{ "cells": [ { "cell_type": "markdown", "id": "e83425e9", "metadata": {}, "source": [ "# AlignPre / AlignPost — the keystone\n", "\n", "**What you'll learn / who it's for (simulation *and* training).** This is the\n", "central design of ``brainpy.state`` and the single most important page in this\n", "documentation. You'll learn why a naive simulator drowns in synaptic state, how\n", "**AlignPre** and **AlignPost** reduce that state from per-*synapse* to per-*neuron*\n", "— *exactly*, not approximately — the four components every projection is built\n", "from, and a decision table for choosing between the two. The chapter closes on the\n", "reason this matters twice over: the same alignment that makes simulation\n", "memory-efficient is what makes gradient-based and online learning memory-efficient.\n", "\n", "A deep-learning reader can read \"synapse\" as \"the recurrent hidden state of a\n", "layer\"; a neuroscience reader can read it literally. Both arrive at the same place." ] }, { "cell_type": "markdown", "id": "5df48197", "metadata": {}, "source": [ "## 1. The synaptic-state explosion\n", "\n", "Give every synapse its own dynamical variable and the bookkeeping grows with the\n", "number of *connections*. For a projection from $N_{\\text{pre}}$ to\n", "$N_{\\text{post}}$ neurons at connection density $p$, naive per-synapse state costs\n", "\n", "$$\\mathcal{O}\\!\\left(p \\cdot N_{\\text{pre}} \\cdot N_{\\text{post}}\\right).$$\n", "\n", "Make it concrete. A modest cortical column might wire $10^4$ neurons to $10^4$\n", "neurons at $10\\%$ density. That is $\\approx 10^7$ real synapses — but a naive\n", "implementation that materializes a variable for *every* possible pre–post pair\n", "allocates on the order of $10^8$ floats, and updates all of them every step.\n", "Most of that is wasted: synapses that share dynamics are tracked redundantly.\n", "\n", "The fix is not to approximate the dynamics. It is to notice that the redundancy is\n", "*exact*, and to store one variable where many identical ones used to live." ] }, { "cell_type": "markdown", "id": "c3d786a1", "metadata": {}, "source": [ "## 2. The key observation\n", "\n", "> *All synaptic variables sharing the same linear dynamics can be reduced to a\n", "> single one.*\n", "\n", "If a group of synapses obey the same differential equation and are driven by the\n", "same input, their states are identical for all time — so one state suffices for the\n", "whole group. The only question is **which dimension** the surviving variable should\n", "live on. Align it to the **presynaptic** neurons and you get **AlignPre**; align it\n", "to the **postsynaptic** neurons and you get **AlignPost**. Each is exact under a\n", "clearly stated condition, and each is natural for a different connectivity shape." ] }, { "cell_type": "markdown", "id": "9bf51156", "metadata": {}, "source": [ "## 3. Decoupling dynamics from communication — the four roles\n", "\n", "``brainpy.state`` does not write projections as monolithic connection objects.\n", "Every projection is composed from four interchangeable roles, and the *order* of\n", "two of them is what distinguishes the two alignments:\n", "\n", "- **``comm``** — *communication*. The connectivity itself: a sparse or dense weight\n", " matrix, or, equivalently, a deep-learning layer (``EventFixedProb``, ``Linear``,\n", " ``AllToAllProj``, …). It maps a presynaptic signal to a postsynaptic one.\n", "- **``syn``** — *synapse dynamics*. The temporal filter applied to spikes\n", " (``Expon``, ``DualExpon``, ``AMPA``, ``GABAa``, ``BioNMDA``, …).\n", "- **``out``** — *output*. How conductance becomes current: ``COBA`` (conductance-\n", " based, with reversal potential ``E``), ``CUBA`` (current-based), or ``MgBlock``\n", " (NMDA's voltage-dependent magnesium block).\n", "- **``post``** — the postsynaptic ``Dynamics`` population that receives the current.\n", "\n", "Because the roles are decoupled, you swap connectivity, kinetics, and biophysics\n", "independently — and you place ``syn`` either **before** ``comm`` (AlignPre) or\n", "**after** it (AlignPost). That single placement choice is the whole idea, and the\n", "diagram below is the picture to hold in your head for the rest of the page." ] }, { "cell_type": "markdown", "id": "9e42c3aa", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": "```{eval-rst}\n.. figure:: /_static/alignpre-alignpost.png\n :alt: Two panels. Left, \"AlignPre\": presynaptic neurons (orange) feed a\n synapse-dynamics box, then the green connection matrix, then the\n postsynaptic neurons (blue) -- synapse state lives BEFORE the matrix,\n on the presynaptic side, O(N_pre). Right, \"AlignPost\": presynaptic\n neurons (orange) feed the green connection matrix FIRST, then a\n synapse-dynamics box on the postsynaptic side, then the postsynaptic\n neurons (blue) -- synapse state lives AFTER the matrix, O(N_post).\n :width: 95%\n\n **AlignPre vs AlignPost.** The synapse-dynamics block sits *before* the\n connection matrix on the left (state aligned to the presynaptic population,\n :math:`\\mathcal{O}(N_\\text{pre})`, works for all synapses, natural for\n one-to-many) and *after* it on the right (state aligned to the postsynaptic\n population, :math:`\\mathcal{O}(N_\\text{post})`, exponential-family synapses,\n natural for many-to-one). *(Orange = presynaptic, blue = postsynaptic,\n green = connection matrix.)*\n```" }, { "cell_type": "markdown", "id": "c747beb7", "metadata": {}, "source": [ "## 4. AlignPost — state aligned to the postsynaptic neurons\n", "\n", "Put the synapse dynamics **after** ``comm``. Now the surviving state lives on the\n", "$N_{\\text{post}}$ postsynaptic neurons: memory is $\\mathcal{O}(N_{\\text{post}})$,\n", "*independent of how many presynaptic neurons or connections feed in*.\n", "\n", "Why is this exact? Recall the exponential synapse from\n", "{doc}`/concepts/model-anatomy`: each arriving spike updates the postsynaptic\n", "conductance by $g \\leftarrow g + 1$, **regardless of which presynaptic neuron\n", "emitted it**. Spikes from many sources therefore *superpose* — their separate\n", "contributions sum linearly into one merged postsynaptic conductance. Tracking that\n", "single merged variable reproduces the full per-synapse dynamics with no\n", "approximation. The price of the trick is its precondition: it works **only for\n", "synapse models with exponential (linear) dynamics**.\n", "\n", "AlignPost is the natural choice for **many-to-one** fan-in (the dominant pattern in\n", "recurrent networks) and is **event-driven**: only neurons that actually spiked\n", "contribute." ] }, { "cell_type": "markdown", "id": "a4db1c9f", "metadata": {}, "source": [ "### Worked example: the COBA excitatory–inhibitory network\n", "\n", "The canonical balanced E–I network (Vogels & Abbott, 2005; Brette et al., 2007)\n", "wires 4000 neurons to themselves through two AlignPost projections — one excitatory\n", "(``E = 0 mV``), one inhibitory (``E = -80 mV``). Both use an exponential synapse, so\n", "AlignPost applies. Note ``syn`` and ``out`` are passed as **describers**\n", "(``Expon.desc(...)``, ``COBA.desc(...)``): the projection instantiates one shared\n", "postsynaptic synapse from the description." ] }, { "cell_type": "code", "execution_count": 1, "id": "c7150451", "metadata": { "execution": { "iopub.execute_input": "2026-06-17T09:10:28.622733Z", "iopub.status.busy": "2026-06-17T09:10:28.622265Z", "iopub.status.idle": "2026-06-17T09:10:32.660403Z", "shell.execute_reply": "2026-06-17T09:10:32.659455Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.\n" ] } ], "source": [ "import brainpy\n", "import brainstate\n", "import braintools\n", "import brainunit as u\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "class EINet(brainstate.nn.Module):\n", " def __init__(self):\n", " super().__init__()\n", " self.n_exc, self.n_inh = 3200, 800\n", " self.num = self.n_exc + self.n_inh\n", " # one postsynaptic population of 4000 LIF-with-refractory neurons\n", " self.N = brainpy.state.LIFRef(\n", " self.num,\n", " V_rest=-60. * u.mV, V_th=-50. * u.mV, V_reset=-60. * u.mV,\n", " tau=20. * u.ms, tau_ref=5. * u.ms,\n", " V_initializer=braintools.init.Normal(-55., 2., unit=u.mV),\n", " )\n", " # excitatory AlignPost projection: state aligned to the 4000 post neurons\n", " self.E = brainpy.state.AlignPostProj(\n", " comm=brainstate.nn.EventFixedProb(self.n_exc, self.num,\n", " conn_num=0.02, conn_weight=0.6 * u.mS),\n", " syn=brainpy.state.Expon.desc(self.num, tau=5. * u.ms),\n", " out=brainpy.state.COBA.desc(E=0. * u.mV),\n", " post=self.N,\n", " )\n", " # inhibitory AlignPost projection: shares the same post population\n", " self.I = brainpy.state.AlignPostProj(\n", " comm=brainstate.nn.EventFixedProb(self.n_inh, self.num,\n", " conn_num=0.02, conn_weight=6.7 * u.mS),\n", " syn=brainpy.state.Expon.desc(self.num, tau=10. * u.ms),\n", " out=brainpy.state.COBA.desc(E=-80. * u.mV),\n", " post=self.N,\n", " )\n", "\n", " def update(self, t, inp):\n", " with brainstate.environ.context(t=t):\n", " spk = self.N.get_spike() != 0.\n", " self.E(spk[:self.n_exc]) # excitatory neurons' spikes\n", " self.I(spk[self.n_exc:]) # inhibitory neurons' spikes\n", " self.N(inp) # integrate synaptic + external current\n", " return self.N.get_spike()" ] }, { "cell_type": "code", "execution_count": 2, "id": "40d65c24", "metadata": { "execution": { "iopub.execute_input": "2026-06-17T09:10:32.662954Z", "iopub.status.busy": "2026-06-17T09:10:32.662564Z", "iopub.status.idle": "2026-06-17T09:10:40.114878Z", "shell.execute_reply": "2026-06-17T09:10:40.113617Z" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "0d33f182126a46d0b600ab6cecdbc877", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/10000 [00:00" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "net = EINet()\n", "brainstate.nn.init_all_states(net)\n", "\n", "with brainstate.environ.context(dt=0.1 * u.ms):\n", " times = u.math.arange(0. * u.ms, 1000. * u.ms, brainstate.environ.get_dt())\n", " spikes = brainstate.transform.for_loop(\n", " lambda t: net.update(t, 20. * u.mA), times,\n", " pbar=brainstate.transform.ProgressBar(10),\n", " )\n", "\n", "# raster plot\n", "t_idx, n_idx = u.math.where(spikes)\n", "plt.figure(figsize=(10, 4))\n", "plt.scatter(times[t_idx].to_decimal(u.ms), n_idx, s=0.5)\n", "plt.xlabel('time (ms)'); plt.ylabel('neuron index')\n", "plt.title('COBA E–I balanced network (two AlignPost projections)')\n", "plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "fa88584b", "metadata": {}, "source": [ "The synaptic state for each projection is a length-``num`` (4000) vector — one entry\n", "per postsynaptic neuron — *no matter how many presynaptic spikes arrive each step*.\n", "That is the $\\mathcal{O}(N_{\\text{post}})$ memory of AlignPost in practice." ] }, { "cell_type": "markdown", "id": "69d5c06c", "metadata": {}, "source": [ "## 5. AlignPre — state aligned to the presynaptic neurons\n", "\n", "Put the synapse dynamics **before** ``comm``. Now the surviving state lives on the\n", "$N_{\\text{pre}}$ presynaptic neurons: memory is $\\mathcal{O}(N_{\\text{pre}})$.\n", "\n", "Why exact here? With **homogeneous synaptic parameters per presynaptic neuron**,\n", "every synapse leaving a given source neuron is driven by the *same* spike train\n", "through the *same* dynamics — so they share one trace. Filter the spike train *once*\n", "per presynaptic neuron, then let ``comm`` distribute the result. Because the\n", "filtering happens before the (linear) connection matrix, the synapse model need\n", "**not** be linear: AlignPre works for **all** synapse models, including the\n", "voltage- and concentration-dependent ones — ``AMPA``, ``GABAa``, and ``BioNMDA``\n", "(whose nonlinear kinetics rule out AlignPost).\n", "\n", "AlignPre is the natural choice for **one-to-many** fan-out — one source population\n", "broadcasting to several targets, where the single per-source trace is reused for\n", "each." ] }, { "cell_type": "markdown", "id": "3a836a5f", "metadata": {}, "source": [ "### The canonical AlignPre API\n", "\n", "AlignPre is exposed as the **function** ``brainpy.state.align_pre_projection`` —\n", "there is intentionally no ``AlignPreProj`` class (AlignPost has both a class,\n", "``AlignPostProj``, and a function, ``align_post_projection``). The function takes a\n", "spike generator, then the same four roles, with ``syn`` placed *first* in the\n", "pipeline so it filters in presynaptic space:" ] }, { "cell_type": "code", "execution_count": 3, "id": "a00b636d", "metadata": { "execution": { "iopub.execute_input": "2026-06-17T09:10:40.118374Z", "iopub.status.busy": "2026-06-17T09:10:40.117689Z", "iopub.status.idle": "2026-06-17T09:10:40.122335Z", "shell.execute_reply": "2026-06-17T09:10:40.121178Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "align_pre_projection is a function: True\n" ] } ], "source": [ "# A one-to-many fan-out with a nonlinear AMPA synapse -- AlignPost could not do this,\n", "# because AMPA's kinetics are not a single linear exponential.\n", "#\n", "# Pattern (the canonical AlignPre call):\n", "#\n", "# proj = brainpy.state.align_pre_projection(\n", "# pre, # spike generator (the source population)\n", "# syn=brainpy.state.AMPA(n_pre), # synapse dynamics in PRE space\n", "# comm=brainstate.nn.Linear(n_pre, n_post,\n", "# w_init=braintools.init.KaimingNormal(unit=u.mS),\n", "# b_init=None),\n", "# out=brainpy.state.COBA(E=0. * u.mV), # conductance -> current\n", "# post=post, # postsynaptic population\n", "# )\n", "#\n", "# Per update: pre spikes -> syn filters them (one trace per presynaptic neuron)\n", "# -> comm distributes -> out -> post.\n", "print('align_pre_projection is a function:',\n", " callable(brainpy.state.align_pre_projection))" ] }, { "cell_type": "markdown", "id": "7e57d3d1", "metadata": {}, "source": [ "### Seeing where the state lives\n", "\n", "The defining property of AlignPre is that the synapse state is sized by the\n", "**presynaptic** population, not the postsynaptic one. The clearest way to *show*\n", "that is to assemble the pipeline from its lower-level pieces — a ``syn`` evolving in\n", "presynaptic space followed by a ``CurrentProj`` (the ``comm → out → post`` half that\n", "``align_pre_projection`` wraps for you). Watch the shapes: ``syn.g`` has one entry\n", "per *presynaptic* neuron, while the postsynaptic voltage has one entry per *target*." ] }, { "cell_type": "code", "execution_count": 4, "id": "f673cb84", "metadata": { "execution": { "iopub.execute_input": "2026-06-17T09:10:40.124723Z", "iopub.status.busy": "2026-06-17T09:10:40.124445Z", "iopub.status.idle": "2026-06-17T09:10:41.028375Z", "shell.execute_reply": "2026-06-17T09:10:41.027287Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "syn.g lives on PRE neurons -> (400,) (== n_pre = 400)\n", "post.V lives on POST neurons -> (100,) (== n_post = 100)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "post spike raster shape: (1000, 100)\n" ] } ], "source": [ "class FanOut(brainstate.nn.Module):\n", " def __init__(self, n_pre=400, n_post=100):\n", " super().__init__()\n", " self.pre = brainpy.state.LIF(\n", " n_pre, tau=20. * u.ms, V_rest=-60. * u.mV, V_th=-50. * u.mV,\n", " V_reset=-60. * u.mV,\n", " V_initializer=braintools.init.Normal(-55., 2., unit=u.mV))\n", " self.post = brainpy.state.LIF(\n", " n_post, tau=20. * u.ms, V_rest=-60. * u.mV, V_th=-50. * u.mV,\n", " V_reset=-60. * u.mV)\n", " # synapse in PRE space: its state vector is length n_pre\n", " self.syn = brainpy.state.Expon(\n", " n_pre, tau=5. * u.ms, g_initializer=braintools.init.Constant(0.))\n", " # comm -> out -> post (what align_pre_projection wraps internally)\n", " self.proj = brainpy.state.CurrentProj(\n", " comm=brainstate.nn.Linear(n_pre, n_post,\n", " w_init=braintools.init.KaimingNormal(unit=u.mS),\n", " b_init=None),\n", " out=brainpy.state.COBA(E=0. * u.mV),\n", " post=self.post,\n", " )\n", "\n", " def update(self, t, inp):\n", " with brainstate.environ.context(t=t):\n", " g_pre = self.syn(self.pre.get_spike()) # filter in PRE space\n", " self.proj(g_pre) # distribute to POST\n", " self.pre(inp)\n", " self.post(0. * u.mA)\n", " return self.post.get_spike()\n", "\n", "\n", "net = FanOut()\n", "brainstate.nn.init_all_states(net)\n", "print('syn.g lives on PRE neurons ->', net.syn.g.value.shape, '(== n_pre = 400)')\n", "print('post.V lives on POST neurons ->', net.post.V.value.shape, '(== n_post = 100)')\n", "\n", "with brainstate.environ.context(dt=0.1 * u.ms):\n", " times = u.math.arange(0. * u.ms, 100. * u.ms, brainstate.environ.get_dt())\n", " spk = brainstate.transform.for_loop(lambda t: net.update(t, 30. * u.mA), times)\n", "print('post spike raster shape:', spk.shape)" ] }, { "cell_type": "markdown", "id": "2983d110", "metadata": {}, "source": [ "The synapse vector is length 400 (the presynaptic count); the postsynaptic state is\n", "length 100. Broadcast that one source population to a second or third target and the\n", "*same* 400-entry trace is reused — that is the $\\mathcal{O}(N_{\\text{pre}})$ payoff\n", "of AlignPre for one-to-many fan-out." ] }, { "cell_type": "markdown", "id": "fedb8946", "metadata": {}, "source": [ "## 6. Exact, not approximate\n", "\n", "It bears repeating, because it is the property that makes the whole design\n", "trustworthy rather than a heuristic:\n", "\n", "> *These projections are not approximations. They accurately compute the same\n", "> dynamics as the original projections while providing new benefits.*\n", "> — Wang et al., ICLR 2024.\n", "\n", "Each alignment is exact **under its stated condition**:\n", "\n", "- **AlignPre** requires **homogeneous synaptic parameters per presynaptic neuron**,\n", " so that all synapses from one source share a single trace. As the paper puts it:\n", " *\"with homogeneous synaptic parameters, the spike train coming from the same\n", " presynaptic neuron will lead to the same synaptic dynamics … all synapses\n", " originating from the same presynaptic neuron can share a single dynamical\n", " variable … AlignPre … is suitable for all types of synapse models.\"*\n", "- **AlignPost** requires **linear (exponential) synaptic dynamics**, so that\n", " contributions superpose. Again from the paper: *\"the applicability of AlignPost is\n", " limited to synapse models that exhibit exponential dynamics … the conductance g of\n", " a post-synaptic neuron is updated according to* $g \\leftarrow g + 1$ *whenever a\n", " spike arrives and regardless of which presynaptic neuron emitted this spike.\"*\n", "\n", "When its condition holds, the reduction changes the memory footprint and nothing\n", "else." ] }, { "cell_type": "markdown", "id": "a98482b8", "metadata": {}, "source": [ "## 7. Automatic merging\n", "\n", "Because synaptic state is keyed by a *neuron* dimension (plus the synapse/output\n", "description), projections that target the same place with the same kinetics can\n", "**share a single synapse instance** automatically:\n", "\n", "- **AlignPost** — multiple projections into the same ``post`` population with the\n", " same ``syn``/``out`` descriptor share one postsynaptic synapse; their inputs sum\n", " into the merged conductance.\n", "- **AlignPre** — projections from the same ``pre`` population (with the same delay)\n", " share one presynaptic synapse.\n", "\n", "This is the additive-input convention from {doc}`/concepts/model-anatomy` paying\n", "off: convergent pathways merge with no extra memory, and you express them simply by\n", "pointing several projections at the same population." ] }, { "cell_type": "markdown", "id": "dd237624", "metadata": {}, "source": [ "## 8. Choosing between them\n", "\n", "Reach for **AlignPost** when synapses are exponential-family and the wiring fans\n", "*in* (many sources, one target) — the common recurrent-network case. Reach for\n", "**AlignPre** when the synapse is nonlinear, or when one source fans *out* to many\n", "targets. Both are exact; the choice is about which dimension is smaller and which\n", "condition your synapse satisfies." ] }, { "cell_type": "markdown", "id": "6f2146b2", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": "```{eval-rst}\n.. list-table:: When to use AlignPre vs AlignPost\n :header-rows: 1\n :widths: 22 22 18 22 16\n\n * - Want\n - Synapse type\n - Connectivity\n - Use\n - State\n * - Event-driven fan-in\n - exponential-family (``Expon``, ``DualExpon``)\n - many → one\n - **AlignPost** (``AlignPostProj`` / ``align_post_projection``)\n - :math:`\\mathcal{O}(N_\\text{post})`\n * - Nonlinear kinetics\n - ``AMPA``, ``BioNMDA``, ``GABAa``\n - any\n - **AlignPre** (``align_pre_projection``)\n - :math:`\\mathcal{O}(N_\\text{pre})`\n * - One source → many targets\n - any\n - one → many\n - **AlignPre** (``align_pre_projection``)\n - :math:`\\mathcal{O}(N_\\text{pre})`\n * - Direct current / no synapse dynamics\n - —\n - any\n - ``CurrentProj`` / ``DeltaProj``\n - —\n```" }, { "cell_type": "markdown", "id": "c2bb2091", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": "```{eval-rst}\n.. list-table:: The three memory regimes\n :header-rows: 1\n :widths: 24 22 26 18 18\n\n * - Scheme\n - State lives on\n - State memory\n - Applies to\n - Best for\n * - Naïve per-synapse\n - each synapse\n - :math:`\\mathcal{O}(p \\cdot N_\\text{pre} \\cdot N_\\text{post})`\n - any\n - *(wasteful)*\n * - **AlignPre**\n - presynaptic neurons\n - :math:`\\mathcal{O}(N_\\text{pre})`\n - **all** synapse models\n - one-to-many\n * - **AlignPost**\n - postsynaptic neurons\n - :math:`\\mathcal{O}(N_\\text{post})`\n - exponential-family only\n - many-to-one\n```" }, { "cell_type": "markdown", "id": "7f9869a8", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": "```{eval-rst}\n.. figure:: /_static/memory-complexity.png\n :alt: Three panels comparing memory. Panel 1 \"Naive per-synapse\": a dense full\n grid of connections between an orange presynaptic column and a blue\n postsynaptic column, labelled O(p * N_pre * N_post), marked wasteful.\n Panel 2 \"AlignPre\": each orange presynaptic neuron carries one trace that\n fans out to many blue postsynaptic neurons, labelled O(N_pre),\n one-to-many. Panel 3 \"AlignPost\": many orange presynaptic arrows converge\n into one merged trace on each blue postsynaptic neuron, labelled\n O(N_post), many-to-one, event-driven.\n :width: 95%\n\n **Three memory regimes.** Naive per-synapse state scales with the number of\n connections; AlignPre collapses it onto the presynaptic neurons\n (:math:`\\mathcal{O}(N_\\text{pre})`) and AlignPost onto the postsynaptic neurons\n (:math:`\\mathcal{O}(N_\\text{post})`) — both exactly.\n```" }, { "cell_type": "markdown", "id": "04cc7631", "metadata": {}, "source": [ "## 9. The bridge to learning\n", "\n", "Here is why this chapter is the keystone of the whole framework, not just a memory\n", "optimization.\n", "\n", "Aligning synaptic state to a **neuron** dimension instead of a **weight** dimension\n", "does more than shrink the forward pass. It is *also* what makes gradient-based and\n", "online learning tractable. Backpropagation-through-time differentiates the very\n", "``for_loop`` you used above, and neuron-aligned state keeps the activations it must\n", "remember small (see {doc}`/concepts/differentiability`). More dramatically, in\n", "**real-time recurrent learning (RTRL)** the same superposition that makes AlignPost's\n", "*forward* pass exact is reused on the *backward* pass: the eligibility traces and\n", "Jacobians that would otherwise scale cubically/quadratically with the number of\n", "hidden units collapse to **linear** memory. That is the result of Wang et al. (2026,\n", "*Nature Communications*), and it is what puts whole-brain-scale online learning\n", "within reach.\n", "\n", "In one sentence: **the alignment that makes simulation memory-efficient is the\n", "alignment that makes learning memory-efficient.** The two worlds — brain simulation\n", "and brain-inspired computing — meet exactly here.\n", "\n", "Continue to {doc}`/concepts/online-learning` for the linear-memory story." ] }, { "cell_type": "markdown", "id": "62de2dd4", "metadata": {}, "source": [ "## 10. API pointers\n", "\n", "- **AlignPost** — class ``brainpy.state.AlignPostProj`` and function\n", " ``brainpy.state.align_post_projection`` (``syn``/``out`` as ``.desc(...)``\n", " describers).\n", "- **AlignPre** — function ``brainpy.state.align_pre_projection`` (no class).\n", "- **Direct injection** — ``brainpy.state.CurrentProj`` (continuous current, no\n", " synapse) and ``brainpy.state.DeltaProj`` (instantaneous delta input).\n", "- **Gap junctions** — ``brainpy.state.SymmetryGapJunction`` /\n", " ``brainpy.state.AsymmetryGapJunction`` for electrical coupling.\n", "- **Short-term plasticity** — pass ``stp=brainpy.state.STP(...)`` (or ``STD``) to\n", " ``align_pre_projection`` / ``align_post_projection``.\n", "\n", "See {doc}`/apis/index` for full signatures." ] }, { "cell_type": "markdown", "id": "45d1d89e", "metadata": {}, "source": [ "## References\n", "\n", "- Wang, C., Zhang, T., He, S., Gu, H., Li, S., Wu, S. (2024). *A differentiable\n", " brain simulator bridging brain simulation and brain-inspired computing.* ICLR\n", " 2024. (arXiv:2311.05106). —\n", " introduces AlignPre / AlignPost.\n", "- Vogels, T. P. & Abbott, L. F. (2005). *Signal propagation and logic gating in\n", " networks of integrate-and-fire neurons.* J. Neurosci. 25(46), 10786–95. — the\n", " balanced E–I network reproduced above.\n", "\n", "## See also\n", "\n", "- {doc}`/concepts/model-anatomy` — the ``comm`` / ``syn`` / ``out`` / ``post``\n", " pieces and the ``g ← g + 1`` increment this design exploits.\n", "- {doc}`/concepts/differentiability` — backpropagation-through-time over the same\n", " models.\n", "- {doc}`/concepts/online-learning` — linear-memory RTRL, the learning-side payoff.\n", "- {doc}`/brainpy-style/index` — projections applied in tutorials and how-to guides." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.11" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": { "0d33f182126a46d0b600ab6cecdbc877": { 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