Model Complexity of Program Phases

In resource limited computing systems, sequence prediction models must operate under tight constraints. Various models are available that cater to prediction under these conditions that in some way focus on reducing the cost of implementation. These resource constrained sequence prediction models, in practice, exhibit a fundamental tradeoff between the cost of implementation and the quality of its predictions. This fundamental tradeoff seems to be largely unexplored for models for different tasks. Here we formulate the necessary theory and an associated empirical procedure to explore this tradeoff space for a particular family of machine learning models such as deep neural networks. We anticipate that the knowledge of the behavior of this tradeoff may be beneficial in understanding the theoretical and practical limits of creation and deployment of models for resource constrained tasks

Energy-based General Sequential Episodic Memory Networks at the Adiabatic Limit

The General Associative Memory Model (GAMM) has a constant state-dependant energy surface that leads the output dynamics to fixed points, retrieving single memories from a collection of memories that can be asynchronously preloaded. We introduce a new class of General Sequential Episodic Memory Models (GSEMM) that, in the adiabatic limit, exhibit temporally changing energy surface, leading to a series of meta-stable states that are sequential episodic memories. The dynamic energy surface is enabled by newly introduced asymmetric synapses with signal propagation delays in the network's hidden layer. We study the theoretical and empirical properties of two memory models from the GSEMM class, differing in their activation functions. LISEM has non-linearities in the feature layer, whereas DSEM has non-linearity in the hidden layer. In principle, DSEM has a storage capacity that grows exponentially with the number of neurons in the network. We introduce a learning rule for the synapses based on the energy minimization principle and show it can learn single memories and their sequential relationships online. This rule is similar to the Hebbian learning algorithm and Spike-Timing Dependent Plasticity (STDP), which describe conditions under which synapses between neurons change strength. Thus, GSEMM combines the static and dynamic properties of episodic memory under a single theoretical framework and bridges neuroscience, machine learning, and artificial intelligence