Stable Autonomous Flow Matching

In contexts where data samples represent a physically stable state, it is often assumed that the data points represent the local minima of an energy landscape. In control theory, it is well-known that energy can serve as an effective Lyapunov function. Despite this, connections between control theory and generative models in the literature are sparse, even though there are several machine learning applications with physically stable data points. In this paper, we focus on such data and a recent class of deep generative models called flow matching. We apply tools of stochastic stability for time-independent systems to flow matching models. In doing so, we characterize the space of flow matching models that are amenable to this treatment, as well as draw connections to other control theory principles. We demonstrate our theoretical results on two examples.

Protein sequence-to-structure learning: Is this the end(-to-end revolution)?

The potential of deep learning has been recognized in the protein structure prediction community for some time, and became indisputable after CASP13. In CASP14, deep learning has boosted the field to unanticipated levels reaching near-experimental accuracy. This success comes from advances transferred from other machine learning areas, as well as methods specifically designed to deal with protein sequences and structures, and their abstractions. Novel emerging approaches include (i) geometric learning, i.e. learning on representations such as graphs, 3D Voronoi tessellations, and point clouds; (ii) pre-trained protein language models leveraging attention; (iii) equivariant architectures preserving the symmetry of 3D space; (iv) use of large meta-genome databases; (v) combinations of protein representations; (vi) and finally truly end-to-end architectures, i.e. differentiable models starting from a sequence and returning a 3D structure. Here, we provide an overview and our opinion of the novel deep learning approaches developed in the last two years and widely used in CASP14.