Beyond Simple Inversion: Building and Applying Inverse Neural Networks

Author(s): Shenggang Li

Originally published on Towards AI.

Theory, training tricks, and real‑world case studies — solving multi‑root equations and beyondPhoto by Marisa Harris on Unsplash

Inverse problems ask a fundamental question: Given the output y, what was the input x? Traditional methods like Newton’s algorithm work only when the forward function is smooth, well-behaved, and one-to-one. They quickly fall short in real-world scenarios where the system is noisy, multi-valued, or completely opaque. Inverse Neural Networks (INNs) offer a modern and scalable alternative.

An INN consists of two models: a forward network that learns the mapping x → y and an inverse network that maps y → x while satisfying realistic constraints. Unlike naive regression, INNs incorporate cycle-consistency loss, range constraints, and optionally latent noise, this will generate diverse and plausible solutions even when the inverse map is not uniquely defined.

While standard multilayer Perceptrons (MLPs) are often sufficient, we also explore Kolmogorov–Arnold Networks (KANs) for improved expressiveness and parameter efficiency. KANs use learnable splines in activations, enabling smoother and more precise inverse mappings in structured problems like the sinc equation.

From reconstructing images and signals to profiling customers or diagnosing systems from sparse outputs, INNs are a general-purpose tool for solving inverse problems across domains. This paper presents several case studies and practical examples to showcase how INNs can infer meaningful structure from… Read the full blog for free on Medium.

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Published via Towards AI