TY - GEN
T1 - Network Restructuring Control for Conic Invariance with Application to Neural Networks
AU - Singh, Matthew F.
AU - Ching, Shinung
N1 - Funding Information:
Psychology, and Electrical and Systems Engineering at Washington University in St. Louis, USA, [email protected] SC is with the Department of Electrical and Systems Engineering and Biomedical Engineering, at Washington University in St. Louis, USA, [email protected] MS was funded by NSF-DGE-1143954 from the US National Science Foundation. SC holds a Career Award at the Scientific Interface from the Burroughs-Wellcome Fund. Portions of this work were supported by AFOSR 15RT0189, NSF ECCS 1509342, NSF CMMI 1537015 and 1653589, from the US Air Force Office of Scientific Research and the US National Science Foundation, respectively.
Publisher Copyright:
© 2018 IEEE.
PY - 2018/7/2
Y1 - 2018/7/2
N2 - Recent advances in the study of artificial and biological neural networks support the power of dynamic representations-computing with information stored as nontrivial limit-sets rather than fixed-point attractors. Understanding and manipulating these computations in nonlinear networks requires a theory of control for abstract objective functions. Towards this end, we consider two properties of limit-sets: their topological dimension and orientation (covariance) in phase space and combine these abstract properties into a single well-defined objective: conic control-invariant sets in the derivative space (i.e., the vector field). Real-world applications, such as neural-medicine, constrain which control laws are feasible with less-invasive controllers being preferable. To this end, we derive a feedback control-law for conic invariance which corresponds to constrained restructuring of the network connections as might occur with pharmacological intervention (as opposed to a physically separate control unit). We demonstrate the ease and efficacy of the technique in controlling the orientation and dimension of limit sets in high-dimensional neural networks.
AB - Recent advances in the study of artificial and biological neural networks support the power of dynamic representations-computing with information stored as nontrivial limit-sets rather than fixed-point attractors. Understanding and manipulating these computations in nonlinear networks requires a theory of control for abstract objective functions. Towards this end, we consider two properties of limit-sets: their topological dimension and orientation (covariance) in phase space and combine these abstract properties into a single well-defined objective: conic control-invariant sets in the derivative space (i.e., the vector field). Real-world applications, such as neural-medicine, constrain which control laws are feasible with less-invasive controllers being preferable. To this end, we derive a feedback control-law for conic invariance which corresponds to constrained restructuring of the network connections as might occur with pharmacological intervention (as opposed to a physically separate control unit). We demonstrate the ease and efficacy of the technique in controlling the orientation and dimension of limit sets in high-dimensional neural networks.
UR - http://www.scopus.com/inward/record.url?scp=85062179142&partnerID=8YFLogxK
U2 - 10.1109/CDC.2018.8618729
DO - 10.1109/CDC.2018.8618729
M3 - Conference contribution
AN - SCOPUS:85062179142
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 2704
EP - 2709
BT - 2018 IEEE Conference on Decision and Control, CDC 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 57th IEEE Conference on Decision and Control, CDC 2018
Y2 - 17 December 2018 through 19 December 2018
ER -