Update course book

neuromatch · Aug 20, 2024 · 5d62e44 · 5d62e44
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diff --git a/_sources/tutorials/W2D2_NeuroSymbolicMethods/student/W2D2_Tutorial1.ipynb b/_sources/tutorials/W2D2_NeuroSymbolicMethods/student/W2D2_Tutorial1.ipynb
@@ -343,7 +343,7 @@
     "    - title (str): title of the plot.\n",
     "    \"\"\"\n",
     "    with plt.xkcd():\n",
-    "        plt.plot(x_range, sims)\n",
+    "        plt.plot(x_range, sim_mat)\n",
     "    plt.xlabel('x')\n",
     "    plt.ylabel('Similarity')\n",
     "    plt.title(title)"
@@ -382,6 +382,100 @@
     "set_seed(seed = 42)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "##  Helper functions\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "cellView": "form",
+    "execution": {},
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "# @title Helper functions\n",
+    "\n",
+    "# mainly contains solutions to exercises for correct plot output; please don't take a look!\n",
+    "set_seed(42)\n",
+    "\n",
+    "vector_length = 1024\n",
+    "symbol_names = ['circle','square','triangle']\n",
+    "discrete_space = sspspace.DiscreteSPSpace(symbol_names, ssp_dim=vector_length, optimize = False)\n",
+    "\n",
+    "circle = discrete_space.encode('circle')\n",
+    "square = discrete_space.encode('square')\n",
+    "triangle = discrete_space.encode('triangle')\n",
+    "\n",
+    "shape = (circle + square + triangle).normalize()\n",
+    "\n",
+    "shape_sim_mat = np.zeros((4,4))\n",
+    "\n",
+    "shape_sim_mat[0,0] = (circle | circle).item()\n",
+    "shape_sim_mat[1,1] = (square | square).item()\n",
+    "shape_sim_mat[2,2] = (triangle | triangle).item()\n",
+    "shape_sim_mat[3,3] = (shape | shape).item()\n",
+    "\n",
+    "shape_sim_mat[0,1] = shape_sim_mat[1,0] = (circle | square).item()\n",
+    "shape_sim_mat[0,2] = shape_sim_mat[2,0] = (circle | triangle).item()\n",
+    "shape_sim_mat[0,3] = shape_sim_mat[3,0] = (circle | shape).item()\n",
+    "\n",
+    "shape_sim_mat[1,2] = shape_sim_mat[2,1] = (square | triangle).item()\n",
+    "shape_sim_mat[1,3] = shape_sim_mat[3,1] = (square | shape).item()\n",
+    "\n",
+    "shape_sim_mat[2,3] = shape_sim_mat[3,2] = (triangle | shape).item()\n",
+    "\n",
+    "new_symbol_names = ['circle','square','triangle', 'red', 'blue', 'green']\n",
+    "new_discrete_space = sspspace.DiscreteSPSpace(new_symbol_names, ssp_dim=vector_length, optimize=False)\n",
+    "\n",
+    "objs = {n:new_discrete_space.encode(np.array([n])) for n in new_symbol_names}\n",
+    "\n",
+    "objs['red*circle'] = objs['red'] * objs['circle']\n",
+    "objs['blue*triangle'] = objs['blue'] * objs['triangle']\n",
+    "objs['green*square'] = objs['green'] * objs['square']\n",
+    "\n",
+    "new_object_names = ['red','red^','red*circle','circle','circle^']\n",
+    "new_objs = objs.copy()\n",
+    "\n",
+    "new_objs['red^'] = new_objs['red*circle'] * ~new_objs['circle']\n",
+    "new_objs['circle^'] = new_objs['red*circle'] * ~new_objs['red']\n",
+    "\n",
+    "axis_vectors = ['one']\n",
+    "\n",
+    "encoder = sspspace.DiscreteSPSpace(axis_vectors, ssp_dim=1024, optimize=False)\n",
+    "\n",
+    "vocab = {w:encoder.encode(w) for w in axis_vectors}\n",
+    "\n",
+    "integers = [vocab['one']]\n",
+    "\n",
+    "max_int = 5\n",
+    "for i in range(2, max_int + 1):\n",
+    "    integers.append(integers[-1] * vocab['one'])\n",
+    "\n",
+    "integers = np.array(integers).squeeze()\n",
+    "integer_sims = integers @ integers.T\n",
+    "\n",
+    "five_unbind_two = sspspace.SSP(integers[4]) * ~sspspace.SSP(integers[1])\n",
+    "five_unbind_two_sims = five_unbind_two @ integers.T\n",
+    "\n",
+    "new_encoder = sspspace.RandomSSPSpace(domain_dim=1, ssp_dim=1024)\n",
+    "\n",
+    "xs = np.linspace(-4,4,401)[:,None]\n",
+    "phis = new_encoder.encode(xs)\n",
+    "\n",
+    "real_line_sims = phis[200, :] @ phis.T\n",
+    "\n",
+    "phi_shifted = phis[200,:][None,:] * new_encoder.encode([[np.pi/2]])\n",
+    "shifted_real_line_sims = phi_shifted.flatten() @ phis.T"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {
@@ -587,17 +681,17 @@
    },
    "outputs": [],
    "source": [
-    "sim_mat = np.zeros((3,3))\n",
+    "concepts_sim_mat = np.zeros((3,3))\n",
     "\n",
-    "sim_mat[0,0] = (circle | circle).item()\n",
-    "sim_mat[1,1] = (square | square).item()\n",
-    "sim_mat[2,2] = (triangle | triangle).item()\n",
+    "concepts_sim_mat[0,0] = (circle | circle).item()\n",
+    "concepts_sim_mat[1,1] = (square | square).item()\n",
+    "concepts_sim_mat[2,2] = (triangle | triangle).item()\n",
     "\n",
-    "sim_mat[0,1] = sim_mat[1,0] = (circle | square).item()\n",
-    "sim_mat[0,2] = sim_mat[2,0] = (circle | triangle).item()\n",
-    "sim_mat[1,2] = sim_mat[2,1] = (square | triangle).item()\n",
+    "concepts_sim_mat[0,1] = concepts_sim_mat[1,0] = (circle | square).item()\n",
+    "concepts_sim_mat[0,2] = concepts_sim_mat[2,0] = (circle | triangle).item()\n",
+    "concepts_sim_mat[1,2] = concepts_sim_mat[2,1] = (square | triangle).item()\n",
     "\n",
-    "plot_similarity_matrix(sim_mat, symbol_names)"
+    "plot_similarity_matrix(concepts_sim_mat, symbol_names)"
    ]
   },
   {
@@ -780,21 +874,21 @@
     "raise NotImplementedError(\"Student exercise: complete calcualtion of similarity matrix.\")\n",
     "###################################################################\n",
     "\n",
-    "sim_mat = np.zeros((4,4))\n",
+    "shape_sim_mat = np.zeros((4,4))\n",
     "\n",
-    "sim_mat[0,0] = (circle | circle).item()\n",
-    "sim_mat[1,1] = (square | square).item()\n",
-    "sim_mat[2,2] = (triangle | ...).item()\n",
-    "sim_mat[3,3] = (shape | ...).item()\n",
+    "shape_sim_mat[0,0] = (circle | circle).item()\n",
+    "shape_sim_mat[1,1] = (square | square).item()\n",
+    "shape_sim_mat[2,2] = (triangle | ...).item()\n",
+    "shape_sim_mat[3,3] = (shape | ...).item()\n",
     "\n",
-    "sim_mat[0,1] = sim_mat[1,0] = (circle | square).item()\n",
-    "sim_mat[0,2] = sim_mat[2,0] = (circle | triangle).item()\n",
-    "sim_mat[0,3] = sim_mat[3,0] = (circle | shape).item()\n",
+    "shape_sim_mat[0,1] = shape_sim_mat[1,0] = (circle | square).item()\n",
+    "shape_sim_mat[0,2] = shape_sim_mat[2,0] = (circle | triangle).item()\n",
+    "shape_sim_mat[0,3] = shape_sim_mat[3,0] = (circle | shape).item()\n",
     "\n",
-    "sim_mat[1,2] = sim_mat[2,1] = (square | triangle).item()\n",
-    "sim_mat[1,3] = sim_mat[3,1] = (square | shape).item()\n",
+    "shape_sim_mat[1,2] = shape_sim_mat[2,1] = (square | triangle).item()\n",
+    "shape_sim_mat[1,3] = shape_sim_mat[3,1] = (square | shape).item()\n",
     "\n",
-    "sim_mat[2,3] = sim_mat[3,2] = (... | ...).item()"
+    "shape_sim_mat[2,3] = shape_sim_mat[3,2] = (... | ...).item()"
    ]
   },
   {
@@ -804,7 +898,7 @@
     "execution": {}
    },
    "source": [
-    "[*Click for solution*](https://github.com/neuromatch/NeuroAI_Course/tree/main/tutorials/W2D2_NeuroSymbolicMethods/solutions/W2D2_Tutorial1_Solution_8d8fa911.py)\n",
+    "[*Click for solution*](https://github.com/neuromatch/NeuroAI_Course/tree/main/tutorials/W2D2_NeuroSymbolicMethods/solutions/W2D2_Tutorial1_Solution_708701bb.py)\n",
     "\n"
    ]
   },
@@ -816,7 +910,7 @@
    },
    "outputs": [],
    "source": [
-    "plot_similarity_matrix(sim_mat, symbol_names + [\"shape\"], values = True)"
+    "plot_similarity_matrix(shape_sim_mat, symbol_names + [\"shape\"], values = True)"
    ]
   },
   {
@@ -998,10 +1092,10 @@
    "source": [
     "set_seed(42)\n",
     "\n",
-    "symbol_names = ['circle','square','triangle', 'red', 'blue', 'green']\n",
-    "discrete_space = sspspace.DiscreteSPSpace(symbol_names, ssp_dim=vector_length, optimize=False)\n",
+    "new_symbol_names = ['circle','square','triangle', 'red', 'blue', 'green']\n",
+    "new_discrete_space = sspspace.DiscreteSPSpace(new_symbol_names, ssp_dim=vector_length, optimize=False)\n",
     "\n",
-    "objs = {n:discrete_space.encode(np.array([n])) for n in symbol_names}"
+    "objs = {n:new_discrete_space.encode(np.array([n])) for n in new_symbol_names}"
    ]
   },
   {
@@ -1082,13 +1176,13 @@
    "outputs": [],
    "source": [
     "object_names = list(objs.keys())\n",
-    "sims = np.zeros((len(object_names), len(object_names)))\n",
+    "obj_sims = np.zeros((len(object_names), len(object_names)))\n",
     "\n",
     "for name_idx, name in enumerate(object_names):\n",
     "    for other_idx in range(name_idx, len(object_names)):\n",
-    "        sims[name_idx, other_idx] = sims[other_idx, name_idx] = (objs[name] | objs[object_names[other_idx]]).item()\n",
+    "        obj_sims[name_idx, other_idx] = obj_sims[other_idx, name_idx] = (objs[name] | objs[object_names[other_idx]]).item()\n",
     "\n",
-    "plot_similarity_matrix(sims, object_names)"
+    "plot_similarity_matrix(obj_sims, object_names)"
    ]
   },
   {
@@ -1270,15 +1364,16 @@
    },
    "outputs": [],
    "source": [
-    "object_names = ['red','red^','red*circle','circle','circle^']\n",
+    "new_object_names = ['red','red^','red*circle','circle','circle^']\n",
+    "new_objs = objs\n",
     "\n",
     "###################################################################\n",
     "## Fill out the following then remove\n",
     "raise NotImplementedError(\"Student exercise: complete derivation of default objects using pseudoinverse.\")\n",
     "###################################################################\n",
     "\n",
-    "objs['red^'] = objs['red*circle'] * ~objs['circle']\n",
-    "objs['circle^'] = objs[...] * ~objs[...]"
+    "new_objs['red^'] = new_objs['red*circle'] * ~new_objs['circle']\n",
+    "new_objs['circle^'] = new_objs[...] * ~new_objs[...]"
    ]
   },
   {
@@ -1288,7 +1383,7 @@
     "execution": {}
    },
    "source": [
-    "[*Click for solution*](https://github.com/neuromatch/NeuroAI_Course/tree/main/tutorials/W2D2_NeuroSymbolicMethods/solutions/W2D2_Tutorial1_Solution_685af726.py)\n",
+    "[*Click for solution*](https://github.com/neuromatch/NeuroAI_Course/tree/main/tutorials/W2D2_NeuroSymbolicMethods/solutions/W2D2_Tutorial1_Solution_f77f76dd.py)\n",
     "\n"
    ]
   },
@@ -1300,13 +1395,13 @@
    },
    "outputs": [],
    "source": [
-    "sims = np.zeros((len(object_names), len(object_names)))\n",
+    "new_obj_sims = np.zeros((len(new_object_names), len(new_object_names)))\n",
     "\n",
-    "for name_idx, name in enumerate(object_names):\n",
-    "    for other_idx in range(name_idx, len(object_names)):\n",
-    "        sims[name_idx, other_idx] = sims[other_idx, name_idx] = (objs[name] | objs[object_names[other_idx]]).item()\n",
+    "for name_idx, name in enumerate(new_object_names):\n",
+    "    for other_idx in range(name_idx, len(new_object_names)):\n",
+    "        new_obj_sims[name_idx, other_idx] = new_obj_sims[other_idx, name_idx] = (new_objs[name] | new_objs[new_object_names[other_idx]]).item()\n",
     "\n",
-    "plot_similarity_matrix(sims, object_names, values = True)"
+    "plot_similarity_matrix(new_obj_sims, new_object_names, values = True)"
    ]
   },
   {
@@ -2054,13 +2149,13 @@
     "###################################################################\n",
     "\n",
     "set_seed(42)\n",
-    "encoder = sspspace.RandomSSPSpace(domain_dim=1, ssp_dim=1024)\n",
+    "new_encoder = sspspace.RandomSSPSpace(domain_dim=1, ssp_dim=1024)\n",
     "\n",
     "xs = np.linspace(-4,4,401)[:,None] #we expect the encoded values to be two-dimensional in `encoder.encode()` so we add extra dimension\n",
-    "phis = encoder.encode(xs)\n",
+    "phis = new_encoder.encode(xs)\n",
     "\n",
     "#`0` element is right in the middle of phis array! notice that we have 401 samples inside it\n",
-    "sims = phis[..., :] @ phis.T"
+    "real_line_sims = phis[..., :] @ phis.T"
    ]
   },
   {
@@ -2070,7 +2165,7 @@
     "execution": {}
    },
    "source": [
-    "[*Click for solution*](https://github.com/neuromatch/NeuroAI_Course/tree/main/tutorials/W2D2_NeuroSymbolicMethods/solutions/W2D2_Tutorial1_Solution_06eca8eb.py)\n",
+    "[*Click for solution*](https://github.com/neuromatch/NeuroAI_Course/tree/main/tutorials/W2D2_NeuroSymbolicMethods/solutions/W2D2_Tutorial1_Solution_f5f2174f.py)\n",
     "\n"
    ]
   },
@@ -2082,7 +2177,7 @@
    },
    "outputs": [],
    "source": [
-    "plot_real_valued_line_similarity(sims, xs, title = '$\\phi(x)\\cdot\\phi(0)$')"
+    "plot_real_valued_line_similarity(real_line_sims, xs, title = '$\\phi(x)\\cdot\\phi(0)$')"
    ]
   },
   {
@@ -2109,8 +2204,8 @@
     "raise NotImplementedError(\"Student exercise: provide value to shift and observe the usage of the operation.\")\n",
     "###################################################################\n",
     "\n",
-    "phi_shifted = phis[200,:][None,:] * encoder.encode([[...]])\n",
-    "sims = phi_shifted.flatten() @ phis.T"
+    "phi_shifted = phis[200,:][None,:] * new_encoder.encode([[...]])\n",
+    "shifted_real_line_sims = phi_shifted.flatten() @ phis.T"
    ]
   },
   {
@@ -2120,7 +2215,7 @@
     "execution": {}
    },
    "source": [
-    "[*Click for solution*](https://github.com/neuromatch/NeuroAI_Course/tree/main/tutorials/W2D2_NeuroSymbolicMethods/solutions/W2D2_Tutorial1_Solution_d3fe205a.py)\n",
+    "[*Click for solution*](https://github.com/neuromatch/NeuroAI_Course/tree/main/tutorials/W2D2_NeuroSymbolicMethods/solutions/W2D2_Tutorial1_Solution_d25db2a0.py)\n",
     "\n"
    ]
   },
@@ -2132,7 +2227,7 @@
    },
    "outputs": [],
    "source": [
-    "plot_real_valued_line_similarity(sims, xs, title = '$\\phi(x)\\cdot(\\phi(0)\\circledast\\phi(\\pi/2))$')"
+    "plot_real_valued_line_similarity(shifted_real_line_sims, xs, title = '$\\phi(x)\\cdot(\\phi(0)\\circledast\\phi(\\pi/2))$')"
    ]
   },
   {
@@ -2152,8 +2247,8 @@
    },
    "outputs": [],
    "source": [
-    "phi_shifted = phis[200,:][None,:] * encoder.encode([[-1.5*np.pi]])\n",
-    "sims = phi_shifted.flatten() @ phis.T"
+    "new_phi_shifted = phis[200,:][None,:] * new_encoder.encode([[-1.5*np.pi]])\n",
+    "new_shifted_real_line_sims = new_phi_shifted.flatten() @ phis.T"
    ]
   },
   {
@@ -2164,7 +2259,7 @@
    },
    "outputs": [],
    "source": [
-    "plot_real_valued_line_similarity(sims, xs, title = '$\\phi(x)\\cdot(\\phi(0)\\circledast\\phi(-1.5\\pi))$')"
+    "plot_real_valued_line_similarity(new_shifted_real_line_sims, xs, title = '$\\phi(x)\\cdot(\\phi(0)\\circledast\\phi(-1.5\\pi))$')"
    ]
   },
   {