Let a two-player Markov game where both players affect the transition. As we have seen in Section 2.1, in the case of unilateral deviation from joint policy Let a (possibly correlated) joint policy ˆ σ . By Lemma A.1, we know that Where the equality holds due to the zero-sum property, (1). An approximate NE is an approximate global minimum. An approximate global minimum is an approximate NE.

Several recent works demonstrate that transformers can implement algorithms like gradient descent. By a careful construction of weights, these works show that multiple layers of transformers are expressive enough to simulate iterations of gradient descent.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Towards this end, we adoptthe unconstrained-features model (UFM), a recent theoretical model for studying neural collapse, and introduce Simplex-Encoded-Labels Interpolation (SELI) as an invariant characterizationof theneuralcollapsephenomenon.