It is prohibitive to parameterize a natural movie and its respective retinal encoding fully.

Many real-life decision making tasks are stochastic optimization problems, where one needs to make decisions to minimize a cost function that involves stochastic parameters.

Remark 4. The result of Theorem 2 also holds for unstable orbits Remark 5. F or RNNs with ReLU activation functions there are finite compartments in the phase Assume for the sake of contradiction that k W k 1 . There is a direct link between the norms of the Jacobians of the RNN along trajectories and the EVGP . Note that this system is non-autonomous, that is externally forced due to the r.h.s. of eqn. Rössler system Another prime textbook example for a chaotic system is the Rössler system [76] This strongly suggests that the dynamics governing the time series are chaotic. All datasets used were standardized (i.e., centered with unit variance) prior to training.

Our goal is to provide a simple conceptual framework to think about those questions. To derive such a framework, we ask ourselves: what are the ideal requirements that ISSL representations should aim to satisfy? We prove necessary and sufficient requirements to ensure that probes from a specified family, e.g.

AIs can surpass human performance by a large margin.

Y are closest to the ground truth (see Figure S2).

However, proximal inference requires solving an ill-posed integral equation.