demos/path_integration_example.ipynb

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    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/RatInABox-Lab/RatInABox/blob/main/demos/path_integration_example.ipynb)"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "# Case study: Path Integration\n",
    "### We use RatInABox to built a network capable of learning to path integrate in 1D using local learning rules"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This work is closely related to the work done by [Vafidis et al. (2021)](https://www.biorxiv.org/content/10.1101/2021.03.12.435035v1). Although the specific details of our learning rules, parameter settings and architecture are all slightly different we do not claim this work to be novel. Rather include it as a demonstraion of what is possible (even \"easy\") to study using `RatInABox`.\n",
    "\n",
    "To avoid rewritting their paper we give only sparse, key details here. If you intend to make perfect sense of , or even build upon this example, we recommend reading the \n",
    "Vafidis et al. (2021) first, and (optionally but highly recommended too) McNaughton et al. (2006). If you don't intend to do this, this section, and the code below, can still be read, run and referenced as a tutorial for `RatInABox`. \n",
    "\n",
    "For now we will briefly describe the problem of path integration and our approach for how to solve it in 1D using `RatInABox`.\n",
    "\n",
    "### Path integration with ring attractors and velocity inputs\n",
    "Animals need to maintain an encoding of their state in the world even in the absence of sensory input. For one dimensional variables (such as the animals head direction, or location along a linear track) it is often assumed this is done using a ring-attractor network. Ring attractors are a type of continuous attractor neural network (CANN). \n",
    "\n",
    "In a ring attractor network, the neurons are arranged in a 1D ring. A bump of activity is stabilised by local-excitatory and long-range inhibitatory weights between neighbouring cells (sometime long range inhibition is replaced with global inhibition as in Vafidis et al.). \n",
    "\n",
    "Inputs from cells encoding the animals velocity can \"push\" the bump activity around the ring in correspondence with the position of the animal. For each ring attractor neuron, suppose there exists a left and right \"conjunctive velocity neuron\" (conjuctive because the velocity neuron being active is contingent on its corresponding bump attractor neuron being active, this is a small detail your intuitive understanding can probably afford to ignore) which connects assymetrically to the bump attractor neurons. Specifically the left conjuctive velocity cell corresponding to ring attractor cell $i$ might connect in an excitatory manner to cells to the left of cell $i$ and in an inhibitory manner to cells to the right. This way when the animal moves left the velocity neuron becomes active and excites neurons on the left of the bump and inhibits thos on the right, thus pushes the bump leftwards. \n",
    "\n",
    "A lot of work in bump attractors and path integration relates to maintaining knowledge of head direction (a ring manifold of neurons, manifesting topologically as a ring within the brain, has been found in drosophila and linked to path integration of head direction (Kim et al. 2017)). However it is not necesasry for the neurons arrangement in physical space to correspond with the manifold (e.g a 1D ring) their activity lies on. This is the running hyptohesis for the role of entorhinal cortex as a neural substrate for path integration and the \"cognitive map\". We recommend McNaughton (2006) for a good summary of path integration as applied to hippocampus/entorhinal cortex. Specifically the activity profile of grid cells is though to lie on a torodial (torus = 2D equivalent of a 1D ring) manifold. Everything about this system seems pretty well set up to perform path integration, there are even velocity-conjuctive grod cells which would do the pushing of the bump. \n",
    "\n",
    "<img src=\"../.images/demos/pathint.gif\" width=\"700\" align=\"center\">\n",
    "\n",
    " ### Our approach\n",
    "\n",
    " The key problem identified by Vafidis et al. is that the weights (local excitation and long range inhibition for the recurrent connection of the ring-attractor and the asymmetric connectivity profile from the conjunctive velocity cells) need to be fine tuned. It is unliekly these connectivety profiles are hard coded by evolution and, for reasons of flexibility, it would be better (and more flexible) if instead they could be *learned* and better still if the learning rule can be local and Hebbian. \n",
    "\n",
    " To do this we define a classes of `Neurons` called `PyramidalNeurons`. Each pyramidal neuron has three compartments (two dendritic and one somatic). The first (basal) dendritic compartment recieves bottom-up sensory input from a set of `PlaceCells` from which they are driven in a one-to-one manner. This will act as the target signal, i.e. a localised bump of activity correponding to the nearby place cells currently active.. A second compartment recieves top-down input from the conjunctive velocity cells and recurrent inputs. Which dendritic compartment drives the soma can be adaptively controlled by a parameter we call `theta`. \n",
    " \n",
    " The local hebbian learning rule we used is based on a well studied class of neuronal learning rules where the dendritic compartments attempts to adjust their weights to match the somatic compartment firing rate. This has been term \"dendritic prediction of somatic activity\" and, if the dendritc voltage function is linear, looks like a voltage thresholded Hebbian learning rule (see Urbanczik and Senn (2014)).\n",
    "\n",
    " The necessary equations are as follows (note a more biophysically details version of our slimmed down learning rule is implememnted in Vafidis etal. so please see tehre for more details).  \n",
    "\n",
    " $$\\mathsf{V}^{\\textrm{basal}} = \\sum_{i}\\mathsf{w}^{\\textrm{basal}}_{i}\\mathsf{I}_{i}^{\\textrm{basal}}$$\n",
    "\n",
    "  $$\\mathsf{V}^{\\textrm{apical}} = \\sum_{i}\\mathsf{w}^{\\textrm{apical}}_{i}\\mathsf{I}_{i}^{\\textrm{apical}}$$\n",
    "\n",
    " where $\\mathsf{I}_{i}$ is the unitless input from the layer feeding into theis dendritic compartment (just the firing rate of that layer). ${I}_{i}^{\\textrm{basal}} = \\{ {I}_{i}^{\\textrm{place cells}} \\}$ and ${I}_{i}^{\\textrm{apical}} = \\{ {I}_{i}^{\\textrm{ring attractor}}, {I}_{i}^{\\textrm{conjuctive velocity cells}} \\}$. \n",
    "\n",
    " $$\\frac{d\\mathsf{w_{i}^{\\textrm{apical}}}(t)}{dt} \\propto \\big( \\mathsf{V}^{\\textrm{soma}} - \\mathsf{V}^{\\textrm{basal}}\\big)\\mathsf{I}_{i}^{\\textrm{basal}} $$\n",
    "\n",
    " where the somatic voltage is given simply by \n",
    "\n",
    " $$\\mathsf{V}^{\\textrm{soma}} = (1-\\theta(t))\\mathsf{V}^{\\textrm{basal}} + \\theta(t)\\mathsf{V}^{\\textrm{apical}}$$\n",
    "\n",
    " Typically we set theta to be oscillatory. The soma rapidly oscillates between being driven by the top-down inputs from its apical dendritic compartment and bottom-up inputs from its basal compartment. \n",
    "\n",
    " <img src=\"../.images/demos/pathint_network.png\" width=\"750\" align=\"center\"> \n",
    "\n",
    "Green weights are plastic, trained via the local Hebbian learning rule, while blue weights are fixed to sensible values.  \n",
    "\n",
    "Note the agent, the environment, and three of the four cell layers are all taken directly from `RatInABox`. Only one bespoke `Neurons` cell class need to be defined (this is the `PyramidalNeuron` layer which will become the ring attractor. Infact we chooose to define the dendritic compartments of each pyramidal cell as a `Neurons` classes too)\n",
    "\n",
    "Other relevant details include: \n",
    "\n",
    "* The conjuctive velocity neurons each recieve an input from one and only one ring attractor cell as well as a velocity neuron (left or right, depending on which population it resides in). This fixed weight from the ring attractor input is tuned such that when the ring attractor neuron fires fully (i.e. the bump is centred on its part of the ring) the activity in the conjunctive cell reaches threshold. Any additional input from the velocity cell now causes activity on this neuron. This means \n",
    "* The input to the conjuctive velocity cells from the velocity neurons is scaled such that the full sigmoid activity range is covered over the first two standard deviations of the animals likely speed. "
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  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: ratinabox in /Users/tomgeorge/miniconda3/envs/riab/lib/python3.10/site-packages (1.4.0)\n",
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      "Requirement already satisfied: tqdm in /Users/tomgeorge/miniconda3/envs/riab/lib/python3.10/site-packages (4.62.3)\n"
     ]
    }
   ],
   "source": [
    "!pip install ratinabox\n",
    "!pip install tqdm "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "# Import ratinabox\n",
    "import ratinabox\n",
    "from ratinabox.Environment import Environment\n",
    "from ratinabox.Agent import Agent\n",
    "from ratinabox.Neurons import Neurons, PlaceCells, VelocityCells, FeedForwardLayer\n",
    "from ratinabox import utils\n",
    "\n",
    "#stylise and automatically save ratinabox plots/animations\n",
    "ratinabox.stylize_plots(); ratinabox.autosave_plots = True; ratinabox.figure_directory = \"../figures/\"\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Defining the `PyramidalNeurons` class "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "class PyramidalNeurons(Neurons):\n",
    "    \"\"\"The PyramidalNeuorn class defines a layer of Neurons() whos firing rates are derived from the firing rates in two DendriticCompartments. They are theta modulated, during early theta phase the apical DendriticCompartment (self.apical_compartment) drives the soma, during late theta phases the basal DendriticCompartment (self.basal_compartment) drives the soma.\n",
    "\n",
    "    Must be initialised with an Agent and a 'params' dictionary.\n",
    "\n",
    "    Check that the input layers are all named differently.\n",
    "    List of functions:\n",
    "        • get_state()\n",
    "        • update()\n",
    "        • update_dendritic_compartments()\n",
    "        • update_weights()\n",
    "        • plot_loss()\n",
    "        • plot_rate_map()\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, Agent, params={}):\n",
    "        \"\"\"Initialises a layer of pyramidal neurons\n",
    "\n",
    "        Args:\n",
    "            Agent (_type_): _description_\n",
    "            params (dict, optional): _description_. Defaults to {}.\n",
    "        \"\"\"\n",
    "        default_params = {\n",
    "            \"n\": 10,\n",
    "            \"name\": \"PyramidalNeurons\",\n",
    "            # theta params\n",
    "            \"theta_freq\": 5,\n",
    "            \"theta_frac\": 0.5,  # -->0 all basal input, -->1 all apical input\n",
    "        }\n",
    "        default_params.update(params)\n",
    "        self.params = default_params\n",
    "        super().__init__(Agent, self.params)\n",
    "\n",
    "        self.history[\"loss\"] = []\n",
    "        self.error = None\n",
    "\n",
    "        self.basal_compartment = DendriticCompartment(\n",
    "            self.Agent,\n",
    "            params={\n",
    "                \"soma\": self,\n",
    "                \"name\": f\"{self.name}_basal\",\n",
    "                \"n\": self.n,\n",
    "                \"color\": self.color,\n",
    "            },\n",
    "        )\n",
    "        self.apical_compartment = DendriticCompartment(\n",
    "            self.Agent,\n",
    "            params={\n",
    "                \"soma\": self,\n",
    "                \"name\": f\"{self.name}_apical\",\n",
    "                \"n\": self.n,\n",
    "                \"color\": self.color,\n",
    "            },\n",
    "        )\n",
    "\n",
    "    def update(self):\n",
    "        \"\"\"Updates the firing rate of the layer. Saves a loss (lpf difference between basal and apical). Also adds noise.\"\"\"\n",
    "        super().update()  # this sets and saves self.firingrate\n",
    "\n",
    "        dt = self.Agent.dt\n",
    "        tau_smooth = 10\n",
    "        # update a smoothed history of the loss\n",
    "        fr_b, fr_a = (\n",
    "            self.basal_compartment.firingrate,\n",
    "            self.apical_compartment.firingrate,\n",
    "        )\n",
    "        error = np.mean(np.abs(fr_b - fr_a))\n",
    "        if self.Agent.t < 2 / self.theta_freq:\n",
    "            self.error = None\n",
    "        else:\n",
    "            # loss_smoothing_timescale = dt\n",
    "            self.error = (dt / tau_smooth) * error + (1 - dt / tau_smooth) * (\n",
    "                self.error or error\n",
    "            )\n",
    "        self.history[\"loss\"].append(self.error)\n",
    "        return\n",
    "\n",
    "    def update_dendritic_compartments(self):\n",
    "        \"\"\"Individually updates teh basal and apical firing rates.\"\"\"\n",
    "        self.basal_compartment.update()\n",
    "        self.apical_compartment.update()\n",
    "        return\n",
    "\n",
    "    def get_state(self, evaluate_at=\"last\", **kwargs):\n",
    "        \"\"\"Returns the firing rate of the soma. This depends on the firing rates of the basal and apical compartments and the current theta phase. By default the theta  is obtained from self.Agent.t but it can be passed manually as an kwarg to override this.\n",
    "\n",
    "        theta (or theta_gating) is a number between [0,1] controlling flow of information into soma from the two compartment.s 0 = entirely basal. 1 = entirely apical. Between equals weighted combination. he function theta_gating() takes a time and returns theta.\n",
    "        Args:\n",
    "            evaluate_at (str, optional): 'last','agent','all' or None (in which case pos can be passed directly as a kwarg). Defaults to \"last\".\n",
    "        Returns:\n",
    "            firingrate\n",
    "        \"\"\"\n",
    "        # theta can be passed in manually as a kwarg. If it isn't ithe time from the agent will be used to get theta. Theta determines how much basal and how much apical this neurons uses.\n",
    "        if \"theta\" in kwargs:\n",
    "            theta = kwargs[\"theta\"]\n",
    "        else:\n",
    "            theta = theta_gating(\n",
    "                t=self.Agent.t, freq=self.theta_freq, frac=self.theta_frac\n",
    "            )\n",
    "        fr_basal, fr_apical = 0, 0\n",
    "        # these are special cases, no need to even get their fr's if they aren't used\n",
    "        if theta != 0:\n",
    "            fr_apical = self.apical_compartment.get_state(evaluate_at, **kwargs)\n",
    "        if theta != 1:\n",
    "            fr_basal = self.basal_compartment.get_state(evaluate_at, **kwargs)\n",
    "        firingrate = (1 - theta) * fr_basal + (theta) * fr_apical\n",
    "        return firingrate\n",
    "\n",
    "    def update_weights(self):\n",
    "        \"\"\"Trains the weights, this function actually defined in the dendrite class.\"\"\"\n",
    "        if self.Agent.t > 2 / self.theta_freq:\n",
    "            self.basal_compartment.update_weights()\n",
    "            self.apical_compartment.update_weights()\n",
    "        return\n",
    "\n",
    "    def plot_loss(self, fig=None, ax=None):\n",
    "        \"\"\"Plots the loss against time to see if learning working\"\"\"\n",
    "        if fig is None and ax is None:\n",
    "            fig, ax = plt.subplots(figsize=(1.5, 1.5))\n",
    "            ylim = 0\n",
    "        else:\n",
    "            ylim = ax.get_ylim()[1]\n",
    "        t = np.array(self.history[\"t\"]) / 60\n",
    "        loss = self.history[\"loss\"]\n",
    "        ax.plot(t, loss, color=self.color, label=self.name)\n",
    "        ax.set_ylim(\n",
    "            bottom=0, top=max(ylim, np.nanmax(np.array(loss, dtype=np.float64)))\n",
    "        )\n",
    "        ax.set_xlim(left=0)\n",
    "        ax.legend(frameon=False)\n",
    "        ax.set_xlabel(\"Training time / min\")\n",
    "        ax.set_ylabel(\"Loss\")\n",
    "        return fig, ax\n",
    "\n",
    "    def plot_rate_map(self, route=\"basal\", **kwargs):\n",
    "        \"\"\"This is a wrapper function for the general Neuron class function plot_rate_map. It takes the same arguments as Neurons.plot_rate_map() but, in addition, route can be set to basal or apical in which case theta is set correspondingly and teh soma with take its input from downstream or upstream sources entirely.\n",
    "\n",
    "        The arguments for the standard plottiong function plot_rate_map() can be passed as usual as kwargs.\n",
    "\n",
    "        Args:\n",
    "            route (str, optional): _description_. Defaults to 'basal'.\n",
    "        \"\"\"\n",
    "        if route == \"basal\":\n",
    "            theta = 0\n",
    "        elif route == \"apical\":\n",
    "            theta = 1\n",
    "        fig, ax = super().plot_rate_map(**kwargs, theta=theta)\n",
    "        return fig, ax\n",
    "\n",
    "\n",
    "class DendriticCompartment(Neurons):\n",
    "    \"\"\"The DendriticCompartment class defines a layer of Neurons() whos firing rates are an activated linear combination of input layers. This class is a subclass of Neurons() and inherits it properties/plotting functions.\n",
    "\n",
    "    Must be initialised with an Agent and a 'params' dictionary.\n",
    "    Input params dictionary must  contain a list of input_layers which feed into these Neurons. This list looks like [Neurons1, Neurons2,...] where each is a Neurons() class.\n",
    "\n",
    "    Currently supported activations include 'sigmoid' (paramterised by max_fr, min_fr, mid_x, width), 'relu' (gain, threshold) and 'linear' specified with the \"activation_params\" dictionary in the inout params dictionary. See also activate() for full details.\n",
    "\n",
    "    Check that the input layers are all named differently.\n",
    "    List of functions:\n",
    "        • get_state()\n",
    "        • add_input()\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, Agent, params={}):\n",
    "        default_params = {\n",
    "            \"soma\": None,\n",
    "            \"activation_params\": {\n",
    "                \"activation\": \"sigmoid\",\n",
    "                \"max_fr\": 1,\n",
    "                \"min_fr\": 0,\n",
    "                \"mid_x\": 1,\n",
    "                \"width_x\": 2,\n",
    "            },\n",
    "        }\n",
    "        self.Agent = Agent\n",
    "        default_params.update(params)\n",
    "        self.params = default_params\n",
    "        super().__init__(Agent, self.params)\n",
    "\n",
    "        self.firingrate_temp = None\n",
    "        self.firingrate_prime_temp = None\n",
    "        self.inputs = {}\n",
    "\n",
    "    def add_input(\n",
    "        self, input_layer, eta=0.001, w_init=0.1, L1=0.0001, L2=0.001, tau_PI=100e-3\n",
    "    ):\n",
    "        \"\"\"Adds an input layer to the class. Each input layer is stored in a dictionary of self.inputs. Each has an associated matrix of weights which are initialised randomly.\n",
    "\n",
    "        Args:\n",
    "            input_layer (_type_): the layer which feeds into this compartment\n",
    "            eta: learning rate of the weights\n",
    "            w_init: initialisation scale of the weights\n",
    "            L1: how much L1 regularisation\n",
    "            L2: how much L2 regularisation\n",
    "            tau_PI: smoothing timescale of plasticity induction variable\n",
    "        \"\"\"\n",
    "        name = input_layer.name\n",
    "        n_in = input_layer.n\n",
    "        w = np.random.normal(loc=0, scale=w_init / np.sqrt(n_in), size=(self.n, n_in))\n",
    "        I = np.zeros(n_in)\n",
    "        PI = np.zeros(n_in)\n",
    "        if name in self.inputs.keys():\n",
    "            print(\n",
    "                f\"There already exists a layer called {input_layer_name}. Overwriting it now.\"\n",
    "            )\n",
    "        self.inputs[name] = {}\n",
    "        self.inputs[name][\"layer\"] = input_layer\n",
    "        self.inputs[name][\"w\"] = w\n",
    "        self.inputs[name][\"w_init\"] = w.copy()\n",
    "        self.inputs[name][\"I\"] = I  # input current\n",
    "        self.inputs[name][\"I_temp\"] = None  # input current\n",
    "        self.inputs[name][\"PI\"] = PI  # plasticity induction variable\n",
    "        self.inputs[name][\"eta\"] = eta\n",
    "        self.inputs[name][\"L2\"] = L2\n",
    "        self.inputs[name][\"L1\"] = L1\n",
    "        self.inputs[name][\"tau_PI\"] = tau_PI\n",
    "\n",
    "    def get_state(self, evaluate_at=\"last\", **kwargs):\n",
    "        \"\"\"Returns the \"firing rate\" of the dendritic compartment. By default this layer uses the last saved firingrate from its input layers. Alternatively evaluate_at and kwargs can be set to be anything else which will just be passed to the input layer for evaluation.\n",
    "        Once the firing rate of the inout layers is established these are multiplied by the weight matrices and then activated to obtain the firing rate of this FeedForwardLayer.\n",
    "\n",
    "        Args:\n",
    "            evaluate_at (str, optional). Defaults to 'last'.\n",
    "        Returns:\n",
    "            firingrate: array of firing rates\n",
    "        \"\"\"\n",
    "        if evaluate_at == \"last\":\n",
    "            V = np.zeros(self.n)\n",
    "        elif evaluate_at == \"all\":\n",
    "            V = np.zeros(\n",
    "                (self.n, self.Agent.Environment.flattened_discrete_coords.shape[0])\n",
    "            )\n",
    "        else:\n",
    "            V = np.zeros((self.n, kwargs[\"pos\"].shape[0]))\n",
    "\n",
    "        for inputlayer in self.inputs.values():\n",
    "            w = inputlayer[\"w\"]\n",
    "            if evaluate_at == \"last\":\n",
    "                I = inputlayer[\"layer\"].firingrate\n",
    "            else:  # kick can down the road let input layer decide how to evaluate the firingrate\n",
    "                I = inputlayer[\"layer\"].get_state(evaluate_at, **kwargs)\n",
    "            inputlayer[\"I_temp\"] = I\n",
    "            V += np.matmul(w, I)\n",
    "        firingrate = utils.activate(V, other_args=self.activation_params)\n",
    "        firingrate_prime = utils.activate(\n",
    "            V, other_args=self.activation_params, deriv=True\n",
    "        )\n",
    "\n",
    "        self.firingrate_temp = firingrate\n",
    "        self.firingrate_prime_temp = firingrate_prime\n",
    "\n",
    "        return firingrate\n",
    "\n",
    "    def update(self):\n",
    "        \"\"\"Updates firingrate of this compartment and saves it to file\"\"\"\n",
    "        self.get_state()\n",
    "        self.firingrate = self.firingrate_temp.reshape(-1)\n",
    "        self.firingrate_deriv = self.firingrate_prime_temp.reshape(-1)\n",
    "        for inputlayer in self.inputs.values():\n",
    "            inputlayer[\"I\"] = inputlayer[\"I_temp\"].reshape(-1)\n",
    "        self.save_to_history()\n",
    "        return\n",
    "\n",
    "    def update_weights(self):\n",
    "        \"\"\"Implements the weight update: dendritic prediction of somatic activity.\"\"\"\n",
    "        target = self.soma.firingrate\n",
    "        delta = (target - self.firingrate) * (self.firingrate_deriv)\n",
    "        dt = self.Agent.dt\n",
    "        for inputlayer in self.inputs.values():\n",
    "            eta = inputlayer[\"eta\"]\n",
    "            if eta != 0:\n",
    "                tau_PI = inputlayer[\"tau_PI\"]\n",
    "                assert (dt / tau_PI) < 0.2\n",
    "                I = inputlayer[\"I\"]\n",
    "                w = inputlayer[\"w\"]\n",
    "                # first updates plasticity induction variable (smoothed delta error outer product with the input current for this input layer)\n",
    "                PI_old = inputlayer[\"PI\"]\n",
    "                PI_update = np.outer(delta, I)\n",
    "                PI_new = (dt / tau_PI) * PI_update + (1 - dt / tau_PI) * PI_old\n",
    "                inputlayer[\"PI\"] = PI_new\n",
    "                # updates weights\n",
    "                dw = eta * (\n",
    "                    PI_new - inputlayer[\"L2\"] * w - inputlayer[\"L1\"] * np.sign(w)\n",
    "                )\n",
    "                inputlayer[\"w\"] = w + dw\n",
    "        return\n",
    "\n",
    "\n",
    "def theta_gating(t, freq=10, frac=0.5):\n",
    "    T = 1 / freq\n",
    "    phase = ((t / T) % 1) % 1\n",
    "    if phase < frac:\n",
    "        return 1\n",
    "    elif phase >= frac:\n",
    "        return 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Building the network\n",
    "This involves initialising the environment, the agent and all of the cells layers shown in the above figure. Then we must set the inputs to each cell layer) and, for those layers where the weights are fixed, set them correctly. \n",
    "\n",
    "Basically, the following code amounts to constructing the network shown in the above figure. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialise the 1D environment\n",
    "Env = Environment(params={\"dimensionality\": \"1D\", \"boundary_conditions\": \"periodic\"})\n",
    "\n",
    "# Put agent (who will move randomly under the ratinabox Ornstein Uhlenbeck random motion policy) inside the environement\n",
    "Ag = Agent(Env)\n",
    "Ag.speed_mean = 0\n",
    "Ag.speed_std = 0.3\n",
    "\n",
    "n_cells = 50\n",
    "# Place cells provide the target signal\n",
    "PlaceCells_ = PlaceCells(Ag, params={\"n\": n_cells, \"widths\": 0.1, \"name\": \"PlaceCells\"})\n",
    "\n",
    "# The key neuron class: Ring attractor at the centre of the network made from our bespoke, custom-define PyramidalNeurons class.\n",
    "RingAttractor = PyramidalNeurons(Ag, params={\"n\": n_cells, \"name\": \"RingAttractor\"})\n",
    "\n",
    "# Velocity cells encode agent velocity\n",
    "VelocityCells_ = VelocityCells(Ag, params={\"name\": \"VelocityCells\"})\n",
    "\n",
    "# Conjuctive cells\n",
    "ConjunctiveCells_left = FeedForwardLayer(\n",
    "    Ag,\n",
    "    params={\n",
    "        \"n\": n_cells,\n",
    "        \"name\": \"ConjunctiveCells_left\",\n",
    "    },\n",
    ")\n",
    "\n",
    "ConjunctiveCells_right = FeedForwardLayer(\n",
    "    Ag,\n",
    "    params={\n",
    "        \"n\": n_cells,\n",
    "        \"name\": \"ConjunctiveCells_right\",\n",
    "    },\n",
    ")\n",
    "\n",
    "# Set inputs into ring attractor compartments\n",
    "# Make their activation functions linear\n",
    "# Set the fixed weights from place celles to Ring attractor to be fixed\n",
    "RingAttractor.apical_compartment.add_input(RingAttractor)\n",
    "RingAttractor.apical_compartment.add_input(ConjunctiveCells_left)\n",
    "RingAttractor.apical_compartment.add_input(ConjunctiveCells_right)\n",
    "RingAttractor.apical_compartment.activation_params = {\"activation\": \"linear\"}\n",
    "\n",
    "RingAttractor.basal_compartment.add_input(PlaceCells_, eta=0)  # eta=0, these are fixed\n",
    "RingAttractor.basal_compartment.inputs[\"PlaceCells\"][\"w\"] = np.identity(n_cells)\n",
    "RingAttractor.basal_compartment.activation_params = {\"activation\": \"linear\"}\n",
    "\n",
    "# Set inputs into the conjuctive cells\n",
    "# Set the (fixed) weights into the conjunctive cells to be their correct values (identity or just 1's)\n",
    "ConjunctiveCells_left.add_input(VelocityCells_)\n",
    "ConjunctiveCells_left.add_input(RingAttractor)\n",
    "ConjunctiveCells_right.add_input(VelocityCells_)\n",
    "ConjunctiveCells_right.add_input(RingAttractor)\n",
    "ConjunctiveCells_left.inputs[\"VelocityCells\"][\"w\"] = np.ones((n_cells, 2)) * np.array(\n",
    "    [1, -1]\n",
    ")  # thus left velocity excites these cells and right velocity shuts them off\n",
    "ConjunctiveCells_right.inputs[\"VelocityCells\"][\"w\"] = np.ones((n_cells, 2)) * np.array(\n",
    "    [-1, 1]\n",
    ")  # thus right velocity excites these cells and rigleftht velocity shuts them off\n",
    "ConjunctiveCells_left.inputs[\"RingAttractor\"][\"w\"] = np.identity(n_cells)\n",
    "ConjunctiveCells_right.inputs[\"RingAttractor\"][\"w\"] = np.identity(n_cells)\n",
    "ConjunctiveCells_left.activation_params = {\n",
    "    \"activation\": \"relu\",\n",
    "    \"threshold\": 1,\n",
    "    \"width_x\": 2,\n",
    "}\n",
    "ConjunctiveCells_right.activation_params = {\n",
    "    \"activation\": \"relu\",\n",
    "    \"threshold\": 1,\n",
    "    \"width_x\": 2,\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train the network\n",
    "\n",
    "Train it for 20 minutes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 60000/60000 [00:17<00:00, 3457.69it/s]\n"
     ]
    }
   ],
   "source": [
    "for i in tqdm(range(int(10 * 60 / Ag.dt))):\n",
    "    # update agent\n",
    "    Ag.update()\n",
    "    # update firing rates of all the cell layers\n",
    "    PlaceCells_.update()\n",
    "    VelocityCells_.update()\n",
    "    ConjunctiveCells_left.update()\n",
    "    ConjunctiveCells_right.update()\n",
    "    RingAttractor.update_dendritic_compartments()\n",
    "    RingAttractor.update()\n",
    "    # finally, update the weights\n",
    "    RingAttractor.update_weights()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analysis \n",
    "Now training is complete we can see whether it as been successful. \n",
    "First we plot the loss. This is a (smoothed) trace of the mean absolute difference between the voltage in the basal compartment (the ground truth) and the voltage in the apical compartment (the compartment learnign to replicate the ground truth using recurrent and conjunctive velocity inputs). You can think of this as the prediction error. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 225x225 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = RingAttractor.plot_loss()\n",
    "\n",
    "if save_plots == True:\n",
    "    tpl.saveFigure(fig, \"PI_loss\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1800x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1800x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# pull out the weight as they were at initialisation\n",
    "w_ccl_init = RingAttractor.apical_compartment.inputs[\"ConjunctiveCells_left\"][\"w_init\"]\n",
    "w_ccr_init = RingAttractor.apical_compartment.inputs[\"ConjunctiveCells_right\"][\"w_init\"]\n",
    "w_rec_init = RingAttractor.apical_compartment.inputs[\"RingAttractor\"][\"w_init\"]\n",
    "\n",
    "# pull out the weights after training\n",
    "w_ccl = RingAttractor.apical_compartment.inputs[\"ConjunctiveCells_left\"][\"w\"]\n",
    "w_ccr = RingAttractor.apical_compartment.inputs[\"ConjunctiveCells_right\"][\"w\"]\n",
    "w_rec = RingAttractor.apical_compartment.inputs[\"RingAttractor\"][\"w\"]\n",
    "\n",
    "# plot them\n",
    "fig, ax = plt.subplots(1, 3, figsize=(12, 4))\n",
    "ax[0].imshow(w_rec_init)\n",
    "ax[1].imshow(w_ccl_init)\n",
    "ax[2].imshow(w_ccr_init)\n",
    "ax[0].set_ylabel(\"BEFORE TRAINING\")\n",
    "ax[0].set_title(\"Ring attractor \\nto ring attractor\")\n",
    "ax[1].set_title(\"Left conjunctive velocity cells \\nto ring attractor\")\n",
    "ax[2].set_title(\"Right conjunctive velocity cells \\nto ring attractor\")\n",
    "\n",
    "fig1, ax1 = plt.subplots(1, 3, figsize=(12, 4))\n",
    "ax1[0].imshow(w_rec)\n",
    "ax1[1].imshow(w_ccl)\n",
    "ax1[2].imshow(w_ccr)\n",
    "ax1[0].set_ylabel(\"AFTER TRAINING\")\n",
    "ax1[0].set_title(\"Ring attractor \\nto ring attractor\")\n",
    "ax1[1].set_title(\"Left conjunctive velocity cells \\nto ring attractor\")\n",
    "ax1[2].set_title(\"Right conjunctive velocity cells \\nto ring attractor\")\n",
    "\n",
    "if save_plots == True:\n",
    "    tpl.saveFigure(fig, \"PIweights_beforelearning\")\n",
    "    tpl.saveFigure(fig1, \"PIweights_afterlearning\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Further analysis\n",
    "\n",
    "In a seperate analysis (of the same network, but code not given here) we produced the following figures. \n",
    "\n",
    "The first shows the weight matrices before and after learning, along side a row-averaged cross section of the after-learning matrices. One can see how the theoritical hypothsis for how weights should develop in this system is correctly found by the Hebbian local learning rule (in less than 10 minutes of training!). \n",
    "\n",
    "In the movie we summarise an experiment where the animal is left to explore for 60 seconds. For the first 60 seconds sensory *and* top-down inouts are available. For times 30s to 60s the sensory input from the place cells are lesioned and only the velocity integration part (the top-down apical dendritic compartment) drives the soma. As can be seen, although errors accumulate, the network does a decent job at maintaining the position estimate in the total absence of sensory input. Purple shows true position of agent, blue shows position in neural manifold of peak activity. We encourage anyone intersted to replicate this very simple experiment using the above code - perhaps using the decoding_position)_example.ipynb script to train a decoder to decode position fromneural activity and show the decoding is accurate even after sensory input is lesioned.\n",
    "\n",
    " * Proof the connectivity structure matches that of a classically define veloicty-driven path integrator CANN.\n",
    "  \n",
    " <img src=\"../.images/demos/pathint_resultsmatrices.png\" width=\"750\" align=\"center\"> \n",
    " \n",
    "* Proof this connectivity structure can actually perform path integration\n",
    "\n",
    " <img src=\"../.images/demos/pathint_result.gif\" width=\"750\" align=\"center\"> \n"
   ]
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    "### Disclaimer: \n",
    "Please note this script is intended as a tutorial, here only to demonstrate how `RatInABox` could be used for a path integration project in continuous time and space and not as a scientific result regarding the role of hippocampus and entorhinal cortex role in path integration. "
   ]
  }
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