Expand-and-Cluster: Parameter Recovery of Neural Networks

Flavio Martinelli, Berfin Simsek, Wulfram Gerstner, Johanni Brea
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:34895-34919, 2024.

Abstract

Can we identify the weights of a neural network by probing its input-output mapping? At first glance, this problem seems to have many solutions because of permutation, overparameterisation and activation function symmetries. Yet, we show that the incoming weight vector of each neuron is identifiable up to sign or scaling, depending on the activation function. Our novel method ’Expand-and-Cluster’ can identify layer sizes and weights of a target network for all commonly used activation functions. Expand-and-Cluster consists of two phases: (i) to relax the non-convex optimisation problem, we train multiple overparameterised student networks to best imitate the target function; (ii) to reverse engineer the target network’s weights, we employ an ad-hoc clustering procedure that reveals the learnt weight vectors shared between students – these correspond to the target weight vectors. We demonstrate successful weights and size recovery of trained shallow and deep networks with less than 10% overhead in the layer size and describe an ’ease-of-identifiability’ axis by analysing 150 synthetic problems of variable difficulty.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-martinelli24a, title = {Expand-and-Cluster: Parameter Recovery of Neural Networks}, author = {Martinelli, Flavio and Simsek, Berfin and Gerstner, Wulfram and Brea, Johanni}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {34895--34919}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/martinelli24a/martinelli24a.pdf}, url = {https://proceedings.mlr.press/v235/martinelli24a.html}, abstract = {Can we identify the weights of a neural network by probing its input-output mapping? At first glance, this problem seems to have many solutions because of permutation, overparameterisation and activation function symmetries. Yet, we show that the incoming weight vector of each neuron is identifiable up to sign or scaling, depending on the activation function. Our novel method ’Expand-and-Cluster’ can identify layer sizes and weights of a target network for all commonly used activation functions. Expand-and-Cluster consists of two phases: (i) to relax the non-convex optimisation problem, we train multiple overparameterised student networks to best imitate the target function; (ii) to reverse engineer the target network’s weights, we employ an ad-hoc clustering procedure that reveals the learnt weight vectors shared between students – these correspond to the target weight vectors. We demonstrate successful weights and size recovery of trained shallow and deep networks with less than 10% overhead in the layer size and describe an ’ease-of-identifiability’ axis by analysing 150 synthetic problems of variable difficulty.} }
Endnote
%0 Conference Paper %T Expand-and-Cluster: Parameter Recovery of Neural Networks %A Flavio Martinelli %A Berfin Simsek %A Wulfram Gerstner %A Johanni Brea %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-martinelli24a %I PMLR %P 34895--34919 %U https://proceedings.mlr.press/v235/martinelli24a.html %V 235 %X Can we identify the weights of a neural network by probing its input-output mapping? At first glance, this problem seems to have many solutions because of permutation, overparameterisation and activation function symmetries. Yet, we show that the incoming weight vector of each neuron is identifiable up to sign or scaling, depending on the activation function. Our novel method ’Expand-and-Cluster’ can identify layer sizes and weights of a target network for all commonly used activation functions. Expand-and-Cluster consists of two phases: (i) to relax the non-convex optimisation problem, we train multiple overparameterised student networks to best imitate the target function; (ii) to reverse engineer the target network’s weights, we employ an ad-hoc clustering procedure that reveals the learnt weight vectors shared between students – these correspond to the target weight vectors. We demonstrate successful weights and size recovery of trained shallow and deep networks with less than 10% overhead in the layer size and describe an ’ease-of-identifiability’ axis by analysing 150 synthetic problems of variable difficulty.
APA
Martinelli, F., Simsek, B., Gerstner, W. & Brea, J.. (2024). Expand-and-Cluster: Parameter Recovery of Neural Networks. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:34895-34919 Available from https://proceedings.mlr.press/v235/martinelli24a.html.

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