Pseudo-Invertible Neural Networks
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Researchers have introduced Surjective Pseudo-invertible Neural Networks (SPNN), a novel architecture that extends the Moore-Penrose Pseudo-inverse to nonlinear systems, particularly in neural networks. This includes a method called Non-Linear Back-Projection (NLBP), which ensures consistency in solving nonlinear inverse problems. By applying diffusion-based techniques, SPNNs can tackle various non-linear degradations, from optical distortions to semantic classification, enabling zero-shot inversion and precise control over generative outputs without requiring retraining.
Introduction of Surjective Pseudo-Invertible Neural Networks
Researchers have introduced a new class of neural network architectures known as Surjective Pseudo-Invertible Neural Networks (SPNN), generalizing the Moore-Penrose Pseudo-inverse to the non-linear domain. This advancement aims to provide a solution for non-linear inverse problems relevant in neural networks.
Key Features of SPNN
SPNN architectures incorporate a non-linear PInv that maintains essential geometric properties. A standout feature is the null-space projection method, "Back-Projection," which adjusts a sample x to its closest consistent state x' through the equation:
x' = x + A^\dagger(y - Ax)
Applications and Implications
SPNNs have the potential to enhance zero-shot inverse problems. The extension of diffusion-based null-space projections to non-linear degradations broadens applicability, addressing information loss, such as:
- Optical distortions
- Semantic abstractions, such as classification
This framework allows for effective zero-shot inversion of intricate degradations and facilitates precise semantic control over generative outputs without retraining the diffusion prior.
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📰 Original Source: https://arxiv.org/abs/2602.06042v1
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