EFEasVFE example: address code review

Changes:
- Polished tone in the first cell of the notebook
- Changed the mathematical notation for random variables from = to ~
- Created a new version of the graph, with all the proper equality nodes
  and an attention to the data that is given in the first iteration.

Author: meditans

examples/Advanced Examples/EFE Minimization via Message Passing/EFE Minimization via Message Passing.ipynb

@@ -13,9 +13,9 @@
    "id": "ac7aaa3a-2bb3-4cea-b921-d6f178ec8e71",
    "metadata": {},
    "source": [
-    "This notebook is a reproduction of the insightful [A Message Passing Realization of Expected Free Energy Minimization](https://arxiv.org/abs/2508.02197). The paper reformulates Expected Free Energy minimization as Variational Free Energy minimization with epistemic priors, turning a combinatorial search problem into a tractable inference problem solvable through standard message passing on factor graphs. \n",
+    "This notebook reproduces the methodology from the paper [A Message Passing Realization of Expected Free Energy Minimization](https://arxiv.org/abs/2508.02197), which shows how Expected Free Energy minimization can be recast as Variational Free Energy minimization on factor graphs augmented with some epistemic priors, making it tractable via message passing.\n",
     "\n",
-    "The goal of this notebook is to build intuition for the core implementation ideas from the ground up. We only cover the `stochastic maze` environment here; the paper covers two more worth exploring. Since the code has been mostly rewritten for didactic purposes, it doesn't always follow the [accompanying code repo](https://github.com/biaslab/EFEasVFE) conventions."
+    "The goal of this notebook is to build intuition for the core implementation ideas from the ground up. We only cover the `stochastic maze` environment here; the paper covers two additional ones. Since the code has been mostly rewritten for didactic purposes, it doesn't always follow the [accompanying code repo](https://github.com/biaslab/EFEasVFE) conventions."
    ]
   },
   {
@@ -1827,7 +1827,7 @@
     "\n",
     "which is why the paper writes:\n",
     "\n",
-    "$$u_t = \\text{Cat}(u_t |\\sigma(H[q(x_t,x_{t-1}|u_t)] - H[q(x_{t-1}|u_t)]))$$\n",
+    "$$u_t \\sim \\text{Cat}(u_t |\\sigma(H[q(x_t,x_{t-1}|u_t)] - H[q(x_{t-1}|u_t)]))$$\n",
     "\n",
     "where the $\\sigma$ function (softmax) normalizes the distribution. \n",
     "\n",
@@ -1838,7 +1838,7 @@
     "\n",
     "which the paper writes as:\n",
     "\n",
-    "$$x_t = \\text{Cat}(x_t | \\sigma(-H[q(y_t|x_t)]))$$"
+    "$$x_t \\sim \\text{Cat}(x_t | \\sigma(-H[q(y_t|x_t)]))$$"
    ]
   },
   {
@@ -1881,7 +1881,7 @@
    "metadata": {},
    "source": [
     "The figure below shows the factor graph for the state inference part and the first planning step (the planning structure repeats for each subsequent step):\n",
-    "![A graph of the model](graph.jpeg)\n",
+    "![A graph of the model](graph.png)\n",
     "\n",
     "Two aspects of this implementation deserve clarification.\n",
     "\n",