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Computational protein design aims at constructing novel or improved functions on the structure of a given protein backbone and has important applications in the pharmaceutical and biotechnical industry. The underlying combinatorial…
Living cells use phase separation and concentration gradients to organize chemical compartments in space. Here, we present a theoretical study of droplet dynamics in gradient systems. We derive the corresponding growth law of droplets and…
This paper presents a gradient-informed fine-tuning method for large language models under few-shot conditions. The goal is to enhance task adaptability and training stability when data is limited. The method builds on a base loss function…
Fine-tuning over large pretrained language models (PLMs) has established many state-of-the-art results. Despite its superior performance, such fine-tuning can be unstable, resulting in significant variance in performance and potential risks…
The development of nonlinear optimization algorithms capable of performing reliably in the presence of noise has garnered considerable attention lately. This paper advocates for strategies to create noise-tolerant nonlinear optimization…
A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtained analytically in the case of sufficiently large time…
We study Nesterov's accelerated gradient method with constant step-size and momentum parameters in the stochastic approximation setting (unbiased gradients with bounded variance) and the finite-sum setting (where randomness is due to…
Proteins naturally occur in crowded cellular environments and interact with other proteins, nucleic acids, and organelles. Since most previous experimental protein structure determination techniques require that proteins occur in idealized,…
To successfully navigate chemical gradients, microorganisms need to predict how the ligand concentration changes in space. Due to their limited size, they do not take a spatial derivative over their body length but rather a temporal…
The impact of gradient noise on training deep models is widely acknowledged but not well understood. In this context, we study the distribution of gradients during training. We introduce a method, Gradient Clustering, to minimize the…
Gradient clipping is a commonly used technique to stabilize the training process of neural networks. A growing body of studies has shown that gradient clipping is a promising technique for dealing with the heavy-tailed behavior that emerged…
Any gradient descent optimization requires to choose a learning rate. With deeper and deeper models, tuning that learning rate can easily become tedious and does not necessarily lead to an ideal convergence. We propose a variation of the…
Accurate sensor placement is critical for modeling spatio-temporal systems such as environmental and climate processes. Neural Processes (NPs), particularly Convolutional Conditional Neural Processes (ConvCNPs), provide scalable…
Randomly initialized first-order optimization algorithms are the method of choice for solving many high-dimensional nonconvex problems in machine learning, yet general theoretical guarantees cannot rule out convergence to critical points of…
As deep learning models continue to scale, the growing computational demands have amplified the need for effective coreset selection techniques. Coreset selection aims to accelerate training by identifying small, representative subsets of…
Assessment of spontaneous movements can predict the long-term developmental disorders in high-risk infants. In order to develop algorithms for automated prediction of later disorders, highly precise localization of segments and joints by…
Structure determination is key to understanding protein function at a molecular level. Whilst significant advances have been made in predicting structure and function from amino acid sequence, researchers must still rely on expensive,…
Genomic expression depends critically both on the ability of regulatory proteins to locate specific target sites on a DNA within seconds and on the formation of long lived (many minutes) complexes between these proteins and the DNA.…
We prove exponential concentration estimates and a strong law of large numbers for a particle system that is the simplest representative of a general class of models for 2D grain boundary coarsening. The system consists of $n$ particles in…
Many iterative procedures in stochastic optimization exhibit a transient phase followed by a stationary phase. During the transient phase the procedure converges towards a region of interest, and during the stationary phase the procedure…