Ayush Paliwal

Chase van de Geijn, Ayush Paliwal, Timo Lüddecke et al.

Transformers rely on positional encoding to compensate for the inherent permutation invariance of self-attention. Traditional approaches use absolute sinusoidal embeddings or learned positional vectors, while more recent methods emphasize relative encodings to better capture translation equivariances. In this work, we propose RollPE, a novel positional encoding mechanism based on traveling waves, implemented by applying a circular roll operation to the query and key tensors in self-attention. This operation induces a relative shift in phase across positions, allowing the model to compute attention as a function of positional differences rather than absolute indices. We show this simple method significantly outperforms traditional absolute positional embeddings and is comparable to RoPE. We derive a continuous case of RollPE which implicitly imposes a topographic structure on the query and key space. We further derive a mathematical equivalence of RollPE to a particular configuration of RoPE. Viewing RollPE through the lens of traveling waves may allow us to simplify RoPE and relate it to processes of information flow in the brain.

Ayush Paliwal, Oliver Schlenczek, Birte Thiede et al.

Reconstructing the 3D location and size of microparticles from diffraction images - holograms - is a computationally expensive inverse problem that has traditionally been solved using physics-based reconstruction methods. More recently, researchers have used machine learning methods to speed up the process. However, for small particles in large sample volumes the performance of these methods falls short of standard physics-based reconstruction methods. Here we designed a two-stage neural network architecture, FLASH$μ$, to detect small particles (6-100$μ$m) from holograms with large sample depths up to 20cm. Trained only on synthetic data with added physical noise, our method reliably detects particles of at least 9$μ$m diameter in real holograms, comparable to the standard reconstruction-based approaches while operating on smaller crops, at quarter of the original resolution and providing roughly a 600-fold speedup. In addition to introducing a novel approach to a non-local object detection or signal demixing problem, our work could enable low-cost, real-time holographic imaging setups.