相关论文: What Topological and Geometric Structure Do Biolog…

The human connectome represents a network map of the brain's wiring diagram and the pattern into which its connections are organized is thought to play an important role in cognitive function. The generative rules that shape the topology of…

Deep learning has enabled remarkable improvements in grasp synthesis for previously unseen objects from partial object views. However, existing approaches lack the ability to explicitly reason about the full 3D geometry of the object when…

Training model to generate data has increasingly attracted research attention and become important in modern world applications. We propose in this paper a new geometry-based optimization approach to address this problem. Orthogonal to…

Each human genome is a 3 billion base pair set of encoding instructions. Decoding the genome using deep learning fundamentally differs from most tasks, as we do not know the full structure of the data and therefore cannot design…

We investigate the geometric structure of learning dynamics in overparameterized transformer models through carefully controlled modular arithmetic tasks. Our primary finding is that despite operating in high-dimensional parameter spaces…

Advances in experimental neuroscience have transformed our ability to explore the structure and function of neural circuits. At the same time, advances in machine learning have unleashed the remarkable computational power of artificial…

Predicting the structure of multi-protein complexes is a grand challenge in biochemistry, with major implications for basic science and drug discovery. Computational structure prediction methods generally leverage pre-defined structural…

How do transformer language models memorize factual associations? A common view casts internal weight matrices as associative memories over pairs of embeddings, requiring parameter counts that scale linearly with the number of facts. We…

Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational…

The structure and dynamics of a typical biological system are complex due to strong and inhomogeneous interactions between its constituents. The investigation of such systems with classical mathematical tools, such as differential equations…

This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…

In this paper, we propose a data-driven method to learn interpretable topological features of biomolecular data and demonstrate the efficacy of parsimonious models trained on topological features in predicting the stability of synthetic…

Single-cell foundation models learn by reconstructing masked gene expression, implicitly treating technical noise as signal. With dropout rates exceeding 90%, reconstruction objectives encourage models to encode measurement artifacts rather…

A recent body of work has demonstrated that Transformer embeddings can be linearly decomposed into well-defined sums of factors, that can in turn be related to specific network inputs or components. There is however still a dearth of work…

Understanding how cellular morphology, gene expression, and spatial context jointly shape tissue function is a central challenge in biology. Image-based spatial transcriptomics technologies now provide high-resolution measurements of cell…

We study the grokking phenomenon through the lens of topology. Using persistent homology on point clouds derived from the embedding matrices of a range of models trained on modular arithmetic with varying primes, we identify a clear and…

Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances…

Foundation models for single-cell RNA sequencing (scRNA-seq) have shown promising capabilities in capturing gene expression patterns. However, current approaches face critical limitations: they ignore biological prior knowledge encoded in…

This paper brings together three distinct theories with the goal of quantifying shape textures with complex morphologies. Distance fields are central objects in shape representation, while topological data analysis uses algebraic topology…

Surrogate models are used to reduce the burden of expensive-to-evaluate objective functions in optimization. By creating models which map genomes to objective values, these models can estimate the performance of unknown inputs, and so be…