Georgia Institute of Technology College of Sciences

Assemblies are subsets of neurons whose coordinated excitation is hypothesized to represent the subject's thinking of an object, idea, episode, or word. Consequently, they provide a promising basis for a theory of how neurons and synapses give rise to higher-level cognitive phenomena. The existence (and pivotal role) of assemblies was first proposed by Hebb, and has since been experimentally confirmed, as well as rigorously proven to emerge in the model of computation in the brain recently developed by Papadimitriou & Vempala. In light of contemporary studies which have documented the creation and activation of sequences of assemblies of neurons following training on tasks with sequential decisions, we study here the brain's mechanisms for working with sequences in the assemblies model of Papadimitriou & Vempala.  We show that (1) repeated presentation of a sequence of stimuli leads to the creation of a sequence of corresponding assemblies -- upon future presentation of any contiguous sub-sequence of stimuli, the corresponding assemblies are activated and continue until the end of the sequence; (2) when the stimulus sequence is projected to two brain areas in a "scaffold", both memorization and recall are more efficient, giving rigorous backing to the cognitive phenomenon that memorization and recall are easier with scaffolded memories; and (3) existing assemblies can be quite easily linked to simulate an arbitrary finite state machine (FSM), thereby capturing the brain's ability to memorize algorithms. This also makes the assemblies model capable of arbitrary computation simply in response to presentation of a suitable stimulus sequence, without explicit control commands. These findings provide a rigorous, theoretical explanation at the neuronal level of complex phenomena such as sequence memorization in rats and algorithm learning in humans, as well as a concrete hypothesis as to how the brain's remarkable computing and learning abilities could be realized.

Joint work with Christos Papadimitriou and Santosh Vempala.

We consider a service system where incoming tasks are instantaneously assigned to one out of many heterogeneous server pools. All the tasks sharing a server pool are executed in parallel and the execution times do not depend on the class of the server pool or the number of tasks currently contending for service. However, associated with each server pool is a utility function that does depend on the class of the server pool and the number of tasks currently sharing it. These features are characteristic of streaming and online gaming services, where the duration of tasks is mainly determined by the application but congestion can have a strong impact on the quality-of-service (e.g., video resolution and smoothness). We derive an upper bound for the mean overall utility in steady-state and introduce two load balancing policies that achieve this upper bound in a large-scale regime. Also, the transient and stationary behavior of these asymptotically optimal load balancing policies is characterized in the same large-scale regime.

Memory bounds for continual learning

Abstract: Continual learning, or lifelong learning, is a formidable current challenge to machine learning. It requires the learner to solve a sequence of k different learning tasks, one after the other, while with each new task learned it retains its aptitude for earlier tasks; the continual learner should scale better than the obvious solution of developing and maintaining a separate learner for each of the k tasks.  We embark on a complexity-theoretic study of continual learning in the PAC framework. We make novel uses of communication complexity to establish that any continual learner, even an improper one, needs memory that grows linearly with k, strongly suggesting that the problem is intractable.  When logarithmically many passes over the learning tasks are allowed, we provide an algorithm based on multiplicative weights update whose memory requirement scales well; we also establish that improper learning is necessary for such performance. We conjecture that these results may lead to new promising approaches to continual learning.

Based on the joint work with Xi Chen and Christos Papadimitriou.