Next-token prediction is modeled as modus ponens in intuitionistic implicational logic, leading to the Arrow model, a recurrent architecture equivalent in spirit to known multiplicative RNNs.
Smith & Mike Lewis (2022): Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation
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On the (Intuitionistic) Logic of Next-Token Prediction
Next-token prediction is modeled as modus ponens in intuitionistic implicational logic, leading to the Arrow model, a recurrent architecture equivalent in spirit to known multiplicative RNNs.