Neural Simulation

At the turn of the century, most of the laws of physics that govern the natural world had been established. However, our ability to simulate the full complexity of these physical systems has remained elusive. Neural Network based simulation methods have the potential for fast simulation of physics of complex systems. The ability to simulate large, complex environments requires two key components:

• Neural scene representations
• Effecient generative training and inference

"Holy Grail": The ability to simulate a single human cell at ~2Å resolution

Neural Reasoning

Deep learning methods can now solve IMO/Putnam problems with considerable accuracy. Computer-assisted proofs are an integral part of the mathematician's toolbox. However, there appears to be no reason why neural methods need humans at all.

Can problems in pure mathematics and theoretical physics be solved completely using neural reasoning methods with no human 'hints'? I strongly suspect the answer is yes. Initially, machine learning methods will require significant inductive bias to solve difficult problems. However, as both algorithms and methods scale up, it may be possible to train a single model that can solve problems that have confounded humans since the dawn of history (e.g., the distribution of prime numbers) completely from scratch.

"Holy Grail": A human-verifiable proof of the Riemann Hypothesis, generated via a neural network.