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Plasticity and Learning

LECTURE 10. Plasticity and Learning. Introduction Synaptic placticity rules − The basic Hebb rule − The covariance rule − BCM Rule − Non-Hebbian rules − Anti-hebbian rules − Timing-based Rules. Introduction. Hebb’s postulate

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Plasticity and Learning

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  1. LECTURE 10 Plasticity and Learning

  2. Introduction • Synaptic placticity rules • −The basic Hebb rule • − The covariance rule • − BCM Rule • −Non-Hebbian rules • − Anti-hebbian rules • − Timing-based Rules

  3. Introduction Hebb’s postulate “When an axon of cell A is near enough to excite cell B or 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”. Donald O. Hebb (1949) The theory is often summarized as "cells that fire together, wire together".

  4. • Conditioning: － The first attempt to model conditioning in terms of synaptic change. － Behavior ---?--- neural mechanisms • Development: － The formation and refinement of neural circuits need synaptic elimination. － Axonal or synaptic competition in neuromuscular junctions and visual system (Consumptive and interference competition)

  5. • Long term potentiation (LTP) - Long term depression （LTD） － Changes that persist for tens of minutes or longer are generally called LTP and LTD. It lasts for hours in vitro and days and weeks in vivo － The longest-lasting forms appear to require protein synthesis. － First found in Hippocampus － The physiological basis of Hebbian learning － Properties and mechanisms of long-term synaptic plasticity in the mammalian brain may relate to learning and memory. － Inhibitory synapses can also display plasticity, but this has been less thoroughly investigated both experimentally and theoretically

  6. Introduction • Synaptic placticity rules • −The basic Hebb rule • − The covariance rule • − BCM Rule • −Non-Hebbian rules • − Anti-hebbian rules • − Timing-based Rules

  7. The basic Hebb rule pre i post learning rate • : the firing rates of the pre- and postsynaptic neurons • Local mechanism • Interactive mechanism • Time-dependent mechanism

  8. pre The basic Hebb rule is unstable post • The processes of synaptic plasticity are typically much slower than the neural activity dynamics. • If, in addition, the stimuli are presented slowly enough to allow the network to attain its steady-state activity during training,

  9. Theoretically, an upper saturation constraint must be imposed to avoidunbounded growth. But experimentally,

  10. LTP and LTD at the Schaffer collateral inputs to the CA1 region of a rat hippocampal slice Is it due to that the basic Hebb rule has no LTD? Let’s add LTD by introducing the covariance rule

  11. Introduction • Synaptic placticity rules • −The basic Hebb rule • − The covariance rule • − BCM Rule • −Non-Hebbian rules • − Anti-hebbian rules • − Timing-based Rules

  12. The covariance rule postsynaptic threshold, e.g. presynaptic threshold, e.g. the input covariance matrix,

  13. (homosynaptic depression) (heterosynaptic depression) • By the basic Hebb rule, synapses are modified whenever correlated pre- and postsynaptic activity occurs. Such correlated activity can occur purely by chance, rather than reflecting a causal relationship that should be learned. To correct for this, the covariance rather than correlation-based rule is often used by network models •Although the covariance rule allows LTD and reflects a causal pre- and postsynaptic relationshipit is still unstable due to positive feedback

  14. The covariance rules, like the Hebb rule, are unstable and non-competitive pre post Average above equation over the training period: Competitioncan be introduced to allowing threshold to slide as follows

  15. Introduction • Synaptic placticity rules • −The basic Hebb rule • − The covariance rule • − BCM Rule • −Non-Hebbian rules • − Anti-hebbian rules • − Timing-based Rules

  16. BCM Rule Bienenstock, Cooper and Munro (1982) proposed an alternative for which there is experimental evidence where the postsynaptic threshold is dynamic Hebb rule covariance rule One example: LTP 0 y LTD BCM rule Usually set: Postsynaptic activity

  17. LTP 0 LTD Postsynaptic activity －This is again unstable if q is fixed. － However, if the threshold is allowed to grow faster than v we get stability. － depends on postsynaptic activity. For instance, the threshold for LTP decreases when postsynaptic activity is low (y ↓↓) － Here competition between synapses appears since strengthening some synapses results in threshold increasing meaning that it is harder for others to be strengthened

  18. Synaptic weight normalization －It is a more direct way of enforcing competition －Idea is that postsynaptic neuron can only support a certainamount of total synaptic weight so strengthening one leads to weakening others －2 types: subtractive normalisation and multiplicative normalisation

  19. Subtractive normalisation －It is easy to prove that the total increase in the weights is 0.

  20. Evidences for BCM rule Evidence for a sliding threshold: It is easier to obtain LTP in the cortex of dark-reared animalsand it is harder to induced LTD in these cortices － The field potentials evoked in layer III by layer IV stimulation in slices of visual cortex prepared for light-deprived and control rats 4-6 weeks old －The effects can be reserved by as little as two days of light exposure before slice preparation

  21. Experimental evidences for constant total synaptic weights － Low- and high-frequency BLA stimuli (LFS, HFS) are known to, respectively, produce homosynaptic NMDA dependent LTD and LTP in ITC cells. － Whether LFS and HFS also produce inverse heterosynaptic modifications is unclear.

  22. (Royer and Pare2003, Nature) •slices of the amygdala •guinea-pigs (3–5 weeks old) • intercalated (ITC) neurons of the amygdala: 中间神经元 •the basolateral amygdala (BLA): 基底外侧杏仁核 •an array of closely spaced (~150 μm) stimulating electrodes

  23. • Homosynaptic LTP was induced with HFS paired to postsynaptic depolarization. Postsynaptic depolarization was achieved by applying short (2ms) depolarizing current pulses (0.2 nA) timed so that BLA-evoked EPSPs would occur just before or during current-evoked spikes Plot of EPSP amplitude and rise time versus stimulation site (Royer and Pare2003, Nature)

  24. LTD induction produces heterosynaptic LTP (Royer and Pare2003, Nature) Left: Difference between pre- and post-LFS response profiles (EPSP amplitudes) for one cell (top) and average of all cells Right:Time course of changes in response amplitude

  25. Result is similar with high frequency stimuli (Royer and Pare2003, Nature),

  26. － Their results showed that the activity-dependent enhancement or depression of particular inputs to intercalated neurons is accompanied by inverse modifications at heterosynaptic sites, which contributes to total synaptic weight stabilization －The inverse homo- versus heterosynaptic plasticity seems to be a cell- wide event, which needs an intracellular signaling system that can render synapses ‘aware’ of each other or of the mean neuronal activity. －How do unstimulated inputs detect the stimulation frequency at the stimulated pathway?

  27. Introduction • Synaptic placticity rules • −The basic Hebb rule • − The covariance rule • − BCM Rule • −Non-Hebbian rules • − Anti-hebbian rules • − Timing-based Rules

  28. Non-Hebbian forms of synaptic plasticity • They modify synaptic strengths solely on the basis of pre- or postsynaptic firing, are likely to play important roles in homeostatic, developmental, and learning processes •Homeostatic plasticity －It allows neurons to sense how active they are and to adjust their properties to maintain stable function －Loosely defined, a homeostatic form of plasticity is one that acts to stabilize the activity of a neuron or neuronal circuit in the face of perturbations, such as changes in cell size or in synapse number or strength, that alter excitability. － A large number of plasticity phenomena have now been identified (e.g., synaptic scaling and homeostasis of intrinsic excitability of neurons)

  29. Synaptic scaling − A form of synaptic plasticity that adjusts the strength of all of a neuron's excitatory synapses up or down to stabilize firing, avoiding quiescence and hyper-excitation at the level of individual neurons. − Current evidence suggests that neurons detect changes in their own firing rates through a set of calcium-dependent sensors − Review paper: Gina G. Turrigiano. The Self-Tuning Neuron: Synaptic Scaling of Excitatory Synapses. Cell 135: 422-435, October 31, 2008

  30. A model of multiplicative scaling through the removal of AMPA receptors (Turrigiano 1999, TINS)

  31. Homeostasis of intrinsic excitability of neurons • Activity can also modify the intrinsic excitabilityand response properties of neurons • Models of such intrinsic plasticityshow that neurons can be remarkably robust to external perturbations ifthey adjust their conductances to maintain specified functional characteristics • Intrinsic and synaptic plasticity can interact in interesting ways. Forexample, shifts in intrinsic excitability can compensate for changes in thelevel of input to a neuron caused by synaptic plasticity.

  32. Homeostasis of intrinsic excitability of neurons Theoretical and experimental work suggests that intracellular Ca2+ concentration might regulate the balance of inward and outward currents generated by a neuron (Turrigiano 1999, TINS)

  33. Anti-Hebbian plasticity • It causes synapses to decrease (rather than increase) in strength when there is simultaneous pre- and postsynaptic activity. • It is believed to be the predominant form of plasticity at synapses in mormyrid electric fish and those from parallel fibers to Purkinje cells in the cerebellum • Anti-Hebbian modification tends to make weights decrease without bound

  34. Introduction • Synaptic placticity rules • −The basic Hebb rule • − The covariance rule • − BCM Rule • −Non-Hebbian rules • − Anti-hebbian rules • − Timing-based Rules

  35. Timing-Based Rules LTPis induced by repetitive stimulation with positively correlated spike times of post and pre-synaptic neuron LDPis induced by repetitive stimulation with negatively correlated spike times of post and pre-synaptic neuron

  36. Spike Timing Dependent Plasticity (STDP) An intracellular recording of a pair of cortical pyramidal cells in a slice experiment (Markram et al., 1997)

  37. －LTP and LTD of retinotectal synapses recorded in vivo in Xenopus tadpoles (Zhang et al., 1998)

  38. • Simulating the spike-timing dependence of synaptic plasticity requires a spiking model (e.g. Integrate-and-Fire Models). However, an approximate model can be constructed on the basis of firing rates where LTP LTD • Note above equation is based on a Hebbian rule • The STDP rule describes an asymmetriclearning rule

  39. • About H(τ): a function like the solid line in previous figure.

  40. Sequence learning based on STDP • The Timing-Based plasticity rule is applied throughout a training period during which the stimulus being presented moves to the right and excites the different neurons in the network sequentially • After the training period, the neuron with sa = 0 receives strengthened input from the sa=−2 neuron and weakened input from the neuron with sa= 2

  41. • If the same time-dependent stimulus is presented again after training, the neuron with sa= 0 will respond earlier than it did prior to training • The training experience causes neurons to learn a time sequence

  42. Another example on time sequence learning inplace fields • Place field is negatively skewed after experience (Mehta et al. 1997; 2000)

  43. A variety in plasticity • Different cortical regions, such as hippocampus and visual cortex have somewhat different forms of synaptic plasticity. (Abbott and Nelson 2000, Nature)

  44. A few properties of LTP and LTD Long-term plastic changes can be induced in about 1 s or less (i.e. within a rather short period, similar to short-term plasticity) The induced change in synaptic weight typically lasts for hours (if no further changes are induced) The longest-lasting forms appear to require protein synthesis

  45. Three types of training procedures • Unsupervised (or sometimes self-supervised) learning. － A network responds to a series of inputs during training solely on the basis of its intrinsic connections and dynamics •Supervised learning －A desired set of input-output relationships is imposed on the network by a ‘teacher’ during training. － Networks that perform particular tasks can be constructed in this way • Reinforcement learning －It is somewhat intermediate between these cases. －The network output is not constrained by a teacher, but evaluative feedback on network performance is provided in the form of reward or punishment

  46. Homework • 与基本 Hebb 学习律比较, BCM 学习律在哪些方面做了改进? 意义何在? • 举例说明稳态可塑性(Homeostatic plasticity)。 • 如果要实现神经网络的时间序列学习，需要采用那种学习律？为什么？

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