However, in practice, new reconstruction methods could improve performance for at least three other reasons: learning more about the distribution of stimuli, becoming better at reconstructing text or images in general, or exploiting weaknesses in current image and/or text evaluation metrics. Here we disentangle how much of the reconstruction is due to these other factors vs. productively using the neural recordings.

The three-dimensional reconstruction of multiple interacting humans given a monocular image is crucial for the general task of scene understanding, as capturing the subtleties of interaction is often the very reason for taking a picture.

Our technique greatly reduces the appearance of banding, without requiring any additional computation or post-processing at reconstructiontime.

However, one key challenge remains: existing approaches lack explicit multi-view geometry constraints, hence usually fail to generate geometry-consistent surface reconstruction.

Despite advancements in Neural Implicit models for 3D surface reconstruction, handling dynamic environments with interactions between arbitrary rigid, non-rigid, or deformable entities remains challenging. The generic reconstruction methods adaptable to such dynamic scenes often require additional inputs like depth or optical flow or rely on pre-trained image features for reasonable outcomes. These methods typically use latent codes to capture frame-by-frame deformations. Another set of dynamic scene reconstruction methods, are entity-specific, mostly focusing on humans, and relies on template models. In contrast, some template-free methods bypass these requirements and adopt traditional LBS (Linear Blend Skinning) weights for a detailed representation of deformable object motions,although they involve complex optimizations leading to lengthy training times.

Equivariant imaging (EI) enables training signal reconstruction models without requiring ground truth data by leveraging signal symmetries. Deep equilibrium models (DEQs) are a powerful class of neural networks where the output is a fixed point of a learned operator. However, training DEQs with complex EI losses requires implicit differentiation through fixed-point computations, whose implementation can be challenging. We show that backpropagation can be implemented modularly, simplifying training. Experiments demonstrate that DEQs trained with implicit differentiation outperform those trained with Jacobian-free backpropagation and other baseline methods. Additionally, we find evidence that EI-trained DEQs approximate the proximal map of an invariant prior.

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.