Notes

Plasticity & Learning

Why do we need plasticity/learning? The C.Elegans genome stores all synaptic connections. The simple worm C. Elegans, for example, has 302 neurons and about 7000 synapses and in each individual of an inbred strain, the wiring pattern is exactly the same (Chen et al., 2006).

Connections in the human Brain are mostly learned: The human brain has about 10ˆ11 neurons, and more than 10ˆ3 synapses per neuron. Specifying a connection target requires about log_2 10ˆ11 + 35 bits/synapse. Thus, it would take 3.5 x 10ˆ15 bits (approx. 400TB) to specify all 10ˆ14 connections in thebrain. However, the human genome only has about 3 x 10ˆ9 nucleotides, so it cannot encode more than approx. 1GB of information (Wel et al., 2013). Conclusion: Even if every nucleotide of the human genome were devoted to efficiently specifying brain connections, the information capacity is orders of magnitude too small to encode all synaptic connections. Why do we need learning! We need learning to survive and adapt to new situations in a changing environment. Learning as evolutionary survival strategy. Is the brain a Universal Learning Machine? A species using the mixed strategy may thrive if that strategy achieves a higher asymptotic level of performance. Suggested paper: A Critique of Pure Learning: "What Artificial Neural Networks can Learn from Animal Brains" - Zador Intelligent Behaviour Emerges with Learning!

Defining Plasticity/Learning (Learning & Memory vs. Plasticity)

• Learning: The acquisition/storage of knowledge/information or the formation of a memory through experience.
• Memory: Stored information that can be recalled at a later stage in time
  • Learning results in memory - which itself has a further outcome - a change in future behaviour.
  • Learning does not always imply a conscious attempt to learn. Simple observation can lead to the creation of a new memory.
• Plasticity: the biological implementation of learning. Plasticity allows us to form a memory.

Learning in Computer Science

• Machine Learning
  • Supervised Learning (Regression & Classification)
  • Unsupervised Learning (Clustering & Dimensionality Reduction)
  • Reinforcement Learning

Learning in Neuroscience

• Pavlovian Conditioning
• Instrumental Conditioning
• Reward/Aversive Learning
• Social Learning
• Perceptual Learning
• Motor Learning

Network and Systems Plasticity Neural Substrates of Plasticity

How does the brain implement a learning? The Hippocampus as a Model System to Study Learning and Memory

Henry Gustav Molaison (H.M.) 1926 - 20008 Amygdala, hippocampal gyrus, and anterior two third of the hippocampus were removed.

Diagnosis: Severe anterograde amnesia

• Normal STM
• Normal LTM (for events prior to surgery)
• Problem: transfer from STM to LTM
• Could not consolidate new declarative knowledge
• Capable of acquiring implicit knowledge

Conclusions:

• The Hippocampus is not a permanent storage area for explicit knowledge.
• The Hippocampus is involved (with other cortical areas) in consolidation, a longer term process taking months to years (note retrograde amnesia in hippocampus lesion patients for up to 3 years).
• Consolidation is understood to involve biological changes taking place in those other areas of cortex.
• Once this has fully takin place, the hippocampus is not required for retrieval.

Cellular Plasticity, the Perceptron

The Hippocampus and Spatial Memory

Morris Water Maze

How can we measure neuronal plasticity in the Hippocampus?

Plasticity & Memory (LTP, LTD)

Short-term Plasticity: Paired Pulse Facilitation Paired activations of a synapse onto a CA1 neuron. "Residual Ca2+"in terminal for 10 to 100 ms after first stimulus increases probability of release.

Post Tetanic Potentiation and Long-Term Potentiation PTP believed to be caused by a large accumulation of Ca2+ in the terminal caused by a high frequency tetanic stimulation.

Recording of LTP in a Hippocampal Slice & of LTD in the Hippocampus

Summary of LTP and LTD

• LTP
  • LTP after titanic stimulation is (high) frequency dependent.
  • LTP involves multiple mechanisms across time all of which induce long-term synaptic strengthening.
  • LTP mechanisms last from 30min to several hours, but do not involve protein synthesis.
  • LTP mechanisms lasting longer than a few hours require protein synthesis.
• LTD
  • LTD after titanic stimulation is (low) frequency dependent.
  • LTD also involves several different mechanisms acting in concert to induce synaptic depression.
  • LTD and LTP act in concerto to change information coding and to implement new memories in the brain.
  • STDP is thought to arise from the same mechanisms governing LTP and LTD.

Synaptic plasticity, the Hebbian Synapse

Synaptic Plasticity - A Short Recap of Synaptic Function

Plasticity (LTP) at the Synapse

1. Synapse size changes. (Long-term)
2. AMPA/NMDA ratio changes / More vesicles. (Long-term)
3. Number of spines changes. (Very Long-term)

Time Scales of Synaptic Plasticity

Synaptic Plasticity - The NMDA Receptor

The Role of Calcium in LTP/LTD

Hebb's Idea & Spike-Timing Dependent Plasticity (STDP)

Hebb's Idea

Hebb's Postulate

Spike-Timing Dependent Plasticity (STDP)

What can we learn from the Brain?

The Perceptron

The McCulloch & Pitts Neuron AKA The Perceptron

The Perceptron Learning Algorithm Can all logical operations be implemented by a McCulloch Pitts Neuron? OR yes, EQUALITY yes, AND yes, NOT yes, but it cannot implement XOR. Since there is no line which perfectly separates the two classes in the XOR problem. We can overcome this problem by combining multiple neurons in networks -> Neural Networks.

The Perceptron - Summary

• McCulloch-Pitts neurons implement a linear decision boundary (separating hyperplane)
• The weights and bias define the decision boundary
• They can implement many logical operations (AND, OR, NOT)
• They cannot implement XOR (not linearly separable)
• They can be trained on labeled datasets (supervised learning).

Learning to Recognize Handwritten Numbers (MNIST)

• Machine Learning Approach:
  • Linear Classifier: 88 - 92 accuracy.
  • K-Nearest Neighbor: 95 - 98 accuracy.
• Human: 99.8 accuracy.

A Neuronal Network for Classifying Handwritten Digits We can train a multi-layer NN through gradient descent (backpropagation) to minimize the error by changing the weights between neurons.