figure 1: Three paradigms for interpreting model internals. Activation decomposition explains input-dependent activations through learned features; direct vocabulary projection maps a parameter direction

w_{\ell,m,i}

into vocabulary space through the LLM head alone; DV-Lens first propagates the direction through the downstream mapping

\bar{J}_{\ell,m}

and then reads it out in vocabulary space.

Model	$\Delta K$	95% CI
Random baseline	$0.000$	–
OLMo-2-7B	$+0.630$	$[0.284,1.054]$
Yi-1.5-9B	$+1.128$	$[0.561,1.735]$
Qwen2.5-0.5B	$+1.488$	$[0.787,2.316]$
Qwen2.5-14B	$+2.534$	$[1.128,4.283]$
Qwen1.5-14B	$+2.858$	$[0.594,6.522]$

Table 1: Model-level matched-null comparison.

\Delta K=K_{\mathrm{DVL}}-K_{\mathrm{null}}

measures the excess-kurtosis advantage of DV-Lens over matched Gaussian directions. Positive values favor DV-Lens .

Figure 2: Exact DV-Lens readouts recover finite-difference coordinate orientation and high-impact vocabulary regions over 720 frozen cases from nine models, with 80 cases per model. (a) Model-mean coordinate-orientation agreement; the gold dashed line marks the 50% random-orientation baseline. (b) Exact two-tail Top-32 overlap. (c) Two-tail Top-32 Recall@128.

Module	Orient.	Top-32	R@128
Q	0.976	0.313	0.525
K	0.947	0.209	0.375
V	0.988	0.412	0.650
O	0.992	0.537	0.743
FFN	0.997	0.565	0.770
Pooled	0.980	0.407	0.613

Table 2: Finite-difference validation. Orientation agreement, exact two-tail Top-32 overlap, and two-tail Top-32 Recall@128 are reported by module.

Figure 3: Finite-difference prediction by layer depth. The same 720 cases are grouped by the four sampled layer positions, with 180 cases per depth. Curves average nine models; error bars show 95% model-bootstrap CIs. Horizontal positions use mean normalized depths.

Figure 4: Conditional decoded success rates for twelve of the 21 intervention models across six module scopes and three operations. The eight columns in each bank are the perturbed fractions from $0.05\%$ to $5\%$ ; the bottom row is the matched random baseline. All 21 models are shown in Appendix C.2 , and the matched random controls in Appendix C.4 .

Panel of Figure 5 — Figure 5: Decoded intervention cases. Blue/orange cards show clean/edited answers; headers give model, module, operation, and fraction. Blue/orange surfaces show source/target log-probability changes (edited minus clean); positive/negative height indicates promotion/suppression. Edit (%) spans eight fractions logarithmically. Bold traces mark the header’s fraction; floor contours project the surfaces.

Figure 6: Uniform six-task capability rank and DV-Complexity rank on one fixed 48-checkpoint cohort. The equal-width grid is ordered Joint, Q, K, V, O, FFN; every figure uses all 48 paired rank positions.

Figure 7: Benchmark-derived ability ranks advance while the primary DV-Complexity rank remains stationary under complete-benchmark exposure. Orange arrows mark positive non-ceiling joint responses.

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

#	LLM repository	Type
1	tiiuae/Falcon3-1B-Instruct	instruct
2	tiiuae/Falcon3-7B-Instruct	instruct
3	NousResearch/Hermes-2-Pro-Llama-3-8B	chat
4	NousResearch/Hermes-3-Llama-3.1-8B	chat
5	unsloth/Llama-3.1-8B-Instruct	instruct
6	meta-llama/Llama-3.2-1B-Instruct	instruct

Appendix

Table 3: The fixed set of 48 LLMs used with the uniform six-task capability definition. The table lists the LLM and its type. The released version, architecture, and capability score of every LLM are recorded with the supplementary material.

Scope	DV-Complexity $\rho$	Random mean $\rho$	Random SD	$p_{\mathrm{cond}}$
Joint	0.904	0.216	0.005	0.008
Q	0.794	0.217	0.013	0.008
K	0.701	0.214	0.015	0.008
V	0.596	0.180	0.022	0.008
O	0.743	0.149	0.010	0.008
FFN	0.756	0.110	0.012	0.008

Appendix

Table 4: Random-label control with matched cluster sizes on the fixed 48-model set. All six DV-Complexity correlations are larger than those from all 128 random-label permutations, giving the minimum possible conditional randomization value.

Scope	DV-Complexity $\rho$	Baseline $\rho$	$\Delta\rho$	Bootstrap 95% CI
Joint	0.904	0.800	$+0.104$	$[-0.023,\ 0.311]$
Q	0.794	0.653	$+0.141$	$[-0.073,\ 0.457]$
K	0.701	0.519	$+0.181$	$[-0.083,\ 0.532]$
V	0.596	0.593	$+0.003$	$[-0.293,\ 0.331]$
O	0.743	0.689	$+0.054$	$[-0.023,\ 0.210]$
FFN	0.756	0.647	$+0.109$	$[-0.034,\ 0.304]$

Appendix

Table 5: Raw-weight baseline on the fixed 48-model set. Positive

\Delta\rho

means that the DV-Complexity correlation is higher. The last column gives the model-family-cluster bootstrap interval for the difference.

Scope	DV-Complexity $\rho$	$\rho$ range after removal	Median after removal	Max. $\|\Delta\rho\|$
Joint	0.904	$[0.888,\ 0.909]$	0.903	0.016
Q	0.794	$[0.755,\ 0.875]$	0.792	0.082
K	0.701	$[0.643,\ 0.824]$	0.701	0.123
V	0.596	$[0.535,\ 0.723]$	0.600	0.127
O	0.743	$[0.680,\ 0.812]$	0.749	0.069
FFN	0.756	$[0.717,\ 0.851]$	0.748	0.095

Appendix

Table 6: Capability correlations after removing one model family at a time. The range contains 17 values, each computed after removing one complete model family.

Figure 8: Matched-null differences for the 21 models. Circles are model means with cell-bootstrap 95% intervals over the 15 depth-by-module cells; the diamond is the mean over models with a model-bootstrap 95% interval; the gold dashed line marks zero. Both differences are positive for every model.

Figure 9: Single directions and same-model centroids expose distinct vocabulary-tail groups whose readability varies. (a) One fixed Mistral-7B query-projection direction: the upper score tail is dominated by variants of the word field and the lower score tail by variants of the word complete, with coordinate magnitudes and within-tail ordering retained. (b) Six fixed centroids from the same model, including both concept-like and fragment-heavy groups, with four tokens from each score tail per centroid. These selected cases illustrate organization, not population readability.

Figure 10: Conditional decoded success rates for all 21 models. Layout as in Figure 4 ; the bottom row is the matched random baseline averaged over defined model rows; grey cells have a zero denominator.

Figure 11: Future-token probability-direction events for the 21 models. Layout and scale as in Figure 10 . A concept counts when at least one future answer token moves in the specified direction at any checked position; all 3,024 rows are defined. This event is not a decoded-success measure and carries no multiplicity correction.

Figure 12: Matched random-column and same-norm control for the 21 models. Each control cell keeps the primary cell’s model, concept, scope, operation, fraction, strength, eligible layers, denominator, and evaluation rule, but uses norm-matched non-primary columns and isotropic directions rescaled to the primary update norms. Grey cells have a zero denominator. The conditional decoded success rate averages $3.13\%$ against $30.82\%$ for the primary selection; this single draw is a reference control, not a null distribution.

Scope / edit	Prompt excerpt	Clean	Edited
Q $\cdot$ Ablate 2%, $\alpha{=}0.5$ Replay	Discounted cash flow is used for valuation in this field. …	finance …	programming …
K $\cdot$ Swap 2%, $\alpha{=}2$ Replay	…An isotope has a characteristic number of protons but a different number of neutrons here. …	chemistry …	Physics …
V $\cdot$ Steer 2%, $\alpha{=}0.5$ Replay	…The Dolomites rise in the northeastern part of this country. …	Italy …	France …
O $\cdot$ Steer 0.2%, $\alpha{=}8$ Factual	Norbert Wiener’s expertise is	in the field of mathematics and engineering, particularly in the areas of control systems	evident in the harmony and rhythm of the music, and the
FFN $\cdot$ Ablate 2%, $\alpha{=}0.25$ Replay	Choirs coordinate pitch, phrasing, and vocal blend in this discipline. …	music …	mathematics …
Joint $\cdot$ Swap 2%, $\alpha{=}0.5$ Replay	…Reaction heat and enthalpy are topics in this discipline. …	chemistry …	Physics …

Appendix

Table 11: Granite-3.3-8B : decoded intervention cases across all six scopes.

Scope / edit	Prompt excerpt	Clean	Edited
Q $\cdot$ Ablate 2%, $\alpha{=}0.5$ Replay	Molecular spectroscopy identifies substances in this science. …	Chemistry. …	Physics. …
K $\cdot$ Ablate 0.2%, $\alpha{=}2$ Factual	Shawn Fanning’s profession is a	computer programmer and entrepreneur. He is best known for co-founding Napster,	professional wrestler, actor, and stuntman. He is best known for his role
V $\cdot$ Swap 0.05%, $\alpha{=}8$ Factual	William Herschel’s expertise is	in the field of astronomy, particularly in the study of the universe’s structure and	in the field of biology, genetics, and evolutionary biology. He is a renowned
O $\cdot$ Swap 0.05%, $\alpha{=}4$ Factual	William Herschel’s expertise is	in the field of astronomy, particularly in the study of the universe’s structure and	in genetics and biology, and he is a renowned biologist. He is a cell
FFN $\cdot$ Swap 2%, $\alpha{=}0.5$ Replay	Fugue, symphony, concerto, and sonata are forms in this discipline. …	music. …	mathematics. …
Joint $\cdot$ Ablate 0.05%, $\alpha{=}8$ Factual	William Herschel’s expertise is	in the field of astronomy, particularly in the study of the universe’s structure and	in the field of chemistry, particularly in the area of organic chemistry. His research

Appendix

Table 12: Llama-3.2-3B : decoded intervention cases across all six scopes.

Scope / edit	Prompt excerpt	Clean	Edited
Q $\cdot$ Ablate 0.5%, $\alpha{=}1$ Factual	The domain of work of Henri Becquerel is	a very important part of the history of physics. He was a French physicist who	a good example of the way in which the scientific community has been able to recognize
K $\cdot$ Ablate 0.05%, $\alpha{=}4$ Factual	William Herschel’s expertise is	in the field of astronomy, particularly in the study of the solar system and the	in the field of mathematics, specifically in the area of algebraic geometry. His
V $\cdot$ Swap 0.5%, $\alpha{=}2$ Factual	Norbert Wiener’s expertise is	in the field of mathematics, particularly in the areas of harmonic analysis, stochastic processes	in the field of music, and he is a renowned composer and pianist.
O $\cdot$ Swap 2%, $\alpha{=}1$ Replay	…Arithmetic operations on fractions are elementary work in this subject. …	mathematics. (Fractions are a fundamental concept in mathematics.) (Source: Stanford	music …
FFN $\cdot$ Steer 0.1%, $\alpha{=}0.5$ Factual	William Herschel’s expertise is	in the field of astronomy, particularly in the study of the solar system and the	in biology and genetics, with a focus on the biology of aging and the genetics
Joint $\cdot$ Swap 2%, $\alpha{=}0.25$ Replay	…The euro-using republic between Spain and Germany is this country. …	France. (The country between Spain and Germany is France, and the country that	Italy. (Italy is the country between Spain and Germany, and it uses the

Appendix

Table 13: Llama-3.1-8B : decoded intervention cases across all six scopes.

Scope / edit	Prompt excerpt	Clean	Edited
Q $\cdot$ Swap 2%, $\alpha{=}4$ Replay	…A spectrometer can identify a substance from the wavelengths it absorbs in this science. …	chemistry …	Physics …
K $\cdot$ Ablate 0.5%, $\alpha{=}2$ Factual	Norbert Wiener’s expertise is	in the field of mathematics, but he is also known for his work in	in the field of international law, international relations, and international organizations. He is
V $\cdot$ Steer 0.05%, $\alpha{=}4$ Factual	Norbert Wiener’s expertise is	in the field of mathematics, but he is also known for his work in	in the field of music, and he is a composer of some distinction. He
O $\cdot$ Swap 2%, $\alpha{=}2$ Replay	…Ecological succession describes how communities change after disturbance in this field. …	biology	astronomy
FFN $\cdot$ Ablate 2%, $\alpha{=}0.5$ Replay	…This euro-using country lies between Austria and the Mediterranean Sea. …	Italy …	France …
Joint $\cdot$ Swap 2%, $\alpha{=}0.5$ Replay	…Testimony is given under oath and may be challenged by cross-examination here. …	Law	Medicine …

Appendix

Table 14: Mistral-7B : decoded intervention cases across all six scopes.

Scope / edit	Prompt excerpt	Clean	Edited
Q $\cdot$ Ablate 0.05%, $\alpha{=}8$ Factual	Grand Mosque of Paris, which is located in	the 10th arrondissement of Paris, France, is a mosque	the 12th arrondissement, is a mosque for Muslims. It
K $\cdot$ Ablate 0.05%, $\alpha{=}0.25$ Factual	Grand Mosque of Paris, which is located in	the 10th arrondissement of Paris, France, is a mosque	the 10th arrondissement, is a mosque that was built in
V $\cdot$ Steer 0.2%, $\alpha{=}2$ Factual	Limoncello, that was created in	the south of Italy, is a clear, yellow liqueur made from the zest	the south of France, is a clear, yellow liqueur made from the zest
O $\cdot$ Steer 0.2%, $\alpha{=}0.5$ Factual	Limoncello, that was created in	the south of Italy, is a clear, yellow liqueur made from the zest	the south of France, is a clear and very light yellow liqueur made from
FFN $\cdot$ Swap 0.05%, $\alpha{=}4$ Factual	William Herschel’s expertise is	in the field of astronomy. He discovered Uranus and made significant contributions to the	in the field of biology, specifically in the area of bioinformatics. He has
Joint $\cdot$ Steer 0.05%, $\alpha{=}0.25$ Factual	Limoncello, that was created in	the south of Italy, is a clear, yellow liqueur made from the zest	the south of France, is a clear yellow liqueur made from the zest of

Appendix

Table 15: Qwen2.5-3B : decoded intervention cases across all six scopes.

Scope / edit	Prompt excerpt	Clean	Edited
Q $\cdot$ Steer 2%, $\alpha{=}0.5$ Replay	…The canals and gondolas of Venice attract visitors to this country. …	Italy …	France …
K $\cdot$ Ablate 1%, $\alpha{=}0.25$ Factual	Grand Mosque of Paris, which is located in	the heart of Paris, France, is one of the most famous and largest mosques	the heart of Paris, is one of the most famous and iconic mosques in the
V $\cdot$ Swap 2%, $\alpha{=}8$ Replay	…Diversification reduces concentration risk in this discipline. …	Diversification reduces concentration risk in finance. …	Diversification reduces concentration risk in the field of programming. …
O $\cdot$ Ablate 2%, $\alpha{=}4$ Replay	A researcher examining DNA inheritance works in this branch of science. …	The researcher examines DNA inheritance in the field of biology. …	A researcher examining DNA inheritance works in the field of astronomy. …
FFN $\cdot$ Swap 2%, $\alpha{=}4$ Replay	…A white coat, stethoscope, and examination room are associated with this profession. …	Medical Doctor (MD) …	Law Enforcement Officer …
Joint $\cdot$ Ablate 2%, $\alpha{=}2$ Replay	A hospital resident training under senior physicians works in this profession. …	A hospital resident training under senior physicians works in the profession of medicine. …	A resident in a specific field of study, such as law or a related field

Appendix

Table 16: StableLM-2-1.6B : decoded intervention cases across all six scopes.

LLM Interpretability

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Lens methods interpret large language models (LLMs) by mapping intermediate activations to the output vocabulary, revealing how next-token predictions develop through the network. Trained lenses remain expensive: affine-translator parameters grow quadratically with model width, while exact, full-vocabulary Kullback--Leibler (KL) training dominates memory. Consequently, prior trained lenses have been applied to models of at most 20B parameters and remain tied to particular component types. We present OmniLens, which applies a single lens family to any model-width activation, whether residual stream, attention, or MLP, and combines two independent scaling techniques. First, low-rank translators make per-lens parameter growth linear in model width and reduce trainable parameters by up to 98.4%. Second, Subset-KL materializes only selected vocabulary logits: its Top-k mode cuts peak training memory by up to 70%, while its importance-sampled variant retains unbiased stochastic gradients for the full KL. These savings enable a dense ensemble of 482 lenses for LLaMA-3.3-70B, providing 6x the coverage of a residual-stream design at the same depth. Model-wide coverage then reveals what single-component lenses cannot: the components where a behavior is most visible need not be those where intervention is most effective, and the most effective interventions lie outside the attention heads examined by prior lens studies. Across three case studies (prompt-injection detection, multi-hop memory injection, and toxicity localization), OmniLens reproduces key published results at substantially lower cost.

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