ActivationInformedMerging

Model merging, a method that combines the parameters and embeddings of multiple fine-tuned large language models (LLMs), offers a promising approach to enhance model performance across various tasks while maintaining computational efficiency. This paper introduces Activation-Informed Merging (AIM), a technique that integrates the information from the activation space of LLMs into the merging process to improve performance and robustness. AIM is designed as a flexible, complementary solution that is applicable to any existing merging method. It aims to preserve critical weights from the base model, drawing on principles from continual learning(CL) and model compression. Utilizing a task-agnostic calibration set, AIM selectively prioritizes essential weights during merging. We empirically demonstrate that AIM significantly enhances the performance of merged models across multiple benchmarks. Our findings suggest that considering the activation-space information can provide substantial advancements in the model merging strategies for LLMs with up to 40% increase in benchmark performance.

📝 Full Paper | 🤗AIM Checkpoints | 🤗Baseline Checkpoints

Checkpoints Used In Experiments

All checkpoints (merged with and without AIM) that were used for experiments in the paper are provided on huggingface. Below are the links to the aforementioned models:

Models with AIM (Collection 🤗)

Method	Code-Math	Code-Instruction	Math-Instruction	Code-Math-Instruction
DARE Linear	Link 🤗	Link 🤗	Link 🤗	Link 🤗
DARE Ties	Link 🤗	Link 🤗	Link 🤗	Link 🤗
Ties	Link 🤗	Link 🤗	Link 🤗	Link 🤗
Task Arithmetic	Link 🤗	Link 🤗	Link 🤗	Link 🤗
WIDEN	Link 🤗	Link 🤗	Link 🤗	Link 🤗

Models without AIM (Collection 🤗)

Method	Code-Math	Code-Instruction	Math-Instruction	Code-Math-Instruction
DARE Linear	Link 🤗	Link 🤗	Link 🤗	Link 🤗
DARE Ties	Link 🤗	Link 🤗	Link 🤗	Link 🤗
Ties	Link 🤗	Link 🤗	Link 🤗	Link 🤗
Task Arithmetic	Link 🤗	Link 🤗	Link 🤗	Link 🤗
WIDEN	Link 🤗	Link 🤗	Link 🤗	Link 🤗

Usage

You can re-deo the experiments we have here using the provided code. Below we detail how to replicate the experiments.

Merging Models

If you wish to merge the models yourself instead of using the provided checkpoints you can do so with the merge.py script provided. For example to perform DARE Ties merging on the Code, Math and Instruction Tuned models you can run:

python merge.py --method dare_ties --base_model unsloth/llama-2-13b --models_to_merge WizardLMTeam/WizardLM-13B-V1.2,vanillaOVO/WizardMath-13B-V1.0,layoric/llama-2-13b-code-alpaca --save_path ./DARE_TIES_InstructMathCode

Evaluating Models on Benchmarks

Once you have the checkpoints you want to test you can run the evaluate_model.py script to run the benchamrks on the model. For example to run the benchmarks on the model merged above you can run:

python evaluate_model.py --model ./DARE_TIES_InstructMathCode

or if you wanted to use the provided checkpoints:

python evaluate_model.py --model ahn1376/DARETies___Code-Math-Instruction_Tuned

Applying AIM to A Merged Model

If you want to apply AIM to any merged model you will need to provide the merged checkpoint as well as the base model checkpoint. The only hyper-parameter in AIM is $\omega$, which we recommend to be set between $0.2-0.6$ we set this to $0.4$ for the experiments in our paper, but in some cases lower values (more relaxation) will yeild better results. Below is how you can apply AIM to the checkpoint the code above makes:

python performAIM.py --merged_model ./DARE_TIES_InstructMathCode --pretrained_model_name unsloth/llama-2-13b --omega 0.4 --save_path ./DARE_TIES_AIM_InstructMathCode

Summary of Findings

We find that in basically all merging methods we tested applying AIM improves performance and pushed the pareto front of the resulting model population and achieves the highest scrores in benchmarks. The figure below shows how with decreasing $\omega$ (more AIM relaxation) leads to further improvements in some models (HV gain is the hypervolume gained by adding the model to the population models used for merging (more is better)):

We can observe this better by visualizing some of the pareto fronts for different model populations:

Overall the results of our experiments are as follows for the different tests:

Base Models

Method	Model(s)	AIM	HumanEval	MBPP	MMLU	MATH	GSM8K	IFEval	HV Gain
-	Base	-	17.07	27.80	52.18	0.70	4.20	25.10	-
-	Code	-	17.07	31.60	52.91	6.00	24.10	26.25	-
-	Instruction Tuned	-	26.83	34.80	53.41	7.50	43.40	35.67	-
-	Math	-	15.24	27.60	51.89	13.10	59.10	21.58	-

Merged Models

DARE Task Arithmetic

Model(s)	AIM	HumanEval	MBPP	MMLU	MATH	GSM8K	IFEval	HV Gain
Code + Instruction Tuned	No	26.83	34.40	53.53	8.40	45.80	33.42	0.27
	Yes	29.27 (+9.09%)	36.00 (+4.65%)	54.18 (+1.21%)	8.30 (-1.19%)	46.20 (+0.87%)	32.00 (-4.25%)	0.28 (+2.49%)
Code + Math	No	16.46	28.60	51.96	15.10	64.70	22.02	0.23
	Yes	15.85 (-3.71%)	29.60 (+3.50%)	52.50 (+1.04%)	14.80 (-1.99%)	64.10 (-0.93%)	21.91 (-0.50%)	0.23 (-1.65%)
Instruction Tuned + Math	No	5.49	19.00	51.08	9.80	54.30	32.35	0.18
	Yes	12.20 (+122.22%)	28.20 (+48.42%)	52.72 (+3.21%)	12.90 (+31.63%)	62.20 (+14.55%)	31.96 (-1.21%)	0.26 (+40.71%)
Code + Instruction Tuned + Math	No	11.59	19.60	50.89	9.10	49.70	33.20	0.16
	Yes	15.85 (+36.76%)	27.00 (+37.76%)	52.59 (+3.34%)	12.20 (+34.07%)	60.70 (+22.13%)	33.59 (+1.17%)	0.23 (+40.59%)

DARE Ties

Model(s)	AIM	HumanEval	MBPP	MMLU	MATH	GSM8K	IFEval	HV Gain
Code + Instruction Tuned	No	30.49	35.20	53.40	8.60	46.20	33.28	0.28
	Yes	30.49	36.80 (+4.55%)	54.02 (+1.16%)	8.60	47.20 (+2.16%)	33.16 (-0.36%)	0.29 (+1.63%)
Code + Math	No	17.07	27.40	51.92	14.90	63.60	22.53	0.23
	Yes	17.68 (+3.57%)	29.00 (+5.84%)	52.61 (+1.33%)	15.20 (+2.01%)	63.90 (+0.47%)	21.10 (-6.35%)	0.24 (+4.00%)
Instruction Tuned + Math	No	8.54	23.80	51.39	9.20	54.10	33.89	0.20
	Yes	15.85 (+85.60%)	30.20 (+26.89%)	52.89 (+2.92%)	11.60 (+26.09%)	57.80 (+6.84%)	35.63 (+5.13%)	0.26 (+31.22%)
Code + Instruction Tuned + Math	No	13.41	21.20	51.15	8.70	51.50	35.75	0.17
	Yes	19.51 (+45.49%)	28.60 (+34.91%)	52.63 (+2.89%)	11.60 (+33.33%)	57.00 (+10.68%)	36.20 (+1.26%)	0.24 (+41.28%)

Task Arithmetic

Model(s)	AIM	HumanEval	MBPP	MMLU	MATH	GSM8K	IFEval	HV Gain
Code + Instruction Tuned	No	29.27	33.80	53.44	8.60	47.10	31.60	0.28
	Yes	29.88 (+2.08%)	35.80 (+5.92%)	54.12 (+1.27%)	7.80 (-9.30%)	46.60 (-1.06%)	32.01 (+1.30%)	0.28 (+0.61%)
Code + Math	No	18.29	28.60	52.10	15.00	64.70	21.92	0.24
	Yes	17.68 (-3.34%)	29.20 (+2.10%)	52.52 (+0.81%)	14.60 (-2.67%)	64.50 (-0.31%)	21.54 (-1.73%)	0.24 (-2.65%)
Instruction Tuned + Math	No	4.27	20.20	51.50	10.00	54.20	31.31	0.18
	Yes	8.54 (+100.00%)	26.40 (+30.69%)	52.83 (+2.58%)	12.80 (+28.00%)	61.30 (+13.10%)	32.62 (+4.18%)	0.24 (+34.52%)
Code + Instruction Tuned + Math	No	11.59	19.60	51.20	9.00	52.70	32.87	0.16
	Yes	15.24 (+31.49%)	27.40 (+39.80%)	52.63 (+2.79%)	12.00 (+33.33%)	58.10 (+10.25%)	33.91 (+3.16%)	0.22 (+31.97%)

Ties Merging

Model(s)	AIM	HumanEval	MBPP	MMLU	MATH	GSM8K	IFEval	HV Gain
Code + Instruction Tuned	No	16.46	23.60	52.70	2.70	5.40	24.48	0.00
	Yes	15.24 (-7.41%)	24.20 (+2.54%)	53.15 (+0.85%)	2.60 (-3.70%)	5.20 (-3.70%)	22.87 (-6.58%)	0.05 (+inf%)
Code + Math	No	15.85	26.80	51.86	14.30	62.60	21.63	0.20
	Yes	15.85	28.60 (+6.72%)	52.29 (+0.83%)	15.30 (+6.99%)	63.80 (+1.92%)	22.64 (+4.67%)	0.23 (+13.55%)
Instruction Tuned + Math	No	28.05	34.60	54.45	8.70	44.70	34.04	0.23
	Yes	27.44 (-2.17%)	35.00 (+1.16%)	54.74 (+0.53%)	9.30 (+6.90%)	46.10 (+3.13%)	34.51 (+1.38%)	0.25 (+6.38%)
Code + Instruction Tuned + Math	No	21.34	29.20	53.97	6.30	29.20	26.95	0.11
	Yes	20.73 (-2.86%)	29.20	54.46 (+0.91%)	5.70 (-9.52%)	23.70 (-18.84%)	25.98 (-3.60%)	0.11 (+4.33%)

WIDEN

Model(s)	AIM	HumanEval	MBPP	MMLU	MATH	GSM8K	IFEval	HV Gain
Code + Instruction Tuned	No	26.22	35.60	54.90	8.30	45.00	30.42	0.27
	Yes	25.61 (-2.33%)	34.60 (-2.81%)	54.97 (+0.13%)	8.20 (-1.20%)	44.10 (-2.00%)	31.60 (+3.88%)	0.26 (-0.93%)
Code + Math	No	17.07	29.40	53.35	14.20	64.40	24.02	0.24
	Yes	17.07	29.60 (+0.68%)	53.36 (+0.02%)	14.30 (+0.70%)	62.20 (-3.42%)	23.95 (-0.29%)	0.24 (-1.22%)
Instruction Tuned + Math	No	24.39	30.40	54.20	14.60	66.00	30.82	0.30
	Yes	23.78 (-2.50%)	32.00 (+5.26%)	54.69 (+0.90%)	15.10 (+3.42%)	68.20 (+3.33%)	31.23 (+1.33%)	0.31 (+2.54%)
Code + Instruction Tuned + Math	No	25.00	33.20	54.58	13.50	64.20	31.44	0.29
	Yes	26.83 (+7.32%)	32.80 (-1.20%)	54.98 (+0.73%)	14.40 (+6.67%)	64.00 (-0.31%)	32.82 (+4.39%)	0.30 (+4.70%)

Citation

@misc{nobari2025activationinformedmerginglargelanguage,
      title={Activation-Informed Merging of Large Language Models}, 
      author={Amin Heyrani Nobari and Kaveh Alimohammadi and Ali ArjomandBigdeli and Akash Srivastava and Faez Ahmed and Navid Azizan},
      year={2025},
      eprint={2502.02421},
      archivePrefix={arXiv},
      primaryClass={cs.CL},
      url={https://arxiv.org/abs/2502.02421}, 
}