Twin Neural Networks Enable Inversion of Non-Injective Functions

Global: Twin Neural Networks Enable Inversion of Non-Injective Functions

Researchers led by Sebastian J. Wetzel submitted a new preprint to arXiv on Jan. 8, 2026 that proposes a deterministic framework for inverting non‑injective functions. The approach leverages twin neural network regression combined with k‑nearest neighbor search to generate input estimates for target outputs that would otherwise lack a unique inverse. By training the network to predict adjustments from known anchor inputs to new inputs, the method aims to resolve ambiguities inherent in many real‑world mappings.

Background on Non‑Injective Functions

Non‑injective functions map multiple distinct inputs to the same output, making direct inversion mathematically impossible. In practice, such functions appear in robotics, control systems, and various machine‑learning pipelines where the dimensionalities of input and output spaces may differ. Traditional inversion techniques often require restrictive assumptions or exhaustive search, limiting scalability.

Twin Neural Network Regression Approach

The proposed twin neural network architecture consists of two parallel regressors: one learns the relationship between anchor inputs (mathbf{x}^{text{anchor}}) and their outputs (mathbf{y}^{text{anchor}}), while the second predicts the adjustments needed to reach a new input (mathbf{x}^{text{new}}) when the target output changes to (mathbf{y}^{text{new}}). By focusing on differential adjustments rather than absolute values, the model naturally accommodates locally injective sub‑domains within a broader non‑injective function.

Deterministic Framework with k‑Nearest Neighbors

To select a concrete solution from the potentially infinite set of candidates, the author integrates a k‑nearest neighbor (k‑NN) search. After the twin network suggests a candidate adjustment, the k‑NN component identifies the closest previously observed input‑output pair, ensuring that the final estimate aligns with known data points. This combination yields a deterministic output without resorting to stochastic sampling.

Experimental Demonstrations

The framework is evaluated on two categories of problems. First, synthetic toy examples illustrate how the method recovers inputs for functions defined purely by data. Second, a robot arm control scenario demonstrates practical relevance: the system computes joint parameters that achieve a desired end‑effector position, even when the kinematic mapping is many‑to‑one. Both sets of experiments show that the approach can recover plausible inputs with limited error.

Implications and Future Directions

If broadly adopted, this technique could simplify inverse design tasks in robotics, computer graphics, and other domains where non‑injective mappings are common. The author notes that extending the method to higher‑dimensional spaces and integrating uncertainty quantification are promising avenues for further research.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.