Computational Cognitive Neuroscience Lab

1. Computational Cognitive Neuroscience Lab Today: Model Learning

2. Computational Cognitive Neuroscience Lab • Today: • Homework is due Friday, Feb 17 • Chapter 4 homework is shorter than the last one! • Undergrads omit 4.4, 4.5, 4.7c, 4.7d

3. Hebbian Learning • “Neurons that fire together, wire together” • Correlations between sending and receiving activity strengthens the connection between them • “Don’t fire together, unwire” • Anti-correlation between sending and receiving activity weakens the connection

4. LTP/D via NMDA receptors • NMDA receptors allow calcium to enter the (postsynaptic) cell • NMDA are blocked by Mg+ ions, which are cast off when the membrane potential increases • Glutamate (excitatory) binds to unblocked NMDA receptor, causes structural change that allows Ca++ to passthrough

5. Calcium and Synapses • Calcium initiates multiple chemical pathways, dependent on the level of calcium • Low Ca++ long term depression (LTD) • High Ca++ long term potentiation (LTP) • LTP/D effects: new postsynaptic receptors, incresed dendritic spine size, or increased presynaptc release processes (via retrograde messenger)

6. Fixing Hebbian learning • Hebbian learning results in infinite weights! • Oja’s normalization (savg_corr) • When to learn? • Conditional PCA--learn only when you see something interesting • A single unit hogs everything? • kWTA and Contrast enhancement --> specialization

7. Principal Components Analysis (PCA) • Principal, as in primary, not principle, as in some idea • PCA seeks a linear combination of variables such that maximum variance is extracted from the variables. It then removes this variance and seeks a second linear combination which explains the maximum proportion of the remaining variance, and so on until you run out of variance.

8. PCA continued • This is like linear regression, except you take the whole collection of variables (vector) and correlate it with itself to make a matrix. • This is kind of like linear regression, where a whole collection of variables is regressed on itself • The line of best fit through this regression is the first principal component!

9. PCA cartoon

10. Conditional PCA • “Perform PCA only when a particular input is received” • Condition: The forces that determine when a receiving unit is active • Competition means hidden units will specialize for particular inputs • So hidden units only learn when their favorite input is available

11. Self-organizing learning • kWTA determines which hidden units are active for a given input • CPCA ensures those hidden units learn only about a single aspect of that input • Contrast enhancement -- drive high weighs higher, low weights lower • Contrast enhancement helps units specialize (and share)

12. Bias-variance dilemma • High bias--actual experience does not change model much, so biases better be good! • Low bias--experience highly determines learning, so does random error! Model could be different, high model variance

13. Architecture as Bias • Inhibition drives competition, and competition determines which units are active, and the unit activity determines learning • Thus, deciding which units share inhibitory connections (are in the same layer) will affect the learning • This architecture is the learning bias!

14. Fidelity and Simplicity of representations • Information must be lost in the world-to-brain transformation (p118) • There is a tradeoff in the amount of information lost, and the complexity of the representation • Fidelity / simplicity tradeoff is set by • Conditional PCA (first principal component only) • Competition (k value) • Contrast enhancement (savg_corr, wt_gain)