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Paper · 2307.08192 · 2023

HOPE: High-order Polynomial Expansion of Black-box Neural Networks

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 18 functions out of this paper's own repositories and ran 16 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
harrypotterxtx/hope canonical 16 of 18
FunctionStatusWhere it lives
Activation Ran harrypotterxtx/hope/utils/Network.py
pointer only (licence: NONE) · get_code("a6212c5c5a7f9674")
JudgeAct Ran harrypotterxtx/hope/utils/Activation.py
pointer only (licence: NONE) · get_code("e9954d5dd966b612")
ModuleDict Ran harrypotterxtx/hope/utils/Network.py
pointer only (licence: NONE) · get_code("5d1cb3ffe100f152")
MultiFormula Ran harrypotterxtx/hope/utils/ChainMatrix.py
pointer only (licence: NONE) · get_code("147b9c268f1914b8")
SingleStrFormula Ran harrypotterxtx/hope/utils/ChainMatrix.py
pointer only (licence: NONE) · get_code("7d7cfb17f0c88bb4")
StrFormula Ran harrypotterxtx/hope/utils/ChainMatrix.py
pointer only (licence: NONE) · get_code("c3a28942febbdd0c")
cald Ran harrypotterxtx/hope/auto.py
pointer only (licence: NONE) · get_code("5b7715594984b84e")
create_code Ran harrypotterxtx/hope/utils/Global.py
pointer only (licence: NONE) · get_code("285713efc578efa9")
create_coords Ran harrypotterxtx/hope/utils/Global.py
pointer only (licence: NONE) · get_code("b10d037ab889007a")
create_flattened_coords Ran harrypotterxtx/hope/utils/Samplers.py
pointer only (licence: NONE) · get_code("33b1630ff701ffed")
create_lr_scheduler Ran harrypotterxtx/hope/utils/Optimizer.py
pointer only (licence: NONE) · get_code("7b0462e7cb6c3b67")
create_optim Ran harrypotterxtx/hope/utils/Optimizer.py
pointer only (licence: NONE) · get_code("553590ed9758f52c")
get_taylor_coef Ran harrypotterxtx/hope/global.py
pointer only (licence: NONE) · get_code("949763c8466649d3")
invnormalize_data Ran harrypotterxtx/hope/utils/Samplers.py
pointer only (licence: NONE) · get_code("49307138b9a6ff3c")
judge_exist Ran harrypotterxtx/hope/global.py
pointer only (licence: NONE) · get_code("a08f4c11483ef0c6")
normalize_data Ran harrypotterxtx/hope/utils/Samplers.py
pointer only (licence: NONE) · get_code("42bca2074e6a5608")
autograd Not yet run harrypotterxtx/hope/auto.py
pointer only (licence: NONE) · get_code("4ac749f921b31097")
taylor_output Not yet run harrypotterxtx/hope/utils/Global.py
pointer only (licence: NONE) · get_code("981cd9c1fb3b7dd6")

Repositories linked to this paper

Some links come from the archived Papers with Code dataset (CC BY-SA 4.0): attribution and licence.

Abstract

Despite their remarkable performance, deep neural networks remain mostly ``black boxes'', suggesting inexplicability and hindering their wide applications in fields requiring making rational decisions. Here we introduce HOPE (High-order Polynomial Expansion), a method for expanding a network into a high-order Taylor polynomial on a reference input. Specifically, we derive the high-order derivative rule for composite functions and extend the rule to neural networks to obtain their high-order derivatives quickly and accurately. From these derivatives, we can then derive the Taylor polynomial of the neural network, which provides an explicit expression of the network's local interpretations. Numerical analysis confirms the high accuracy, low computational complexity, and good convergence of the proposed method. Moreover, we demonstrate HOPE's wide applications built on deep learning, including function discovery, fast inference, and feature selection. The code is available at https://github.com/HarryPotterXTX/HOPE.git.

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