Dreaming Learning

Incorporating novelties into deep learning systems remains a challenging problem. Introducing new information to a machine learning system can interfere with previously stored data and potentially alter the global model paradigm, especially when dealing with non-stationary sources. In such cases, traditional approaches based on validation error minimization offer limited advantages. To address this, we propose a training algorithm inspired by Stuart Kauffman's notion of the Adjacent Possible. This novel training methodology explores new data spaces during the learning phase. It predisposes the neural network to smoothly accept and integrate data sequences with different statistical characteristics than expected. The maximum distance compatible with such inclusion depends on a specific parameter: the sampling temperature used in the explorative phase of the present method. This algorithm, called Dreaming Learning, anticipates potential regime shifts over time, enhancing the neural network's responsiveness to non-stationary events that alter statistical properties. To assess the advantages of this approach, we apply this methodology to unexpected statistical changes in Markov chains and non-stationary dynamics in textual sequences. We demonstrated its ability to improve the auto-correlation of generated textual sequences by $\sim 29\%$ and enhance the velocity of loss convergence by $\sim 100\%$ in the case of a paradigm shift in Markov chains.

Hybrid Physical-Neural ODEs for Fast N-body Simulations

We present a new scheme to compensate for the small-scales approximations resulting from Particle-Mesh (PM) schemes for cosmological N-body simulations. This kind of simulations are fast and low computational cost realizations of the large scale structures, but lack resolution on small scales. To improve their accuracy, we introduce an additional effective force within the differential equations of the simulation, parameterized by a Fourier-space Neural Network acting on the PM-estimated gravitational potential. We compare the results for the matter power spectrum obtained to the ones obtained by the PGD scheme (Potential gradient descent scheme). We notice a similar improvement in term of power spectrum, but we find that our approach outperforms PGD for the cross-correlation coefficients, and is more robust to changes in simulation settings (different resolutions, different cosmologies).