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The behavior of neural networks still remains opaque, and a recently widelynoted phenomenon is that networks often achieve similar performance wheninitialized with different random parameters. This phenomenon has attractedsignificant attention in measuring the similarity between features learned bydistinct networks. However, feature similarity could be vague in describing thesame feature since equivalent features hardly exist. In this paper, we expandthe concept of equivalent feature and provide the definition of what we callfunctionally equivalent features. These features produce equivalent outputunder certain transformations. Using this definition, we aim to derive a moreintrinsic metric for the so-called feature complexity regarding the redundancyof features learned by a neural network at each layer. We offer a formalinterpretation of our approach through the lens of category theory, awell-developed area in mathematics. To quantify the feature complexity, wefurther propose an efficient algorithm named Iterative Feature Merging. Ourexperimental results validate our ideas and theories from various perspectives.We empirically demonstrate that the functionally equivalence widely existsamong different features learned by the same neural network and we could reducethe number of parameters of the network without affecting the performance.TheIFM shows great potential as a data-agnostic model prune method. We have alsodrawn several interesting empirical findings regarding the defined featurecomplexity.

Going Beyond Neural Network Feature Similarity: The Network Feature Complexity and Its Interpretation Using Category Theory