This paper introduces a novel method for realizing vector-valued affine refinement operators using ReLU (Rectified Linear Unit) activations. The proposed technique, detailed by Bolorkhuu Boldsaikhan, achieves an exact realization with a depth proportional to the number of iterations, particularly for operators with a refinement factor M greater than or equal to 3. A key innovation is the use of a residual memory controller that replaces non-invertible dynamics with an injective skew-product, enabling precise backward replay of residual states. Offset frames are employed to align forcing atoms and prevent ambiguity in state recovery, ensuring exact values are retrieved even for complex forcing terms. AI
IMPACT This research contributes to the theoretical understanding of neural network architectures and their capacity for exact function realization.
RANK_REASON The item is a research paper submitted to arXiv. [lever_c_demoted from research: ic=1 ai=1.0]
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