minor tweaks + init of rl-snn exhibit lesson

Author: Alexander Ororbia

README.md

@@ -122,7 +122,7 @@ $ python install -e .
 </pre>
 
 **Version:**<br>
-2.0.0 <!--1.2.3-Beta--> <!-- -Alpha -->
+2.0.1 <!--1.2.3-Beta--> <!-- -Alpha -->
 
 Author:
 Alexander G. Ororbia II<br>

docs/museum/index.rst

@@ -18,3 +18,4 @@ relevant, referenced publicly available ngc-learn simulation code.
   snn_dc
   snn_bfa
   sindy
+  rl_snn

docs/museum/rl_snn.md

@@ -0,0 +1,35 @@
+# Reinforcement Learning through a Spiking Controller
+
+In this exhibit, we will see how to construct a simple biophysical model for 
+reinforcement learning with a spiking neural network and modulated 
+spike-timing-dependent plasticity. 
+This model incorporates a mechanisms from several different models, including 
+the constrained RL-centric SNN of <b>[1]</b> as well as the simplifications 
+made with respect to the model of <b>[2]</b>. The model code for this
+exhibit can be found
+[here](https://github.com/NACLab/ngc-museum/tree/main/exhibits/rl_snn).
+
+## Modeling Operant Conditioning through Modulation
+
+
+### Reward-Modulated Spike-Timing-Dependent Plasticity (R-STDP)
+
+
+## The Spiking Neural Circuit Model
+
+
+### Neuronal Dynamics
+
+
+## Running the RL-SNN Model
+
+
+<!-- References/Citations -->
+## References
+<b>[1]</b> Chevtchenko, Sérgio F., and Teresa B. Ludermir. "Learning from sparse 
+and delayed rewards with a multilayer spiking neural network." 2020 International 
+Joint Conference on Neural Networks (IJCNN). IEEE, 2020. <br> 
+<b>[2]</b> Diehl, Peter U., and Matthew Cook. "Unsupervised learning of digit
+recognition using spike-timing-dependent plasticity." Frontiers in computational
+neuroscience 9 (2015): 99.
+

ngclearn/components/neurons/graded/gaussianErrorCell.py

@@ -65,6 +65,12 @@ def __init__(self, name, n_units, batch_size=1, sigma=1., shape=None, **kwargs):
         self.modulator = Compartment(restVals + 1.0) # to be set/consumed
         self.mask = Compartment(restVals + 1.0)
 
+    @staticmethod
+    def eval_log_density(target, mu, Sigma):
+        _dmu = (target - mu)
+        log_density = -jnp.sum(jnp.square(_dmu)) * (0.5 / Sigma)
+        return log_density
+
     @transition(output_compartments=["dmu", "dtarget", "dSigma", "L", "mask"])
     @staticmethod
     def advance_state(dt, mu, target, Sigma, modulator, mask): ## compute Gaussian error cell output
@@ -79,6 +85,7 @@ def advance_state(dt, mu, target, Sigma, modulator, mask): ## compute Gaussian e
         dtarget = -dmu  # reverse of e
         dSigma = Sigma * 0 + 1. # no derivative is calculated at this time for sigma
         L = -jnp.sum(jnp.square(_dmu)) * (0.5 / Sigma)
+        #L = GaussianErrorCell.eval_log_density(target, mu, Sigma)
 
         dmu = dmu * modulator * mask ## not sure how mask will apply to a full covariance...
         dtarget = dtarget * modulator * mask

ngclearn/utils/diffeq/ode_utils.py

@@ -112,6 +112,30 @@ def _euler(carry, dfx, dt, params, x_scale=1.):
     new_carry = (_t, _x)
     return new_carry, (new_carry, carry)
 
+@partial(jit, static_argnums=(1))
+def _leapfrog(carry, dfq, dt, params):
+    t, q, p = carry
+    dq_dt = dfq(t, q, params)
+
+    _p = p + dq_dt * (dt/2.)
+    _q = q + p * dt
+    dq_dtpdt = dfq(t+dt, _q, params)
+    _p = _p + dq_dtpdt * (dt/2.)
+    _t = t + dt
+    new_carry = (_t, _q, _p)
+    return new_carry, (new_carry, carry)
+
+@partial(jit, static_argnums=(3, 4))
+def leapfrog(t_curr, q_curr, p_curr, dfq, L, step_size, params):
+    t = t_curr + 0.
+    q = q_curr + 0.
+    p = p_curr + 0.
+    def scanner(carry, _):
+        return _leapfrog(carry, dfq, step_size, params)
+    new_values, (xs_next, xs_carry) = _scan(scanner, init=(t, q, p), xs=jnp.arange(L))
+    t, q, p = new_values
+    return t, q, p
+
 @partial(jit, static_argnums=(2))
 def step_heun(t, x, dfx, dt, params, x_scale=1.):
     """