work-storage-presentations-qualsJC-tamingTheBeast

\documentclass{seminar}

Additional figures

Synaptic scaling

\includegraphics{synapticScaling2.eps}

Synaptic redistribution

\includegraphics{synapticRedist.eps}

Taming the beast

Goals

• Avoid positive feedback loop
• "What is needed is a mechanism that maintains an appropriate level of total excitation, but allows this to be distributed in different ways across the synapses of a network by Hebbian processes."

A simple Hebb rule

\dot{w_{ij}} = \nu \cdot (rate_i \cdot rate_j)

Synaptic strength increases in proportion to the correlation between two inputs (the product of their firing rates).

If you measure firing rate w/r/t some baseline, you get:

\dot{w_{ij}} = \nu \cdot ((rate_i - baseline_i) \cdot (rate_j - baseline_j))

Normalization

Subtractive

\dot{w_{ij}} = k \cdot (rate_i \cdot rate_j - \textrm{badness}(w))

Multiplicative

\dot{w_{ij}} = k \cdot (rate_i \cdot rate_j - \textrm{badness}(w)*w_{ij})

For example, maybe

\begin{align*} \textrm{badness}(w) = \left\{ \begin{array}{ll} 0 & \textrm{when } (\sum_{i,j} w_{i,j}) < 10
(\sum_{i,j} w_{i,j}) - 10 & \textrm{otherwise} \end{array} \right. \end{align*}

\scriptsize{Popular paper: Miller, K. D. and MacKay?, D. J. C. The role of constraints in Hebbian learning. Neural Comput. 6, 100 126 (1994).}

Defns of "Hebbian plasticity"

• Hebb's words: "When an axon of cell A is near enough to excite B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A's efficiency, as one of the cells firing B, is increased"
• New defn: "over time Hebbian plasticity has come to mean any long-lasting form of synaptic modification (strengthening or weakening) that is synapse specific and depends on correlations between pre- and postsynaptic firing."

(note: the second defn has correlation in place of causation. STDP, by requiring a pre-before-post, gets closer to the original causality requirement)

BCM rule

• LTP when correlated activity exceeds a threshold; LTD otherwise
• Sliding threshold: the more active the postsynaptic neuron is, the harder to get LTP

\dot{w}_{pre, post} = k \cdot (f(rate_{post}, \left< rate_{post} \right>) \cdot rate_{pre})

$f(x)$ might be something like $rate_{post} - \left< rate_{post} \right>$ \scriptsize{(I think)}

(orig paper had multiplicative normalization, too)

\scriptsize{Orig paper: Bienenstock, E. L., Cooper, L. N., and Munroe, P. W. (1982). Theory of the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. J. Neurosci., 2:32-48. }

\scriptsize{Book: Theory Of Cortical Plasticity, Leon Cooper, Nathan Intrator, Brian S Blais, Harel Z Shouval. Some chapters online at http://nba.uth.tmc.edu/homepage/shouval/teaching.htm}

Synaptic scaling

Oja rule

\dot{w}_{pre, post} = \nu \cdot (rate_{pre} \cdot rate_{post} - rate_{post}^2 * w_{ij}

\begin{itemize} \item Similar to the "multiplicative normalization" example given above \item Does PCA \end{itemize}

\scriptsize{Orig paper: Oja, E. (1982). A simplified neuron model as a principal component analyzer. J. Math. Biol., 15:267-273.}

Quick PCA "review"

\includegraphics[scale=.4]{PCAintro1.eps}

Quick PCA "review" cont'd

\includegraphics[scale=.4]{PCAintro2.eps}

\bullet direction of greatest variance

\scriptsize{Good PCA intro: http://www.okstate.edu/artsci/botany/ordinate/PCA.htm. See also http://purl.net/net/AIWiki/PCA.}

Synaptic scaling cont'd

• Competition
• Because NMDA receptors may be affected, may do something like the BCM rule
• Can "scale up" quiet cells

STDP

• Helps with timing-sensitive tasks
• Random firing evokes LTD
• If postsynaptic cell is overly active, all firing is effectively "random", and synaptic strengths decrease
• "ultimately leads to a nonuniform distribution of synaptic strengths and a postsynaptic neuron that fires at a reasonable rate, but irregularly". Thus, STDP not only stabilizes Hebbian modification, it drives neurons to a noisy but temporally sensitive state that resembles what has been suggested to exist in vivo."
• Competition
• Sequence memory

Synaptic redistribution

• "Transient efficacy" selectively higher; "steady-state" efficacy not higher
• Allows synapses to be "transiently strong"; allows networks to have strong sporadic activity, without positive feedback loop leading to overly excited steady-state