Discrete symbolic optimization and Boltzmann sampling by continuous neural dynamics: Gradient Symbolic Computation
This work addresses optimization challenges in computational modeling, offering a theoretical foundation for a method that could impact neural and symbolic AI, though it appears incremental as it builds on existing empirical findings.
The paper tackles discrete global optimization problems by proposing Gradient Symbolic Computation, a neurally plausible continuous stochastic dynamical system, and establishes a parameter schedule that ensures convergence to the correct answer with high probability, providing theoretical support for prior empirical results.
Gradient Symbolic Computation is proposed as a means of solving discrete global optimization problems using a neurally plausible continuous stochastic dynamical system. Gradient symbolic dynamics involves two free parameters that must be adjusted as a function of time to obtain the global maximizer at the end of the computation. We provide a summary of what is known about the GSC dynamics for special cases of settings of the parameters, and also establish that there is a schedule for the two parameters for which convergence to the correct answer occurs with high probability. These results put the empirical results already obtained for GSC on a sound theoretical footing.