The Abstraction and Reasoning Corpus: D. Deferred Proofs

Written by escholar | Published 2024/03/11
Tech Story Tags: abstraction-corpus | reasoning-corpus | arc | languagecomplete-instantiation | larc | non-learning-ai | latformer | neural-network-learning

TLDRState-of-the-art machine learning models struggle with generalization which can only be achieved by proper accounting for core knowledge priors.via the TL;DR App

This paper is available on arxiv under CC 4.0 license.

Authors:

(1) Mattia Atzeni, EPFL, Switzerland and [email protected];

(2) Mrinmaya Sachan, ETH Zurich, Switzerland;

(3) Andreas Loukas, Prescient Design, Switzerland.

Table of Links

D. Deferred Proofs

We prove both Theorem 3.1 and 3.2 by induction on the dimensionality of the hypercubic lattice m.

D.1. Base Case for Theorems 1 and 2

D.2. Inductive Step for Theorems 1 and 2

D.3. Proof of Corollary 1

The proof of Corollary 1 follows immediately from Theorem 3.2 and from the property of the Fourier transform according to which multiplying in the Fourier domain implements a convolution in the original domain.


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Published by HackerNoon on 2024/03/11