2. The search for organizing principles of brain function Needed at multiple levels: synapse => cell => brain area (cortical maps) => hierarchy of areas Self-organization: Hebbian learning => feature- analyzing cells => cortical maps Information theory, a neural optimization principle, and applications Prediction, control, and the “local cortical circuit” (LCC)

3. Self-organization Pattern formation (Turing, 1952) from simple local rules (e.g., Hebb, 1949) –Hebb rule: When the firing of cell A contributes to that of cell B, increase the efficiency (synaptic strength) with which A excites B to fire. –An early puzzle: How does a layer of orientation- selective cells (Hubel & Wiesel, 1960-70s) form? –An early example of the power of Hebb learning: Hebb rule + short connections + locally-correlated random electrical activity, can => orientation-selective cells & their patterning in a layer (RL)

4. Self-organization in cortical models Movie: J Sirosh, R Miikkulainen, & JA Bednar (UT Austin), 1996 [courtesy JA Bednar] http://www.cs.utexas.edu/ ~nn/web- pubs/htmlbook96/sirosh/or _quad.mpghttp://www.cs.utexas.edu/ ~nn/web- pubs/htmlbook96/sirosh/or _quad.mpg Click for movie: or_quad.mov or_quad.mov Orientation map (below; R Linsker, 1986)

5. Some higher-level properties that can result from Hebbian learning –Feature-analyzing (selective) cells. –“Infomax” principle (RL): Create a layer of cells whose outputs convey maximum (Shannon) information about its inputs, subject to biological constraints & costs (types of allowed proc’g, wiring length, energy cost, etc.). An optimal encoding principle. Various uses of infomax –Models of neural learning & development –Qual’ve (RL, others) and quant’ve (Atick et al.) exp’tal agreement –Infomax-based ICA (independent component analysis) (Bell & Sejnowski, 1995): Reconstructs N statistically independent sources, given N linear combinations of them. –Nonlinear infomax is one way to generate “sparse representations.” Sparse coding used to reconstruct 3 speech sources given only the composite signal at each of 2 receivers (RL, 2001)

7. time freq. Sparse representation of mixture of sources

8. time freq. Labeling using a source signature Can obtain source signature from: - Relative transfer function (attenuation & phase shift at each frequency) from source to two rcvrs (used here). - Other methods: Pitch tracking; phoneme properties; can de-mix two overlapping sources using two received mixtures, etc. (None used here.)

9. time freq. Masking & reconstruction

10. Acoustic separation demo Mixture of 3 stereo speech sources Source 1: reconstruction & original Source 2: reconstruction & original Source 3: reconstruction & original

11. The “local cortical circuit” (LCC) Substantial uniformity of cell org’n & connectivity across neocortical areas (Mountcastle) Core functions of the LCC “module”? –A recurrent neural net that can combine “bottom-up” data and “top-down” expectations. LCC role in: forming generalizations? stabilizing feature analysis within each cortical processing area? Bayesian inference? –It’s long been clear that prediction, estimation, inference, & goal-directed motor control are important functions of mammalian brains. –Recent work (RL): A neural net alg’m for optimal Kalman estimation (pred’n) and control. The alg’m implies a set of constraints on the NN circuitry & signal flows. This architecture turns out to be similar to LCC.

12. Some other important unsolved problems “Fast learning”: animals vs. neural nets –Learning causal relations: deterministic or statistical? Learning powerful invariances and the “right” representations. Is statistical learning over-emphasized? Principles governing the processing, segregation, & integration of information streams (e.g., color, form, “what” & “where”)? Common ground between perception & human concept formation: Learning similarity metrics that are useful for forming generalizations & for behavior. How is information coded? (Firing rates, spike timing, place coding, synchrony & phase-locking, …?) What representations are really used by the brain? Some surprises -- e.g., “change blindness” (R Rensink demo). The “binding problem”; self-awareness & consciousness Tools: How to probe circuit dynamics (of multiple interconnected cells) at fine spatial & temporal resolution?