NeurIPS 2023 Papers

We propose a novel neural network-based approach to modeling protein dynamics using an implicit representation of a protein’s surface in 3D and time. Our method utilizes the zero-level set of signed distance functions (SDFs) to represent protein surfaces, enabling temporally and spatially continuous representations of protein dynamics. Our experimental results demonstrate that our model accurately captures protein dynamic trajectories and can interpolate and extrapolate in 3D and time. Importantly, this is the first study to introduce this method and successfully model large-scale protein dynamics. This approach offers a promising alternative to current methods, overcoming the limitations of first-principles-based and deep learning methods, and provides a more scalable and efficient approach to modeling protein dynamics. Additionally, our surface representation approach simplifies calculations and allows identifying movement trends and amplitudes of protein domains, making it a useful tool for protein dynamics research. Codes are available at https://github.com/Sundw-818/DSR, and we have a project webpage that shows some video results, https://sundw-818.github.io/DSR/.

Continuous-time score-based generative models consist of a pair of stochastic differential equations (SDEs)—a forward SDE that smoothly transitions data into a noise space and a reverse SDE that incrementally eliminates noise from a Gaussian prior distribution to generate data distribution samples—are intrinsically connected by the time-reversal theory on diffusion processes. In this paper, we investigate the use of stochastic evolution equations in Hilbert spaces, which expand the applicability of SDEs in two aspects: sample space and evolution operator, so they enable encompassing recent variations of diffusion models, such as generating functional data or replacing drift coefficients with image transformation. To this end, we derive a generalized time-reversal formula to build a bridge between probabilistic diffusion models and stochastic evolution equations and propose a score-based generative model called Hilbert Diffusion Model (HDM). Combining with Fourier neural operator, we verify the superiority of HDM for sampling functions from functional datasets with a power of kernel two-sample test of 4.2 on Quadratic, 0.2 on Melbourne, and 3.6 on Gridwatch, which outperforms existing diffusion models formulated in function spaces. Furthermore, the proposed method shows its strength in motion synthesis tasks by utilizing the Wiener process with values in Hilbert space. Finally, our empirical results on image datasets also validate a connection between HDM and diffusion models using heat dissipation, revealing the potential for exploring evolution operators and sample spaces.

Standard regularized training procedures correspond to maximizing a posterior distribution over parameters, known as maximum a posteriori (MAP) estimation. However, model parameters are of interest only insomuch as they combine with the functional form of a model to provide a function that can make good predictions. Moreover, the most likely parameters under the parameter posterior do not generally correspond to the most likely function induced by the parameter posterior. In fact, we can re-parametrize a model such that any setting of parameters can maximize the parameter posterior. As an alternative, we investigate the benefits and drawbacks of directly estimating the most likely function implied by the model and the data. We show that this procedure leads to pathological solutions when using neural networks and prove conditions under which the procedure is well-behaved, as well as a scalable approximation. Under these conditions, we find that function-space MAP estimation can lead to flatter minima, better generalization, and improved robustness to overfitting.

The challenge of replicating research results has posed a significant impediment to the field of molecular biology. The advent of modern intelligent systems has led to notable progress in various domains. Consequently, we embarked on an investigation of intelligent monitoring systems as a means of tackling the issue of the reproducibility crisis. Specifically, we first curate a comprehensive multimodal dataset, named ProBio, as an initial step towards this objective. This dataset comprises fine-grained hierarchical annotations intended for the purpose of studying activity understanding in BioLab. Next, we devise two challenging benchmarks, transparent solution tracking and multimodal action recognition, to emphasize the unique characteristics and difficulties associated with activity understanding in BioLab settings. Finally, we provide a thorough experimental evaluation of contemporary video understanding models and highlight their limitations in this specialized domain to identify potential avenues for future research. We hope ProBio with associated benchmarks may garner increased focus on modern AI techniques in the realm of molecular biology.

Generalizable neural surface reconstruction techniques have attracted great attention in recent years. However, they encounter limitations of low confidence depth distribution and inaccurate surface reasoning due to the oversimplified volume rendering process employed. In this paper, we present Reconstruction TRansformer (ReTR), a novel framework that leverages the transformer architecture to redesign the rendering process, enabling complex render interaction modeling. It introduces a learnable $\textit{meta-ray token}$ and utilizes the cross-attention mechanism to simulate the interaction of rendering process with sampled points and render the observed color. Meanwhile, by operating within a high-dimensional feature space rather than the color space, ReTR mitigates sensitivity to projected colors in source views. Such improvements result in accurate surface assessment with high confidence. We demonstrate the effectiveness of our approach on various datasets, showcasing how our method outperforms the current state-of-the-art approaches in terms of reconstruction quality and generalization ability. $\textit{Our code is available at }$ https://github.com/YixunLiang/ReTR.

Data over non-Euclidean manifolds, often discretized as surface meshes, naturally arise in computer graphics and biological and physical systems. In particular, solutions to partial differential equations (PDEs) over manifolds depend critically on the underlying geometry. While graph neural networks have been successfully applied to PDEs, they do not incorporate surface geometry and do not consider local gauge symmetries of the manifold. Alternatively, recent works on gauge equivariant convolutional and attentional architectures on meshes leverage the underlying geometry but underperform in modeling surface PDEs with complex nonlinear dynamics. To address these issues, we introduce a new gauge equivariant architecture using nonlinear message passing. Our novel architecture achieves higher performance than either convolutional or attentional networks on domains with highly complex and nonlinear dynamics. However, similar to the non-mesh case, design trade-offs favor convolutional, attentional, or message passing networks for different tasks; we investigate in which circumstances our message passing method provides the most benefit.