Although the performance over time is the main performance that we want to benchmark, as pointed out by [3] the posterior matching is another metric to measure how good the inverse models are. Below we show the posterior matching score using Maximum Mean Discrepancy (MMD) as a measurement of how close the inferred posterior density is comparing with the ground truth (rejection sampled) distribution. Note that for a real-life problem (D4: meta-material) with higher dimensionality, the rejection sampling becomes intractable. The 3 MMD kernel used was 0.05, 0.2 and 0.9. The code is also available on the repository.

Neural Information Processing Systems http://nips.cc/

The 3 MMD kernel used was 0.05, 0.2 and 0.9. Table 2: Ablation Study Experimental DesignLabel Add Ω? The results indicate that adding both steps to NA (i.e., transitioning It seems that the left point's failure to find the global minimum However, if we run the whole experiment one more time, it is a different story. The invertible neural network is specially designed to have hard invertibility (full reconstruction). The conditional invertible neural network uses a similar structure as an invertible neural network.

We consider the task of solving inverse problems.

Whenever a quantity of interest cannot be observed directly but only through an indirect measurement process or in the presence of noise, one is faced with an inverse problem. To stabilize the reconstruction and mitigate the information loss inherent in the measurement, it is necessary to incorporate additional knowledge about the unknown data -- its prior distribution, which encodes what one expects the reconstruction to resemble, such as the characteristic features of natural images. Yet our ability to describe natural images in an explicit, algorithmic form remains quite limited. Fortunately, recent years have seen the emergence of data-driven approaches that enable the construction of priors directly from collections of representative samples. While these approaches often surpass classical methods in reconstruction quality, many of them lack theoretical guarantees and remain difficult to interpret. A promising direction explored recently [3, 4, 5, 21] involves invertible neural networks. Thanks to their bidirectional structure, a single network can simultaneously approximate the forward operator and serve as a reconstruction method, with stability ensured by the architecture itself. This hybrid use makes it possible to assess deviations from a known forward operator - or even replace it by a data-based version - while maintaining interpretability of the reconstruction process by the learned measurement model and vice versa. This dual capability is particularly relevant in applications where both high-fidelity reconstructions and a faithful representation of the measurement process are critical, such as scientific imaging and med-Preprint.

Data hiding is essential for secure communication across digital media, and recent advances in Deep Neural Networks (DNNs) provide enhanced methods for embedding secret information effectively. However, previous audio hiding methods often result in unsatisfactory quality when recovering secret audio, due to their inherent limitations in the modeling of time-frequency relationships. In this paper, we explore these limitations and introduce a new DNN-based approach. We use a flow-based invertible neural network to establish a direct link between stego audio, cover audio, and secret audio, enhancing the reversibility of embedding and extracting messages. To address common issues from time-frequency transformations that degrade secret audio quality during recovery, we implement a time-frequency loss on the time-domain signal. This approach not only retains the benefits of time-frequency constraints but also enhances the reversibility of message recovery, which is vital for practical applications. We also add an encryption technique to protect the hidden data from unauthorized access. Experimental results on the VCTK and LibriSpeech datasets demonstrate that our method outperforms previous approaches in terms of subjective and objective metrics and exhibits robustness to various types of noise, suggesting its utility in targeted secure communication scenarios.