.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/eprop_plasticity/eprop_supervised_classification_evidence-accumulation.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_eprop_plasticity_eprop_supervised_classification_evidence-accumulation.py: Tutorial on learning to accumulate evidence with e-prop ------------------------------------------------------- .. only:: html ---- Run this example as a Jupyter notebook: .. card:: :width: 25% :margin: 2 :text-align: center :link: https://lab.ebrains.eu/hub/user-redirect/git-pull?repo=https%3A%2F%2Fgithub.com%2Fnest%2Fnest-simulator-examples&urlpath=lab%2Ftree%2Fnest-simulator-examples%2Fnotebooks%2Fnotebooks%2Feprop_plasticity%2Feprop_supervised_classification_evidence-accumulation.ipynb&branch=main :link-alt: JupyterHub service .. image:: https://nest-simulator.org/TryItOnEBRAINS.png .. grid:: 1 1 1 1 :padding: 0 0 2 0 .. grid-item:: :class: sd-text-muted :margin: 0 0 3 0 :padding: 0 0 3 0 :columns: 4 See :ref:`our guide ` for more information and troubleshooting. ---- Training a classification model using supervised e-prop plasticity to accumulate evidence. Description ~~~~~~~~~~~ This script demonstrates supervised learning of a classification task with the eligibility propagation (e-prop) plasticity mechanism by Bellec et al. [1]_. This type of learning is demonstrated at the proof-of-concept task in [1]_. We based this script on their TensorFlow script given in [2]_. The task, a so-called evidence accumulation task, is inspired by behavioral tasks, where a lab animal (e.g., a mouse) runs along a track, gets cues on the left and right, and has to decide at the end of the track between taking a left and a right turn of which one is correct. After a number of iterations, the animal is able to infer the underlying rationale of the task. Here, the solution is to turn to the side in which more cues were presented. .. image:: ../../../../pynest/examples/eprop_plasticity/eprop_supervised_classification_schematic_evidence-accumulation.png :width: 70 % :alt: See Figure 1 below. :align: center Learning in the neural network model is achieved by optimizing the connection weights with e-prop plasticity. This plasticity rule requires a specific network architecture depicted in Figure 1. The neural network model consists of a recurrent network that receives input from Poisson generators and projects onto two readout neurons - one for the left and one for the right turn at the end. The input neuron population consists of four groups: one group providing background noise of a specific rate for some base activity throughout the experiment, one group providing the input spikes of the left cues and one group providing them for the right cues, and a last group defining the recall window, in which the network has to decide. The readout neuron compares the network signal :math:`\pi_k` with the teacher target signal :math:`\pi_k^*`, which it receives from a rate generator. Since the decision is at the end and all the cues are relevant, the network has to keep the cues in memory. Additional adaptive neurons in the network enable this memory. The network's training error is assessed by employing a cross-entropy error loss. Details on the event-based NEST implementation of e-prop can be found in [3]_. References ~~~~~~~~~~ .. [1] Bellec G, Scherr F, Subramoney F, Hajek E, Salaj D, Legenstein R, Maass W (2020). A solution to the learning dilemma for recurrent networks of spiking neurons. Nature Communications, 11:3625. https://doi.org/10.1038/s41467-020-17236-y .. [2] https://github.com/IGITUGraz/eligibility_propagation/blob/master/Figure_3_and_S7_e_prop_tutorials/tutorial_evidence_accumulation_with_alif.py .. [3] Korcsak-Gorzo A, Stapmanns J, Espinoza Valverde JA, Dahmen D, van Albada SJ, Bolten M, Diesmann M. Event-based implementation of eligibility propagation (in preparation) .. GENERATED FROM PYTHON SOURCE LINES 76-79 Import libraries ~~~~~~~~~~~~~~~~ We begin by importing all libraries required for the simulation, analysis, and visualization. .. GENERATED FROM PYTHON SOURCE LINES 79-87 .. code-block:: Python import matplotlib as mpl import matplotlib.pyplot as plt import nest import numpy as np from cycler import cycler from IPython.display import Image .. GENERATED FROM PYTHON SOURCE LINES 88-93 Schematic of network architecture ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This figure, identical to the one in the description, shows the required network architecture in the center, the input and output of the pattern generation task above, and lists of the required NEST device, neuron, and synapse models below. The connections that must be established are numbered 1 to 7. .. GENERATED FROM PYTHON SOURCE LINES 93-99 .. code-block:: Python try: Image(filename="./eprop_supervised_classification_schematic_evidence-accumulation.png") except Exception: pass .. GENERATED FROM PYTHON SOURCE LINES 100-102 Setup ~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 104-108 Initialize random generator ........................... We seed the numpy random generator, which will generate random initial weights as well as random input and output. .. GENERATED FROM PYTHON SOURCE LINES 108-112 .. code-block:: Python rng_seed = 1 # numpy random seed np.random.seed(rng_seed) # fix numpy random seed .. GENERATED FROM PYTHON SOURCE LINES 113-118 Define timing of task ..................... The task's temporal structure is then defined, once as time steps and once as durations in milliseconds. Using a batch size larger than one aids the network in generalization, facilitating the solution to this task. The original number of iterations requires distributed computing. .. GENERATED FROM PYTHON SOURCE LINES 118-158 .. code-block:: Python n_batch = 1 # batch size, 64 in reference [2], 32 in the README to reference [2] n_iter = 5 # number of iterations, 2000 in reference [2], 50 with n_batch 32 converges n_input_symbols = 4 # number of input populations, e.g. 4 = left, right, recall, noise n_cues = 7 # number of cues given before decision prob_group = 0.3 # probability with which one input group is present steps = { "cue": 100, # time steps in one cue presentation "spacing": 50, # time steps of break between two cues "bg_noise": 1050, # time steps of background noise "recall": 150, # time steps of recall } steps["cues"] = n_cues * (steps["cue"] + steps["spacing"]) # time steps of all cues steps["sequence"] = steps["cues"] + steps["bg_noise"] + steps["recall"] # time steps of one full sequence steps["learning_window"] = steps["recall"] # time steps of window with non-zero learning signals steps["task"] = n_iter * n_batch * steps["sequence"] # time steps of task steps.update( { "offset_gen": 1, # offset since generator signals start from time step 1 "delay_in_rec": 1, # connection delay between input and recurrent neurons "delay_rec_out": 1, # connection delay between recurrent and output neurons "delay_out_norm": 1, # connection delay between output neurons for normalization "extension_sim": 1, # extra time step to close right-open simulation time interval in Simulate() } ) steps["delays"] = steps["delay_in_rec"] + steps["delay_rec_out"] + steps["delay_out_norm"] # time steps of delays steps["total_offset"] = steps["offset_gen"] + steps["delays"] # time steps of total offset steps["sim"] = steps["task"] + steps["total_offset"] + steps["extension_sim"] # time steps of simulation duration = {"step": 1.0} # ms, temporal resolution of the simulation duration.update({key: value * duration["step"] for key, value in steps.items()}) # ms, durations .. GENERATED FROM PYTHON SOURCE LINES 159-163 Set up simulation ................. As last step of the setup, we reset the NEST kernel to remove all existing NEST simulation settings and objects and set some NEST kernel parameters, some of which are e-prop-related. .. GENERATED FROM PYTHON SOURCE LINES 163-173 .. code-block:: Python params_setup = { "eprop_learning_window": duration["learning_window"], "eprop_reset_neurons_on_update": True, # if True, reset dynamic variables at start of each update interval "eprop_update_interval": duration["sequence"], # ms, time interval for updating the synaptic weights "print_time": False, # if True, print time progress bar during simulation, set False if run as code cell "resolution": duration["step"], "total_num_virtual_procs": 1, # number of virtual processes, set in case of distributed computing } .. GENERATED FROM PYTHON SOURCE LINES 174-178 .. code-block:: Python nest.ResetKernel() nest.set(**params_setup) .. GENERATED FROM PYTHON SOURCE LINES 179-185 Create neurons ~~~~~~~~~~~~~~ We proceed by creating a certain number of input, recurrent, and readout neurons and setting their parameters. Additionally, we already create an input spike generator and an output target rate generator, which we will configure later. Within the recurrent network, alongside a population of regular neurons, we introduce a population of adaptive neurons, to enhance the network's memory retention. .. GENERATED FROM PYTHON SOURCE LINES 185-240 .. code-block:: Python n_in = 40 # number of input neurons n_ad = 50 # number of adaptive neurons n_reg = 50 # number of regular neurons n_rec = n_ad + n_reg # number of recurrent neurons n_out = 2 # number of readout neurons params_nrn_reg = { "C_m": 1.0, # pF, membrane capacitance - takes effect only if neurons get current input (here not the case) "c_reg": 2.0, # firing rate regularization scaling - double the TF c_reg for technical reasons "E_L": 0.0, # mV, leak / resting membrane potential "f_target": 10.0, # spikes/s, target firing rate for firing rate regularization "gamma": 0.3, # scaling of the pseudo derivative "I_e": 0.0, # pA, external current input "regular_spike_arrival": True, # If True, input spikes arrive at end of time step, if False at beginning "surrogate_gradient_function": "piecewise_linear", # surrogate gradient / pseudo-derivative function "t_ref": 5.0, # ms, duration of refractory period "tau_m": 20.0, # ms, membrane time constant "V_m": 0.0, # mV, initial value of the membrane voltage "V_th": 0.6, # mV, spike threshold membrane voltage } params_nrn_ad = { "adapt_tau": 2000.0, # ms, time constant of adaptive threshold "adaptation": 0.0, # initial value of the spike threshold adaptation "C_m": 1.0, "c_reg": 2.0, "E_L": 0.0, "f_target": 10.0, "gamma": 0.3, "I_e": 0.0, "regular_spike_arrival": True, "surrogate_gradient_function": "piecewise_linear", "t_ref": 5.0, "tau_m": 20.0, "V_m": 0.0, "V_th": 0.6, } params_nrn_ad["adapt_beta"] = 1.7 * ( (1.0 - np.exp(-duration["step"] / params_nrn_ad["adapt_tau"])) / (1.0 - np.exp(-duration["step"] / params_nrn_ad["tau_m"])) ) # prefactor of adaptive threshold params_nrn_out = { "C_m": 1.0, "E_L": 0.0, "I_e": 0.0, "loss": "cross_entropy", # loss function "regular_spike_arrival": False, "tau_m": 20.0, "V_m": 0.0, } .. GENERATED FROM PYTHON SOURCE LINES 241-258 .. code-block:: Python # Intermediate parrot neurons required between input spike generators and recurrent neurons, # since devices cannot establish plastic synapses for technical reasons gen_spk_in = nest.Create("spike_generator", n_in) nrns_in = nest.Create("parrot_neuron", n_in) # The suffix _bsshslm_2020 follows the NEST convention to indicate in the model name the paper # that introduced it by the first letter of the authors' last names and the publication year. nrns_reg = nest.Create("eprop_iaf_bsshslm_2020", n_reg, params_nrn_reg) nrns_ad = nest.Create("eprop_iaf_adapt_bsshslm_2020", n_ad, params_nrn_ad) nrns_out = nest.Create("eprop_readout_bsshslm_2020", n_out, params_nrn_out) gen_rate_target = nest.Create("step_rate_generator", n_out) nrns_rec = nrns_reg + nrns_ad .. GENERATED FROM PYTHON SOURCE LINES 259-266 Create recorders ~~~~~~~~~~~~~~~~ We also create recorders, which, while not required for the training, will allow us to track various dynamic variables of the neurons, spikes, and changes in synaptic weights. To save computing time and memory, the recorders, the recorded variables, neurons, and synapses can be limited to the ones relevant to the experiment, and the recording interval can be increased (see the documentation on the specific recorders). By default, recordings are stored in memory but can also be written to file. .. GENERATED FROM PYTHON SOURCE LINES 266-306 .. code-block:: Python n_record = 1 # number of neurons per type to record dynamic variables from - this script requires n_record >= 1 n_record_w = 3 # number of senders and targets to record weights from - this script requires n_record_w >=1 if n_record == 0 or n_record_w == 0: raise ValueError("n_record and n_record_w >= 1 required") params_mm_reg = { "interval": duration["step"], # interval between two recorded time points "record_from": ["V_m", "surrogate_gradient", "learning_signal"], # dynamic variables to record "start": duration["offset_gen"] + duration["delay_in_rec"], # start time of recording "stop": duration["offset_gen"] + duration["delay_in_rec"] + duration["task"], # stop time of recording } params_mm_ad = { "interval": duration["step"], "record_from": params_mm_reg["record_from"] + ["V_th_adapt", "adaptation"], "start": duration["offset_gen"] + duration["delay_in_rec"], "stop": duration["offset_gen"] + duration["delay_in_rec"] + duration["task"], } params_mm_out = { "interval": duration["step"], "record_from": ["V_m", "readout_signal", "readout_signal_unnorm", "target_signal", "error_signal"], "start": duration["total_offset"], "stop": duration["total_offset"] + duration["task"], } params_wr = { "senders": nrns_in[:n_record_w] + nrns_rec[:n_record_w], # limit senders to subsample weights to record "targets": nrns_rec[:n_record_w] + nrns_out, # limit targets to subsample weights to record from "start": duration["total_offset"], "stop": duration["total_offset"] + duration["task"], } params_sr = { "start": duration["total_offset"], "stop": duration["total_offset"] + duration["task"], } .. GENERATED FROM PYTHON SOURCE LINES 307-317 .. code-block:: Python mm_reg = nest.Create("multimeter", params_mm_reg) mm_ad = nest.Create("multimeter", params_mm_ad) mm_out = nest.Create("multimeter", params_mm_out) sr = nest.Create("spike_recorder", params_sr) wr = nest.Create("weight_recorder", params_wr) nrns_reg_record = nrns_reg[:n_record] nrns_ad_record = nrns_ad[:n_record] .. GENERATED FROM PYTHON SOURCE LINES 318-323 Create connections ~~~~~~~~~~~~~~~~~~ Now, we define the connectivity and set up the synaptic parameters, with the synaptic weights drawn from normal distributions. After these preparations, we establish the enumerated connections of the core network, as well as additional connections to the recorders. .. GENERATED FROM PYTHON SOURCE LINES 323-404 .. code-block:: Python params_conn_all_to_all = {"rule": "all_to_all", "allow_autapses": False} params_conn_one_to_one = {"rule": "one_to_one"} def calculate_glorot_dist(fan_in, fan_out): glorot_scale = 1.0 / max(1.0, (fan_in + fan_out) / 2.0) glorot_limit = np.sqrt(3.0 * glorot_scale) glorot_distribution = np.random.uniform(low=-glorot_limit, high=glorot_limit, size=(fan_in, fan_out)) return glorot_distribution dtype_weights = np.float32 # data type of weights - for reproducing TF results set to np.float32 weights_in_rec = np.array(np.random.randn(n_in, n_rec).T / np.sqrt(n_in), dtype=dtype_weights) weights_rec_rec = np.array(np.random.randn(n_rec, n_rec).T / np.sqrt(n_rec), dtype=dtype_weights) np.fill_diagonal(weights_rec_rec, 0.0) # since no autapses set corresponding weights to zero weights_rec_out = np.array(calculate_glorot_dist(n_rec, n_out).T, dtype=dtype_weights) weights_out_rec = np.array(np.random.randn(n_rec, n_out), dtype=dtype_weights) params_common_syn_eprop = { "optimizer": { "type": "adam", # algorithm to optimize the weights "batch_size": n_batch, "beta_1": 0.9, # exponential decay rate for 1st moment estimate of Adam optimizer "beta_2": 0.999, # exponential decay rate for 2nd moment raw estimate of Adam optimizer "epsilon": 1e-8, # small numerical stabilization constant of Adam optimizer "eta": 5e-3, # learning rate "Wmin": -100.0, # pA, minimal limit of the synaptic weights "Wmax": 100.0, # pA, maximal limit of the synaptic weights }, "average_gradient": True, # if True, average the gradient over the learning window "weight_recorder": wr, } params_syn_base = { "synapse_model": "eprop_synapse_bsshslm_2020", "delay": duration["step"], # ms, dendritic delay "tau_m_readout": params_nrn_out["tau_m"], # ms, for technical reasons pass readout neuron membrane time constant } params_syn_in = params_syn_base.copy() params_syn_in["weight"] = weights_in_rec # pA, initial values for the synaptic weights params_syn_rec = params_syn_base.copy() params_syn_rec["weight"] = weights_rec_rec params_syn_out = params_syn_base.copy() params_syn_out["weight"] = weights_rec_out params_syn_feedback = { "synapse_model": "eprop_learning_signal_connection_bsshslm_2020", "delay": duration["step"], "weight": weights_out_rec, } params_syn_out_out = { "synapse_model": "rate_connection_delayed", "delay": duration["step"], "receptor_type": 1, # receptor type of readout neuron to receive other readout neuron's signals for softmax "weight": 1.0, # pA, weight 1.0 required for correct softmax computation for technical reasons } params_syn_rate_target = { "synapse_model": "rate_connection_delayed", "delay": duration["step"], "receptor_type": 2, # receptor type over which readout neuron receives target signal } params_syn_static = { "synapse_model": "static_synapse", "delay": duration["step"], } params_init_optimizer = { "optimizer": { "m": 0.0, # initial 1st moment estimate m of Adam optimizer "v": 0.0, # initial 2nd moment raw estimate v of Adam optimizer } } .. GENERATED FROM PYTHON SOURCE LINES 405-427 .. code-block:: Python nest.SetDefaults("eprop_synapse_bsshslm_2020", params_common_syn_eprop) nest.Connect(gen_spk_in, nrns_in, params_conn_one_to_one, params_syn_static) # connection 1 nest.Connect(nrns_in, nrns_rec, params_conn_all_to_all, params_syn_in) # connection 2 nest.Connect(nrns_rec, nrns_rec, params_conn_all_to_all, params_syn_rec) # connection 3 nest.Connect(nrns_rec, nrns_out, params_conn_all_to_all, params_syn_out) # connection 4 nest.Connect(nrns_out, nrns_rec, params_conn_all_to_all, params_syn_feedback) # connection 5 nest.Connect(gen_rate_target, nrns_out, params_conn_one_to_one, params_syn_rate_target) # connection 6 nest.Connect(nrns_out, nrns_out, params_conn_all_to_all, params_syn_out_out) # connection 7 nest.Connect(nrns_in + nrns_rec, sr, params_conn_all_to_all, params_syn_static) nest.Connect(mm_reg, nrns_reg_record, params_conn_all_to_all, params_syn_static) nest.Connect(mm_ad, nrns_ad_record, params_conn_all_to_all, params_syn_static) nest.Connect(mm_out, nrns_out, params_conn_all_to_all, params_syn_static) # After creating the connections, we can individually initialize the optimizer's # dynamic variables for single synapses (here exemplarily for two connections). nest.GetConnections(nrns_rec[0], nrns_rec[1:3]).set([params_init_optimizer] * 2) .. GENERATED FROM PYTHON SOURCE LINES 428-434 Create input and output ~~~~~~~~~~~~~~~~~~~~~~~ We generate the input as four neuron populations, two producing the left and right cues, respectively, one the recall signal and one the background input throughout the task. The sequence of cues is drawn with a probability that favors one side. For each such sequence, the favored side, the solution or target, is assigned randomly to the left or right. .. GENERATED FROM PYTHON SOURCE LINES 434-509 .. code-block:: Python def generate_evidence_accumulation_input_output( n_batch, n_in, prob_group, input_spike_prob, n_cues, n_input_symbols, steps ): n_pop_nrn = n_in // n_input_symbols prob_choices = np.array([prob_group, 1 - prob_group], dtype=np.float32) idx = np.random.choice([0, 1], n_batch) probs = np.zeros((n_batch, 2), dtype=np.float32) probs[:, 0] = prob_choices[idx] probs[:, 1] = prob_choices[1 - idx] batched_cues = np.zeros((n_batch, n_cues), dtype=int) for b_idx in range(n_batch): batched_cues[b_idx, :] = np.random.choice([0, 1], n_cues, p=probs[b_idx]) input_spike_probs = np.zeros((n_batch, steps["sequence"], n_in)) for b_idx in range(n_batch): for c_idx in range(n_cues): cue = batched_cues[b_idx, c_idx] step_start = c_idx * (steps["cue"] + steps["spacing"]) + steps["spacing"] step_stop = step_start + steps["cue"] pop_nrn_start = cue * n_pop_nrn pop_nrn_stop = pop_nrn_start + n_pop_nrn input_spike_probs[b_idx, step_start:step_stop, pop_nrn_start:pop_nrn_stop] = input_spike_prob input_spike_probs[:, -steps["recall"] :, 2 * n_pop_nrn : 3 * n_pop_nrn] = input_spike_prob input_spike_probs[:, :, 3 * n_pop_nrn :] = input_spike_prob / 4.0 input_spike_bools = input_spike_probs > np.random.rand(input_spike_probs.size).reshape(input_spike_probs.shape) input_spike_bools[:, 0, :] = 0 # remove spikes in 0th time step of every sequence for technical reasons target_cues = np.zeros(n_batch, dtype=int) target_cues[:] = np.sum(batched_cues, axis=1) > int(n_cues / 2) return input_spike_bools, target_cues input_spike_prob = 0.04 # spike probability of frozen input noise dtype_in_spks = np.float32 # data type of input spikes - for reproducing TF results set to np.float32 input_spike_bools_list = [] target_cues_list = [] for iteration in range(n_iter): input_spike_bools, target_cues = generate_evidence_accumulation_input_output( n_batch, n_in, prob_group, input_spike_prob, n_cues, n_input_symbols, steps ) input_spike_bools_list.append(input_spike_bools) target_cues_list.extend(target_cues.tolist()) input_spike_bools_arr = np.array(input_spike_bools_list).reshape(steps["task"], n_in) timeline_task = np.arange(0.0, duration["task"], duration["step"]) + duration["offset_gen"] params_gen_spk_in = [ {"spike_times": timeline_task[input_spike_bools_arr[:, nrn_in_idx]].astype(dtype_in_spks)} for nrn_in_idx in range(n_in) ] target_rate_changes = np.zeros((n_out, n_batch * n_iter)) target_rate_changes[np.array(target_cues_list), np.arange(n_batch * n_iter)] = 1 params_gen_rate_target = [ { "amplitude_times": np.arange(0.0, duration["task"], duration["sequence"]) + duration["total_offset"], "amplitude_values": target_rate_changes[nrn_out_idx], } for nrn_out_idx in range(n_out) ] .. GENERATED FROM PYTHON SOURCE LINES 510-514 .. code-block:: Python nest.SetStatus(gen_spk_in, params_gen_spk_in) nest.SetStatus(gen_rate_target, params_gen_rate_target) .. GENERATED FROM PYTHON SOURCE LINES 515-522 Force final update ~~~~~~~~~~~~~~~~~~ Synapses only get active, that is, the correct weight update calculated and applied, when they transmit a spike. To still be able to read out the correct weights at the end of the simulation, we force spiking of the presynaptic neuron and thus an update of all synapses, including those that have not transmitted a spike in the last update interval, by sending a strong spike to all neurons that form the presynaptic side of an eprop synapse. This step is required purely for technical reasons. .. GENERATED FROM PYTHON SOURCE LINES 522-527 .. code-block:: Python gen_spk_final_update = nest.Create("spike_generator", 1, {"spike_times": [duration["task"] + duration["delays"]]}) nest.Connect(gen_spk_final_update, nrns_in + nrns_rec, "all_to_all", {"weight": 1000.0}) .. GENERATED FROM PYTHON SOURCE LINES 528-532 Read out pre-training weights ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Before we begin training, we read out the initial weight matrices so that we can eventually compare them to the optimized weights. .. GENERATED FROM PYTHON SOURCE LINES 532-550 .. code-block:: Python def get_weights(pop_pre, pop_post): conns = nest.GetConnections(pop_pre, pop_post).get(["source", "target", "weight"]) conns["senders"] = np.array(conns["source"]) - np.min(conns["source"]) conns["targets"] = np.array(conns["target"]) - np.min(conns["target"]) conns["weight_matrix"] = np.zeros((len(pop_post), len(pop_pre))) conns["weight_matrix"][conns["targets"], conns["senders"]] = conns["weight"] return conns weights_pre_train = { "in_rec": get_weights(nrns_in, nrns_rec), "rec_rec": get_weights(nrns_rec, nrns_rec), "rec_out": get_weights(nrns_rec, nrns_out), } .. GENERATED FROM PYTHON SOURCE LINES 551-555 Simulate ~~~~~~~~ We train the network by simulating for a set simulation time, determined by the number of iterations and the batch size and the length of one sequence. .. GENERATED FROM PYTHON SOURCE LINES 555-558 .. code-block:: Python nest.Simulate(duration["sim"]) .. GENERATED FROM PYTHON SOURCE LINES 559-562 Read out post-training weights ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ After the training, we can read out the optimized final weights. .. GENERATED FROM PYTHON SOURCE LINES 562-569 .. code-block:: Python weights_post_train = { "in_rec": get_weights(nrns_in, nrns_rec), "rec_rec": get_weights(nrns_rec, nrns_rec), "rec_out": get_weights(nrns_rec, nrns_out), } .. GENERATED FROM PYTHON SOURCE LINES 570-573 Read out recorders ~~~~~~~~~~~~~~~~~~ We can also retrieve the recorded history of the dynamic variables and weights, as well as detected spikes. .. GENERATED FROM PYTHON SOURCE LINES 573-580 .. code-block:: Python events_mm_reg = mm_reg.get("events") events_mm_ad = mm_ad.get("events") events_mm_out = mm_out.get("events") events_sr = sr.get("events") events_wr = wr.get("events") .. GENERATED FROM PYTHON SOURCE LINES 581-585 Evaluate training error ~~~~~~~~~~~~~~~~~~~~~~~ We evaluate the network's training error by calculating a loss - in this case, the cross-entropy error between the integrated recurrent network activity and the target rate. .. GENERATED FROM PYTHON SOURCE LINES 585-606 .. code-block:: Python readout_signal = events_mm_out["readout_signal"] # corresponds to softmax target_signal = events_mm_out["target_signal"] senders = events_mm_out["senders"] readout_signal = np.array([readout_signal[senders == i] for i in set(senders)]) target_signal = np.array([target_signal[senders == i] for i in set(senders)]) readout_signal = readout_signal.reshape((n_out, n_iter, n_batch, steps["sequence"])) readout_signal = readout_signal[:, :, :, -steps["learning_window"] :] target_signal = target_signal.reshape((n_out, n_iter, n_batch, steps["sequence"])) target_signal = target_signal[:, :, :, -steps["learning_window"] :] loss = -np.mean(np.sum(target_signal * np.log(readout_signal), axis=0), axis=(1, 2)) y_prediction = np.argmax(np.mean(readout_signal, axis=3), axis=0) y_target = np.argmax(np.mean(target_signal, axis=3), axis=0) accuracy = np.mean((y_target == y_prediction), axis=1) recall_errors = 1.0 - accuracy .. GENERATED FROM PYTHON SOURCE LINES 607-610 Plot results ~~~~~~~~~~~~ Then, we plot a series of plots. .. GENERATED FROM PYTHON SOURCE LINES 610-631 .. code-block:: Python do_plotting = True # if True, plot the results if not do_plotting: exit() colors = { "blue": "#2854c5ff", "red": "#e04b40ff", "white": "#ffffffff", } plt.rcParams.update( { "font.sans-serif": "Arial", "axes.spines.right": False, "axes.spines.top": False, "axes.prop_cycle": cycler(color=[colors["blue"], colors["red"]]), } ) .. GENERATED FROM PYTHON SOURCE LINES 632-636 Plot training error ................... We begin with two plots visualizing the training error of the network: the loss and the recall error, both plotted against the iterations. .. GENERATED FROM PYTHON SOURCE LINES 636-651 .. code-block:: Python fig, axs = plt.subplots(2, 1, sharex=True) axs[0].plot(range(1, n_iter + 1), loss) axs[0].set_ylabel(r"$E = -\sum_{t,k} \pi_k^{*,t} \log \pi_k^t$") axs[1].plot(range(1, n_iter + 1), recall_errors) axs[1].set_ylabel("recall errors") axs[-1].set_xlabel("training iteration") axs[-1].set_xlim(1, n_iter) axs[-1].xaxis.get_major_locator().set_params(integer=True) fig.tight_layout() .. GENERATED FROM PYTHON SOURCE LINES 652-656 Plot spikes and dynamic variables ................................. This plotting routine shows how to plot all of the recorded dynamic variables and spikes across time. We take one snapshot in the first iteration and one snapshot at the end. .. GENERATED FROM PYTHON SOURCE LINES 656-707 .. code-block:: Python def plot_recordable(ax, events, recordable, ylabel, xlims): for sender in set(events["senders"]): idc_sender = events["senders"] == sender idc_times = (events["times"][idc_sender] > xlims[0]) & (events["times"][idc_sender] < xlims[1]) ax.plot(events["times"][idc_sender][idc_times], events[recordable][idc_sender][idc_times], lw=0.5) ax.set_ylabel(ylabel) margin = np.abs(np.max(events[recordable]) - np.min(events[recordable])) * 0.1 ax.set_ylim(np.min(events[recordable]) - margin, np.max(events[recordable]) + margin) def plot_spikes(ax, events, nrns, ylabel, xlims): idc_times = (events["times"] > xlims[0]) & (events["times"] < xlims[1]) idc_sender = np.isin(events["senders"][idc_times], nrns.tolist()) senders_subset = events["senders"][idc_times][idc_sender] times_subset = events["times"][idc_times][idc_sender] ax.scatter(times_subset, senders_subset, s=0.1) ax.set_ylabel(ylabel) margin = np.abs(np.max(senders_subset) - np.min(senders_subset)) * 0.1 ax.set_ylim(np.min(senders_subset) - margin, np.max(senders_subset) + margin) for xlims in [(0, steps["sequence"]), (steps["task"] - steps["sequence"], steps["task"])]: fig, axs = plt.subplots(14, 1, sharex=True, figsize=(8, 14), gridspec_kw={"hspace": 0.4, "left": 0.2}) plot_spikes(axs[0], events_sr, nrns_in, r"$z_i$" + "\n", xlims) plot_spikes(axs[1], events_sr, nrns_reg, r"$z_j$" + "\n", xlims) plot_recordable(axs[2], events_mm_reg, "V_m", r"$v_j$" + "\n(mV)", xlims) plot_recordable(axs[3], events_mm_reg, "surrogate_gradient", r"$\psi_j$" + "\n", xlims) plot_recordable(axs[4], events_mm_reg, "learning_signal", r"$L_j$" + "\n(pA)", xlims) plot_spikes(axs[5], events_sr, nrns_ad, r"$z_j$" + "\n", xlims) plot_recordable(axs[6], events_mm_ad, "V_m", r"$v_j$" + "\n(mV)", xlims) plot_recordable(axs[7], events_mm_ad, "surrogate_gradient", r"$\psi_j$" + "\n", xlims) plot_recordable(axs[8], events_mm_ad, "V_th_adapt", r"$A_j$" + "\n(mV)", xlims) plot_recordable(axs[9], events_mm_ad, "learning_signal", r"$L_j$" + "\n(pA)", xlims) plot_recordable(axs[10], events_mm_out, "V_m", r"$v_k$" + "\n(mV)", xlims) plot_recordable(axs[11], events_mm_out, "target_signal", r"$\pi^*_k$" + "\n", xlims) plot_recordable(axs[12], events_mm_out, "readout_signal", r"$\pi_k$" + "\n", xlims) plot_recordable(axs[13], events_mm_out, "error_signal", r"$\pi_k-\pi^*_k$" + "\n", xlims) axs[-1].set_xlabel(r"$t$ (ms)") axs[-1].set_xlim(*xlims) fig.align_ylabels() .. GENERATED FROM PYTHON SOURCE LINES 708-714 Plot weight time courses ........................ Similarly, we can plot the weight histories. Note that the weight recorder, attached to the synapses, works differently than the other recorders. Since synapses only get activated when they transmit a spike, the weight recorder only records the weight in those moments. That is why the first weight registrations do not start in the first time step and we add the initial weights manually. .. GENERATED FROM PYTHON SOURCE LINES 714-746 .. code-block:: Python def plot_weight_time_course(ax, events, nrns_senders, nrns_targets, label, ylabel): for sender in nrns_senders.tolist(): for target in nrns_targets.tolist(): idc_syn = (events["senders"] == sender) & (events["targets"] == target) idc_syn_pre = (weights_pre_train[label]["source"] == sender) & ( weights_pre_train[label]["target"] == target ) times = [0.0] + events["times"][idc_syn].tolist() weights = [weights_pre_train[label]["weight"][idc_syn_pre]] + events["weights"][idc_syn].tolist() ax.step(times, weights, c=colors["blue"]) ax.set_ylabel(ylabel) ax.set_ylim(-0.6, 0.6) fig, axs = plt.subplots(3, 1, sharex=True, figsize=(3, 4)) plot_weight_time_course(axs[0], events_wr, nrns_in[:n_record_w], nrns_rec[:n_record_w], "in_rec", r"$W_\text{in}$ (pA)") plot_weight_time_course( axs[1], events_wr, nrns_rec[:n_record_w], nrns_rec[:n_record_w], "rec_rec", r"$W_\text{rec}$ (pA)" ) plot_weight_time_course(axs[2], events_wr, nrns_rec[:n_record_w], nrns_out, "rec_out", r"$W_\text{out}$ (pA)") axs[-1].set_xlabel(r"$t$ (ms)") axs[-1].set_xlim(0, steps["task"]) fig.align_ylabels() fig.tight_layout() .. GENERATED FROM PYTHON SOURCE LINES 747-752 Plot weight matrices .................... If one is not interested in the time course of the weights, it is possible to read out only the initial and final weights, which requires less computing time and memory than the weight recorder approach. Here, we plot the corresponding weight matrices before and after the optimization. .. GENERATED FROM PYTHON SOURCE LINES 752-790 .. code-block:: Python cmap = mpl.colors.LinearSegmentedColormap.from_list( "cmap", ((0.0, colors["blue"]), (0.5, colors["white"]), (1.0, colors["red"])) ) fig, axs = plt.subplots(3, 2, sharex="col", sharey="row") all_w_extrema = [] for k in weights_pre_train.keys(): w_pre = weights_pre_train[k]["weight"] w_post = weights_post_train[k]["weight"] all_w_extrema.append([np.min(w_pre), np.max(w_pre), np.min(w_post), np.max(w_post)]) args = {"cmap": cmap, "vmin": np.min(all_w_extrema), "vmax": np.max(all_w_extrema)} for i, weights in zip([0, 1], [weights_pre_train, weights_post_train]): axs[0, i].pcolormesh(weights["in_rec"]["weight_matrix"].T, **args) axs[1, i].pcolormesh(weights["rec_rec"]["weight_matrix"], **args) cmesh = axs[2, i].pcolormesh(weights["rec_out"]["weight_matrix"], **args) axs[2, i].set_xlabel("recurrent\nneurons") axs[0, 0].set_ylabel("input\nneurons") axs[1, 0].set_ylabel("recurrent\nneurons") axs[2, 0].set_ylabel("readout\nneurons") fig.align_ylabels(axs[:, 0]) axs[0, 0].text(0.5, 1.1, "pre-training", transform=axs[0, 0].transAxes, ha="center") axs[0, 1].text(0.5, 1.1, "post-training", transform=axs[0, 1].transAxes, ha="center") axs[2, 0].yaxis.get_major_locator().set_params(integer=True) cbar = plt.colorbar(cmesh, cax=axs[1, 1].inset_axes([1.1, 0.2, 0.05, 0.8]), label="weight (pA)") fig.tight_layout() plt.show() .. _sphx_glr_download_auto_examples_eprop_plasticity_eprop_supervised_classification_evidence-accumulation.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: eprop_supervised_classification_evidence-accumulation.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: eprop_supervised_classification_evidence-accumulation.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_