QLS Seminar - Tuesday 2 February at 15:00 (CET)

[ICTP/qls - Valassi Barbara]

Dear All,


Tuesday 2 February 2021 at 15:00 CET, Rainer Engelken, Columbia 
University, will give a webinar titled:

*Quantifying dynamic stability and signal propagation: Lyapunov spectra 
of recurrent neural networks*

*Abstract*:Brains process information through the collective dynamics of 
large neural networks. Collective chaos was suggested to underlie the 
complex ongoing dynamics observed in cerebral cortical circuits and 
determine the impact and processing of incoming information streams. 
While dynamic mean-field theory has uncovered key properties of 
recurrent network models such as the onset of chaos and their largest 
Lyapunov exponent, fundamental features of their dynamics remain 
unknown. In particular, chaotic dynamics in dissipative high-dimensional 
systems takes place on a subset of phase space of reduced dimension and 
is organized by a complex tangle of stable, neutral and unstable 
manifolds. Key topological invariants of this phase space structure such 
as attractor dimension, and Kolmogorov-Sinai entropy so far remained 
elusive.

Here we calculate the complete Lyapunov spectrum of recurrent neural 
networks. We show that chaos in these networks is extensive with a 
size-invariant Lyapunov spectrum and characterized by attractor 
dimensions much smaller than the number of phase space dimensions. The 
attractor dimension and entropy rate increases with coupling strength 
near the onset of chaos but decreases far from onset, reflecting a 
reduction in the number of unstable directions. We find that near the 
onset of chaos, for very intense chaos, and discrete-time dynamics, 
random matrix theory provides good analytical approximations to the full 
Lyapunov spectrum. We show that a generalized time-reversal symmetry of 
the network dynamics induces a point-symmetry of the Lyapunov spectrum 
reminiscent of the symplectic structure of chaotic Hamiltonian systems. 
Temporally fluctuating input can drastically reduce both the entropy 
rate and the attractor dimension. For trained recurrent networks, we 
find that Lyapunov spectrum analysis provides a quantification of error 
propagation and stability achieved by distinct learning algorithms. Our 
methods apply to systems of arbitrary connectivity, and we describe a 
comprehensive set of controls for the accuracy and convergence of 
Lyapunov exponents.

Our results open a novel avenue for characterizing the complex dynamics 
of recurrent neural networks and the geometry of the corresponding 
high-dimensional chaotic attractor. They also highlight the potential of 
Lyapunov spectrum analysis as a diagnostic for machine learning 
applications of recurrent networks..


Indico webpage: http://indico.ictp.it/event/9543/ 
<http://indico.ictp.it/event/9543/>

Zoom Meeting ID to attend the online seminar: 475-819-702


Join Zoom Meeting: https://zoom.us/j/475819702

 
<https://zoom.us/j/475819702

>


If you haven't registered for previous QLS webinars, please contact 
qls at ictp.it <mailto:qls at ictp.it>to obtain the PASSWORD for this zoom 
meeting.

Kind regards,
Barbara Valassi for QLS Section