diff --git a/.github/workflows/test-docs.yaml b/.github/workflows/test-docs.yaml index 21a546845..d4020b509 100644 --- a/.github/workflows/test-docs.yaml +++ b/.github/workflows/test-docs.yaml @@ -37,5 +37,5 @@ jobs: run: | mkdir build cd build - cmake .. -DARB_WITH_PYTHON=ON -DPython3_EXECUTABLE=`which python` + cmake .. -DARB_WITH_PYTHON=ON -DARB_BUILD_PYTHON_STUBS=OFF -DPython3_EXECUTABLE=`which python` make html diff --git a/doc/tutorial/index.rst b/doc/tutorial/index.rst index 8ef283e2d..3adb1567c 100644 --- a/doc/tutorial/index.rst +++ b/doc/tutorial/index.rst @@ -78,6 +78,7 @@ Advanced :maxdepth: 1 nmodl + plasticity Demonstrations -------------- diff --git a/doc/tutorial/plasticity.rst b/doc/tutorial/plasticity.rst new file mode 100644 index 000000000..6dd615f4f --- /dev/null +++ b/doc/tutorial/plasticity.rst @@ -0,0 +1,342 @@ +.. _tutorial_plasticity: + +Structural Plasticity in Arbor +============================== + +In this tutorial, we are going to demonstrate how a network can be built using +plasticity and homeostatic connection rules. Despite not playing towards Arbor's +strengths, we choose a LIF (Leaky Integrate and Fire) neuron model, as we are +primarily interested in examining the required scaffolding. + +We will build up the simulation in stages, starting with an unconnected network +and finishing with a dynamically built connectome. + +.. admonition:: Concepts and Requirements + + We cover some advanced topics in this tutorial, mainly structural + plasticity. Please refer to other tutorials for the basics of network + building. The model employed here --- storing an explicit connection matrix + --- is not advisable in most scenarios. + + In addition to Arbor and its requirements, ``scipy``, ``matplotlib``, and + ``networkx`` need to be installed. + +Unconnected Network +------------------- + +Consider a collection of ``N`` LIF cells. This will be the starting point for +our exploration. For now, we set up each cell with a Poissonian input such that +it will produce spikes periodically at a low frequency. + +The Python file ``01-setup.py`` is the scaffolding we will build our simulation +around and thus contains some passages that might seem redundant now, but will +be helpful in later steps. + +We begin by defining the global settings: + +.. literalinclude:: ../../python/example/plasticity/unconnected.py + :language: python + :lines: 7-15 + +- ``N`` is the cell count of the simulation. +- ``T`` is the total runtime of the simulation in ``ms``. +- ``t_interval`` defines the _interval_ such that the simulation advances in + discrete steps ``[0, 1, 2, ...] t_interval``. Later, this will be the timescale of + plasticity. +- ``dt`` is the numerical timestep on which cells evolve. + +These parameters are used here: + +.. literalinclude:: ../../python/example/plasticity/unconnected.py + :language: python + :lines: 52-62 + +where we run the simulation in increments of ``t_interval``. + +Back to the recipe, we set a prototypical cell: + +.. literalinclude:: ../../python/example/plasticity/unconnected.py + :language: python + :lines: 23 + +and deliver it for all ``gid``: + +.. literalinclude:: ../../python/example/plasticity/unconnected.py + :language: python + :lines: 42-43 + +Also, each cell has an event generator attached, using a Poisson point process seeded with the cell's ``gid``. + +.. literalinclude:: ../../python/example/plasticity/unconnected.py + :language: python + :lines: 33-40 + + +All other parameters are set in the constructor: + +.. literalinclude:: ../../python/example/plasticity/unconnected.py + :language: python + :lines: 19-28 + +We also proceed to add spike recording and generate plots using a helper +function ``plot_spikes`` from ``util.py``. You can skip the following details +for now and come back later if you are interested in how it works. Rates are +computed by binning spikes into ``t_interval`` and the neuron id; the mean rate +is the average across the neurons smoothed using a Savitzky-Golay filter +(``scipy.signal.savgol_filter``). + +We plot per-neuron and mean rates: + +.. figure:: ../../python/example/plasticity/01-rates.svg + :width: 400 + :align: center + +We also generate raster plots via ``scatter``: + +.. figure:: ../../python/example/plasticity/01-raster.svg + :width: 400 + :align: center + + +A Randomly Wired Network +------------------------ + +We use inheritance to derive a new recipe that contains all the functionality of +the ```unconnected`` recipe. We then add a random connectivity matrix during +construction, fix connection weights, and deliver the resulting connections +via the ``connections_on`` callback, with the only extra consideration of +allowing multiple connections between two neurons. + +In detail, the recipe stores the connection matrix, the current +incoming/outgoing connections per neuron, and the maximum for both directions + +.. literalinclude:: ../../python/example/plasticity/random_network.py + :language: python + :lines: 26-31 + +The connection matrix is used to construct connections, + +.. literalinclude:: ../../python/example/plasticity/random_network.py + :language: python + :lines: 33-38 + +together with the fixed connection parameters: + +.. literalinclude:: ../../python/example/plasticity/random_network.py + :language: python + :lines: 24-25 + +We define helper functions ``add|del_connections`` to manipulate the connection +table while upholding these invariants: + +- no self-connections, i.e., ``connection[i, i] == 0`` +- ``inc[i]`` the sum of ``connections[:, i]`` +- no more incoming connections than allowed by ``max_inc``, i.e., ``inc[i] <= max_inc`` +- ``out[i]`` the sum of ``connections[i, :]`` +- no more outgoing connections than allowed by ``max_out``, i.e., ``out[i] <= max_out`` + +These methods return ``True`` on success and ``False`` otherwise. + +.. literalinclude:: ../../python/example/plasticity/random_network.py + :language: python + :lines: 40-54 + +Both are used in ``rewire`` to produce a random connection matrix. + +.. literalinclude:: ../../python/example/plasticity/random_network.py + :language: python + :lines: 56-65 + +We then proceed to run the simulation: + +.. literalinclude:: ../../python/example/plasticity/random_network.py + :language: python + :lines: 68-79 + + and plot the results as before: + +.. figure:: ../../python/example/plasticity/02-rates.svg + :width: 400 + :align: center + + +Note that we added a plot of the network connectivity using ``plot_network`` +from ``util`` as well. This generates images of the graph and connection matrix. + +.. figure:: ../../python/example/plasticity/02-matrix.svg + :width: 400 + :align: center + +.. figure:: ../../python/example/plasticity/02-graph.svg + :width: 400 + :align: center + + + +Adding Homeostasis +------------------ + +Under the homeostatic model, each cell was a setpoint for the firing rate :math:`\nu^*` +which is used to determine the creation or destruction of synaptic connections via + +.. math:: + + \frac{dC}{dt} = \alpha(\nu - \nu^*). + +Thus we need to add some extra information to our simulation, namely the +setpoint :math:`\nu^*_i` for each neuron :math:`i` and the sensitivity parameter +:math:`\alpha`. We will also use a simplified version of the differential +equation above, namely adding/deleting exactly one connection if the difference +of observed to desired spiking frequency exceeds :math:`\pm\alpha`. This is both +for simplicity and to avoid sudden changes in the network structure. + +As before, we set up global parameters: + +.. literalinclude:: ../../python/example/plasticity/homeostasis.py + :language: python + :lines: 10-24 + +and prepare our simulation: + +.. literalinclude:: ../../python/example/plasticity/homeostasis.py + :language: python + :lines: 37-39 + +Note that our new recipe is almost unaltered from the random network. + +.. literalinclude:: ../../python/example/plasticity/homeostasis.py + :language: python + :lines: 27-33 + +All changes are contained in the way we run the simulation. To add a further +interesting feature, we skip the rewiring for the first half of the simulation. +The initial network is unconnected, but could be populated randomly (or any +other way) if desired by calling ``self.rewire()`` in the constructor of +``homeostatic_network`` before setting the maxima to eight. + +Plasticity is implemented by tweaking the connection table inside the recipe +between calls to ``run`` and calling ``simulation.update`` with the modified +recipe: + +.. literalinclude:: ../../python/example/plasticity/homeostasis.py + :language: python + :lines: 70 + +<<<<<<< HEAD +.. note:: + + As it is the central point here, it is worth emphasizing why this yields a + changed network. The call to ``sim.update(rec)`` causes Arbor to internally + re-build the connection table from scratch based on the data returned by + ``rec.connections_on``. However, here, this method just inspects the matrix + in ``rec.connections`` and converts the data into a ``arbor.connection``. + Thus, changing this matrix before ``update`` will build a different network. + + Important caveats: + + - without ``update``, changes to the recipe have no effect. + - vice versa ``update`` has no effect if the recipe doesn't return a different + data than before. + - ``update`` will delete all existing connections and their parameters, so + all connections to be kept must be explicitly re-instantiated. + - ``update`` will **not** delete synapses or their state, e.g., ODEs will + still be integrated even if not connected and currents might be produced; + - neither synapses/targets nor detectors/sources can be altered. Create all + endpoints up front. + - only the network is updated (this might change in future versions!). + - be very aware that ``connections_on`` might be called in arbitrary order + and by multiple (potentially different) threads and processes! This + requires some thought and synchronization when dealing with random numbers + and updating data *inside* ``connections_on``. + +Changes are based on the difference from the current rate we compute from the spikes +during the last interval, +||||||| parent of df94162f (Final thoughts and warnings.) +Changes are based on the difference of current rate we compute from the spikes +during the last interval +======= +.. note:: + + As it is the central point here, it is worth emphasizing why this yields a + changed network. The call to ``sim.update(rec)`` causes Arbor to internally + re-build the connection table from scratch based on the data returned by + ``rec.connections_on``. However, here, this method just inspects the matrix + in ``rec.connections`` and converts the data into a ``arbor.connection``. + Thus, changing this matrix before ``update`` will build a different network. + + Important caveats: + + - without ``update``, changes to the recipe have no effect + - vice versa ``update`` has no effect if the recipe doesn't return different + data than before + - ``update`` will delete all existing connections and their parameters, so + all connections to be kept must be explicitly re-instantiated + - ``update`` will **not** delete synapses or their state, e.g. ODEs will + still be integrated even if not connected and currents might be produced + - neither synapses/targets nor detectors/sources can be altered. Create all + endpoints up front. + - only the network is updated (this might change in future versions!) + - be very aware that ``connections_on`` might be called in arbitrary order + and by multiples (potentially different) threads and processes! This + requires some thought and synchronization when dealing with random numbers + and updating data *inside* ``connections_on``. + +Changes are based on the difference of current rate we compute from the spikes +during the last interval +>>>>>>> df94162f (Final thoughts and warnings.) + +.. literalinclude:: ../../python/example/plasticity/homeostasis.py + :language: python + :lines: 49-54 + +and the setpoint times the sensitivity. + +.. literalinclude:: ../../python/example/plasticity/homeostasis.py + :language: python + :lines: 55 + +Then, each potential pairing of target and source is checked in random +order for whether adding or removing a connection is required: + +.. literalinclude:: ../../python/example/plasticity/homeostasis.py + :language: python + :lines: 59-68 + +If we find an option to fulfill that requirement, we do so and proceed to the +next target. The randomization is important here, especially for adding +connections to avoid biases, in particular when there are too few eligible +connection partners. The ``randrange`` function produces a shuffled range ``[0, +N)``. We leverage the helper functions from the random network recipe to +manipulate the connection table, see the discussion above. + +Finally, we plot spiking rates as before; the jump at the half-way point is the +effect of the plasticity activating after which each neuron moves to the +setpoint. + +.. figure:: ../../python/example/plasticity/03-rates.svg + :width: 400 + :align: center + +And the resulting network: + +.. figure:: ../../python/example/plasticity/03-final-graph.svg + :width: 400 + :align: center + +Conclusion +---------- + +This concludes our foray into structural plasticity. While the building blocks + +- an explicit representation of the connections; +- running the simulation in batches (and calling ``simulation.update``!); +- a rule to derive the change; + +will likely be the same in all approaches, the concrete implementation of the +rules is the centerpiece here. For example, although spike rate homeostasis was +used here, mechanism states and ion concentrations --- extracted via the normal +probe and sample interface --- can be leveraged to build rules. Due to the way +the Python interface is required to link to measurements, using the C++ API for +access to streaming spike and measurement data could help to address performance +issues. Plasticity as shown also meshes with the high-level connection builder. +External tools to build and update connections might be useful as well. diff --git a/python/example/plasticity/01-raster.svg b/python/example/plasticity/01-raster.svg new file mode 100644 index 000000000..11b1a2fbd --- /dev/null +++ b/python/example/plasticity/01-raster.svg @@ -0,0 +1,1863 @@ + + + + + + + + 2024-10-08T11:34:50.435338 + image/svg+xml + + + Matplotlib v3.8.3, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/python/example/plasticity/homeostasis.py b/python/example/plasticity/homeostasis.py new file mode 100644 index 000000000..4edf354ee --- /dev/null +++ b/python/example/plasticity/homeostasis.py @@ -0,0 +1,75 @@ +#!/usr/bin/env python3 + +import arbor as A +from arbor import units as U +import numpy as np + +from util import plot_spikes, plot_network, randrange +from random_network import random_network + +# global parameters +# cell count +N = 10 +# total runtime [ms] +T = 10000 +# one interval [ms] +t_interval = 100 +# numerical time step [ms] +dt = 0.1 +# Set seed for numpy +np.random.seed = 23 +# setpoint rate in kHz +setpoint_rate = 0.1 +# sensitivty towards deviations from setpoint +sensitivity = 200 + + +class homeostatic_network(random_network): + def __init__(self, N, setpoint_rate, sensitivity) -> None: + super().__init__(N) + self.max_inc = 8 + self.max_out = 8 + self.setpoint = setpoint_rate + self.alpha = sensitivity + + +if __name__ == "__main__": + rec = homeostatic_network(N, setpoint_rate, sensitivity) + sim = A.simulation(rec) + sim.record(A.spike_recording.all) + + plot_network(rec, prefix="03-initial-") + + t = 0 + while t < T: + sim.run((t + t_interval) * U.ms, dt * U.ms) + if t < T / 2: + t += t_interval + continue + rates = np.zeros(N) + for (gid, _), time in sim.spikes(): + if time < t: + continue + rates[gid] += 1 + rates /= t_interval # kHz + dC = ((rec.setpoint - rates) * rec.alpha).astype(int) + unchangeable = set() + added = [] + deled = [] + for tgt in randrange(N): + if dC[tgt] == 0: + continue + for src in randrange(N): + if dC[tgt] > 0 and rec.add_connection(src, tgt): + added.append((src, tgt)) + break + elif dC[tgt] < 0 and rec.del_connection(src, tgt): + deled.append((src, tgt)) + break + unchangeable.add(tgt) + sim.update(rec) + print(f" * t={t:>4} f={rates} [!] {list(unchangeable)} [+] {added} [-] {deled}") + t += t_interval + + plot_network(rec, prefix="03-final-") + plot_spikes(sim, N, t_interval, T, prefix="03-") diff --git a/python/example/plasticity/random_network.py b/python/example/plasticity/random_network.py new file mode 100644 index 000000000..cc58c90af --- /dev/null +++ b/python/example/plasticity/random_network.py @@ -0,0 +1,79 @@ +#!/usr/bin/env python3 + +import arbor as A +from arbor import units as U +import numpy as np + +from util import plot_spikes, plot_network +from unconnected import unconnected + +# global parameters +# cell count +N = 10 +# total runtime [ms] +T = 1000 +# one interval [ms] +t_interval = 10 +# numerical time step [ms] +dt = 0.1 + + +class random_network(unconnected): + def __init__(self, N) -> None: + super().__init__(N) + self.syn_weight = 80 + self.syn_delay = 0.5 * U.ms + # format [to, from] + self.connections = np.zeros(shape=(N, N), dtype=np.uint8) + self.inc = np.zeros(N, np.uint8) + self.out = np.zeros(N, np.uint8) + self.max_inc = 4 + self.max_out = 4 + + def connections_on(self, gid: int): + return [ + A.connection((source, "src"), "tgt", self.syn_weight, self.syn_delay) + for source in range(self.N) + for _ in range(self.connections[gid, source]) + ] + + def add_connection(self, src: int, tgt: int) -> bool: + if tgt == src or self.inc[tgt] >= self.max_inc or self.out[src] >= self.max_out: + return False + self.inc[tgt] += 1 + self.out[src] += 1 + self.connections[tgt, src] += 1 + return True + + def del_connection(self, src: int, tgt: int) -> bool: + if tgt == src or self.connections[tgt, src] <= 0: + return False + self.inc[tgt] -= 1 + self.out[src] -= 1 + self.connections[tgt, src] -= 1 + return True + + def rewire(self): + tries = self.N * self.N * self.max_inc * self.max_out + while ( + tries > 0 + and self.inc.sum() < self.N * self.max_inc + and self.out.sum() < self.N * self.max_out + ): + src, tgt = np.random.randint(self.N, size=2, dtype=int) + self.add_connection(src, tgt) + tries -= 1 + + +if __name__ == "__main__": + rec = random_network(10) + rec.rewire() + sim = A.simulation(rec) + sim.record(A.spike_recording.all) + t = 0 + while t < T: + t += t_interval + sim.run(t * U.ms, dt * U.ms) + + plot_network(rec, prefix="02-") + plot_spikes(sim, N, t_interval, T, prefix="02-") diff --git a/python/example/plasticity/unconnected.py b/python/example/plasticity/unconnected.py new file mode 100644 index 000000000..e9a07ec99 --- /dev/null +++ b/python/example/plasticity/unconnected.py @@ -0,0 +1,62 @@ +#!/usr/bin/env python3 + +import arbor as A +from arbor import units as U +from util import plot_spikes + +# global parameters +# cell count +N = 10 +# total runtime [ms] +T = 1000 +# one interval [ms] +t_interval = 10 +# numerical time step [ms] +dt = 0.1 + + +class unconnected(A.recipe): + def __init__(self, N) -> None: + super().__init__() + self.N = N + # Cell prototype + self.cell = A.lif_cell("src", "tgt") + # random seed [0, 100] + self.seed = 42 + # event generator parameters + self.gen_weight = 20 + self.gen_freq = 1 * U.kHz + + def num_cells(self) -> int: + return self.N + + def event_generators(self, gid: int): + return [ + A.event_generator( + "tgt", + self.gen_weight, + A.poisson_schedule(freq=self.gen_freq, seed=self.cell_seed(gid)), + ) + ] + + def cell_description(self, gid: int): + return self.cell + + def cell_kind(self, gid: int) -> A.cell_kind: + return A.cell_kind.lif + + def cell_seed(self, gid: int): + return self.seed + gid * 100 + + +if __name__ == "__main__": + rec = unconnected(N) + sim = A.simulation(rec) + sim.record(A.spike_recording.all) + + t = 0 + while t < T: + t += t_interval + sim.run(t * U.ms, dt * U.ms) + + plot_spikes(sim, rec.num_cells(), t_interval, T, prefix="01-") diff --git a/python/example/plasticity/util.py b/python/example/plasticity/util.py new file mode 100644 index 000000000..554259ad3 --- /dev/null +++ b/python/example/plasticity/util.py @@ -0,0 +1,71 @@ +#!/usr/bin/env python3 + +import matplotlib.pyplot as plt +import numpy as np +from scipy.signal import savgol_filter +import networkx as nx + + +def plot_network(rec, prefix=""): + fg, ax = plt.subplots() + ax.matshow(rec.connections) + fg.savefig(f"{prefix}matrix.pdf") + fg.savefig(f"{prefix}matrix.png") + fg.savefig(f"{prefix}matrix.svg") + + n = rec.num_cells() + fg, ax = plt.subplots() + g = nx.MultiDiGraph() + g.add_nodes_from(np.arange(n)) + for i in range(n): + for j in range(n): + for _ in range(rec.connections[i, j]): + g.add_edge(i, j) + nx.draw(g, with_labels=True, font_weight="bold") + fg.savefig(f"{prefix}graph.pdf") + fg.savefig(f"{prefix}graph.png") + fg.savefig(f"{prefix}graph.svg") + + +def plot_spikes(sim, n_cells, t_interval, T, prefix=""): + # number of intervals + n_interval = int((T + t_interval - 1) // t_interval) + print(n_interval, T, t_interval) + + # Extract spikes + times = [] + gids = [] + rates = np.zeros(shape=(n_interval, n_cells)) + for (gid, _), time in sim.spikes(): + times.append(time) + gids.append(gid) + it = int(time // t_interval) + rates[it, gid] += 1 + + fg, ax = plt.subplots() + ax.scatter(times, gids, c=gids) + ax.set_xlabel("Time $(t/ms)$") + ax.set_ylabel("GID") + ax.set_xlim(0, T) + fg.savefig(f"{prefix}raster.pdf") + fg.savefig(f"{prefix}raster.png") + fg.savefig(f"{prefix}raster.svg") + + ts = np.arange(n_interval) * t_interval + mean_rate = savgol_filter(rates.mean(axis=1), window_length=5, polyorder=2) + fg, ax = plt.subplots() + ax.plot(ts, rates) + ax.plot(ts, mean_rate, color="0.8", lw=4, label="Mean rate") + ax.set_xlabel("Time $(t/ms)$") + ax.legend() + ax.set_ylabel("Rate $(kHz)$") + ax.set_xlim(0, T) + fg.savefig(f"{prefix}rates.pdf") + fg.savefig(f"{prefix}rates.png") + fg.savefig(f"{prefix}rates.svg") + + +def randrange(n: int): + res = np.arange(n, dtype=int) + np.random.shuffle(res) + return res