Fix typos/wording

notebooks/generative-vs-discriminative-circuit.ipynb

@@ -190,8 +190,8 @@
     "Can we do better?\n",
     "\n",
     "\n",
-    "### Parameter Sharing\n",
-    "Yes! We can use **parameter sharing**, i.e., we can share the early layers of our circuit and only adapt the output layer to produce our conditional distributions.\n",
+    "### Shared Representations\n",
+    "Yes! We can share the early layers of our circuit and only adapt the output layer to produce our conditional distributions.\n",
     "Since there are $10$ classes, we change the last layer of our circuit to output $10$ log-probabilities: the probability mass over images conditioned on each class, $p(\\mathbf{x} \\mid y)$.\n",
     "We can do so by specifying the `num_classes` option in `data_modalities.image_data`.\n",
     "\n",
@@ -347,7 +347,7 @@
     "\n",
     "</div>\n",
     "\n",
-    "The RAT SPN papepr also considers training using a trade-off between the two objectives.\n",
+    "The RAT SPN paper also considers training using a trade-off between the two objectives.\n",
     "To do so, it introduces a parameter $\\lambda \\in [0, 1]$ and minimize a combined loss:\n",
     "\n",
     "$$\n",
@@ -357,7 +357,7 @@
     "where we divide $\\mathcal{L}_{gen}(\\theta)$ by the number of pixels in the image, $|X|$, such that the losses are on a comparable scale[<sup>2</sup>](#fn2).\n",
     "\n",
     "* $\\lambda = 0  \\rightarrow$ Model trained only generatively\n",
-    "* $\\lambda = 1  \\rightarrow$ Model trained only contrastively\n",
+    "* $\\lambda = 1  \\rightarrow$ Model trained only discriminatively\n",
     "* $\\lambda \\in (0, 1) \\rightarrow$ Trade-off between losses\n",
     "\n",
     "<span style=\"font-size: .75em;\"> [<sup id=\"fn2\">2</sup>](#fn2-back) Note that $\\mathcal{L}_{gen}$ and $\\mathcal{L}_{dis}$ are on different scales, primarily because they are defined on a different number of random variables.\n",
@@ -1222,7 +1222,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.7"
+   "version": "3.10.12"
   }
  },
  "nbformat": 4,