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"# Customize EncoderMap: Custom loss functions\n",
"\n",
"**Welcome**\n",
"\n",
"Welcome to the second part of the customization section.\n",
"\n",
"Run this notebook on Google Colab:\n",
"\n",
"[](https://colab.research.google.com/github/AG-Peter/encodermap/blob/main/tutorials/notebooks_customization/02_custom_loss_functions.ipynb)\n",
"\n",
"Find the documentation of EncoderMap:\n",
"\n",
"https://ag-peter.github.io/encodermap\n",
"\n",
"**Goals:**\n",
"\n",
"In this tuorial you will learn:\n",
"- [A few general concepts about loss functions.](#what-are-loss-functions)\n",
"- [What loss functions are implemented in EncoderMap.](#cost-functions)\n",
"- [How you can write your own loss functions.](#custom-cost-functions)\n",
"- [Another example for a custom loss function.](#adding-a-unit-circle-loss)\n",
"\n",
"**For Google colab only**\n",
"\n",
"If you're on Google colab, please uncomment these lines and install EncoderMap."
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"# !wget https://gist.githubusercontent.com/kevinsawade/deda578a3c6f26640ae905a3557e4ed1/raw/b7403a37710cb881839186da96d4d117e50abf36/install_encodermap_google_colab.sh\n",
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"## Import Libraries\n",
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"In this tutorial we will learn how to write our own loss functions and add them to EncoderMap. Let us start with the imports:"
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"/home/kevin/git/encoder_map_private/encodermap/__init__.py:194: GPUsAreDisabledWarning: EncoderMap disables the GPU per default because most tensorflow code runs with a higher compatibility when the GPU is disabled. If you want to enable GPUs manually, set the environment variable 'ENCODERMAP_ENABLE_GPU' to 'True' before importing EncoderMap. To do this in python you can run:\n",
"\n",
"import os; os.environ['ENCODERMAP_ENABLE_GPU'] = 'True'\n",
"\n",
"before importing encodermap.\n",
" _warnings.warn(\n"
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"import numpy as np\n",
"import pandas as pd\n",
"import plotly\n",
"import plotly.express as px\n",
"import plotly.graph_objects as go\n",
"import plotly.subplots as ps\n",
"import tensorflow as tf\n",
"\n",
"import encodermap as em\n",
"\n",
"from pathlib import Path\n",
"\n",
"%load_ext autoreload\n",
"%autoreload 2"
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"\n",
"\n",
"## What are loss functions\n",
"\n",
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"def y_hat(x, w):\n",
" return w * x\n",
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"def J(w):\n",
" loss = 0\n",
" for x_sample, y_true in zip(x, y):\n",
" y_pred = y_hat(x_sample, w)\n",
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" return loss\n",
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"test_w = np.linspace(0, 2, 20)\n",
"test_J = [J(w) for w in test_w]\n",
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"Doing so, we can get a good idea, what $w$ might produce the best fit for our data. However, to find the minimum algorithmically, we need to write a gradient descent algorithm. For that we need the derivative $\\frac{d}{dw}$ of our cost function $J(w)$, i.e. the gradient.\n",
"\n",
"\\begin{equation}\n",
"\\frac{d}{dw} J(w) = \\frac{1}{m} \\sum_{i=1}^m \\left( \\hat{y}^{(i)} - y^{(i)} \\right)x^{(i)}\n",
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"source": [
"def gradient_descent(epochs, alpha=0.001, J_conv=0.01):\n",
" w_test = np.random.random((1, ))[0] * 2\n",
" losses = []\n",
" for i in range(epochs):\n",
" loss_derivative = 0\n",
" for x_sample, y_sample in zip(x, y):\n",
" loss_derivative += (y_hat(x_sample, w_test) - y_sample) * x_sample\n",
" loss_derivative /= len(x)\n",
" w_test -= alpha * loss_derivative\n",
" loss = J(w_test)\n",
" losses.append((i, \"w\", w_test))\n",
" losses.append((i, \"J\", loss))\n",
" return pd.DataFrame(np.array(losses), columns=[\"epoch\", \"type\", \"value\"]).astype({\"epoch\": int, \"type\": str, \"value\": float})\n",
"\n",
"\n",
"history = gradient_descent(200)\n",
"fig = px.line(history, x=\"epoch\", y=\"value\", color=\"type\")\n",
"fig.update_traces(mode=\"lines\", hovertemplate=\"%{y:.4f}\")\n",
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"\n",
"fig.show()"
]
},
{
"cell_type": "markdown",
"id": "0f56341f-85b2-4cf6-9771-4183a52df563",
"metadata": {},
"source": [
"We can now use this value to plot our regression line."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "22b1e4b8-50b0-433e-9f78-b7c1a00fc0b2",
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"iopub.execute_input": "2025-06-19T23:04:46.536185Z",
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"iopub.status.idle": "2025-06-19T23:04:46.568251Z",
"shell.execute_reply": "2025-06-19T23:04:46.567534Z"
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"w = history[history[\"type\"] == \"w\"][\"value\"].values[-1]\n",
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" go.Scatter(x=x, y=y, mode=\"markers\", name=\"data\"),\n",
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]
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{
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"def get_confidence(y_hat, y, y_fit, ci=0.95):\n",
" # standard deviation of y_hat = y_bar\n",
" sum_errs = sum((y - y_fit) ** 2)\n",
" y_bar = np.sqrt(1 / (len(y_fit) - 2) * sum_errs)\n",
"\n",
" # interval for standard normal distribution\n",
" # ci = 1 - ci\n",
" ppf = 1 - (ci / 2)\n",
" z_score_lookup = (ppf - 0) / 0.5\n",
"\n",
" interval = z_score_lookup * y_bar\n",
"\n",
" lower = y_hat - interval\n",
" upper = y_hat + interval\n",
" return lower, upper\n",
"\n",
"lower = []\n",
"upper = []\n",
"for i in y_fit:\n",
" l, u = get_confidence(i, y, y_fit)\n",
" lower.append(l)\n",
" upper.append(u)"
]
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"y_fit = y_hat(x, w)\n",
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" go.Scatter(x=x, y=y, mode=\"markers\", name=\"data\"),\n",
" go.Scatter(x=x, y=y_fit, mode=\"lines\", name=\"fit\"),\n",
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"\n",
"\n",
"## Cost functions\n",
"\n",
"### Cost functions in TensorFlow\n",
"\n",
"Cost functions in TensorFlow can easily be implemented via simple functions, that take the actual and predicted values of a neural network model, do custom arithmetic and return a scalar value. The cost function of the linear regression in TensorFlow can be written as:"
]
},
{
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"execution_count": 9,
"id": "73122d2d-a488-41b8-95f4-223d9af6682a",
"metadata": {
"execution": {
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},
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"id": "2e66f0aa-dac0-4040-becd-0ec70e60a64f",
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"This function can now without any alterations be used as the cost function for our model. To predict the slope of our data we have can use a TensorFlow model with a single neuron. That neuron's weight will be adjusted by the optimizer until the loss function is minimal. This should give us a similar result than what our custom gradient descent implementation has produced."
]
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"text": [
"\r",
"1/7 [===>..........................] - ETA: 0s - loss: 38.3508"
]
},
{
"name": "stdout",
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"text": [
"\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r",
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"model = tf.keras.models.Sequential([\n",
" tf.keras.layers.Dense(units=1, activation=\"linear\", input_shape=(1, ))\n",
"])\n",
"\n",
"model.compile(loss=J_tf)\n",
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]
},
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"source": [
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]
},
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""
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"source": [
"y_fit = model.predict(x)[:, 0]\n",
"fig = go.Figure(\n",
" data=[\n",
" go.Scatter(x=x, y=y, mode=\"markers\", name=\"data\"),\n",
" go.Scatter(x=x, y=y_fit, mode=\"lines\", name=\"fit\"),\n",
" ]\n",
")\n",
"fig.update_layout(\n",
" {\n",
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]
},
{
"cell_type": "markdown",
"id": "715b120c-3329-45dc-b599-7ae3fc7d7a6c",
"metadata": {},
"source": [
"### Cost functions in EncoderMap\n",
"\n",
"The model EncoderMap employs is a bit more complicated than the single neuron linear regression model we've just created. The main difference lies in EncoderMap calculating costs from intermediate layers. The multi-dimensional scaling like cost functions for example use the output of the latent (bottleneck) layer and the input of the network to calculate a scalar loss. That's why EncoderMap's cost functions are almost always closures. Meaning they return a function and not a value. This is done, so that the inner functions have access to the TensorFlow model and can access intermediate layers. Let's look at an example closure:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "1df8a9ef-1f66-46f6-b51b-6ab5bab41a7b",
"metadata": {
"execution": {
"iopub.execute_input": "2025-06-19T23:04:47.111080Z",
"iopub.status.busy": "2025-06-19T23:04:47.110909Z",
"iopub.status.idle": "2025-06-19T23:04:47.137463Z",
"shell.execute_reply": "2025-06-19T23:04:47.136994Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Setting up inner function\n",
"Setting up inner function\n"
]
}
],
"source": [
"def outer(argument):\n",
" print(\"Setting up inner function\")\n",
" def inner(different_argument):\n",
" print(\n",
" f\"The inner function has access to the \"\n",
" f\"Outer namespace {argument=} but also \"\n",
" f\"to its own namespace {different_argument=}\"\n",
" )\n",
" return inner\n",
"\n",
"func = outer(\"Hello!\")\n",
"func2 = outer(\"Foo\")"
]
},
{
"cell_type": "markdown",
"id": "815c0ec9-3309-4d19-b811-4e79c2a8f34e",
"metadata": {},
"source": [
"The function returned by the closure can now be called normally."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "a887abc5-3af7-4d9c-8b1c-02c805ba5ab0",
"metadata": {
"execution": {
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"shell.execute_reply": "2025-06-19T23:04:47.164798Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The inner function has access to the Outer namespace argument='Hello!' but also to its own namespace different_argument='World!'\n"
]
}
],
"source": [
"func(\"World!\")"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "f764a2f9-8ed3-4601-9bad-31925674fdb8",
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"execution": {
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},
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{
"name": "stdout",
"output_type": "stream",
"text": [
"The inner function has access to the Outer namespace argument='Foo' but also to its own namespace different_argument='Bar'\n"
]
}
],
"source": [
"func2(\"Bar\")"
]
},
{
"cell_type": "markdown",
"id": "7b4f3528-afaa-4e80-8804-57d017cad24a",
"metadata": {},
"source": [
"#### Autoencoder cost\n",
"\n",
"Let us first take a look at the *auto_cost*. This function can be summarized as follows: \n",
"\n",
"- Take the input of the autoencoder network as $y$\n",
"- Take the output of the autoencoder network as $\\hat{y}$\n",
"- Build the difference $d = y - \\hat{y}$\n",
"- Make this difference positive by using one of these functions:\n",
" - absolute $l = \\lvert d \\rvert$\n",
" - square $l = d^2$\n",
" - norm $l = \\lVert d \\rVert$\n",
"- Take the mean of all samples as the scalar cost value.\n",
"\n",
"This loss function can be implemented like so:\n",
"\n",
"```python\n",
"def auto_loss(model, parameters=None):\n",
" if parameters is None:\n",
" p = Parameters()\n",
" else:\n",
" p = parameters\n",
" def auto_loss_func(y_true, y_pred=None):\n",
" if y_pred is None:\n",
" y_pred = model(y_true)\n",
" if p.auto_cost_scale is not None:\n",
" if p.auto_cost_variant == \"mean_square\":\n",
" auto_cost = tf.reduce_mean(\n",
" tf.square(periodic_distance(y_true, y_pred, p.periodicity))\n",
" )\n",
" elif p.auto_cost_variant == \"mean_abs\":\n",
" auto_cost = tf.reduce_mean(\n",
" tf.abs(periodic_distance(y_true, y_pred, p.periodicity))\n",
" )\n",
" elif p.auto_cost_variant == \"mean_norm\":\n",
" auto_cost = tf.reduce_mean(\n",
" tf.norm(periodic_distance(y_true, y_pred, p.periodicity), axis=1)\n",
" )\n",
" else:\n",
" raise ValueError(\n",
" \"auto_cost_variant {} not available\".format(p.auto_cost_variant)\n",
" )\n",
" if p.auto_cost_scale != 0:\n",
" auto_cost *= p.auto_cost_scale\n",
" else:\n",
" auto_cost = 0.0\n",
" return auto_cost\n",
"\n",
" return auto_loss_func\n",
" \n",
"```\n",
"\n",
"Let's look at this function in a bit more detail. The outer function of the close (`auto_loss()`) takes a TensorFlow model and a instance of `em.Parameters` as its inputs. The `model` argument is used in the inner function (`auto_loss_func()`) to get the `y_pred` value regardless of whether it was provided to the inner function. The `p` variable from the outer function is used in the inner function to define a periodicity (`p.periodicity`) for input data that lie in a periodic space (angles). Furthermore it is used to define a `p.auto_cost_scale` and a `p.auto_cost_variant`. These options can be set by the user in the parameter class and are finally brough to use here. Let's have a look at another cost function in EncoderMap employing the output of intermediate layers.\n",
"\n",
"#### Distance loss\n",
"\n",
"The so-called *distance loss* compares the output of the neurons in the latent space with the network input. Thus, it needs access to these intermediate neurons, which is - again - done via a closue.\n",
"\n",
"```python\n",
"def distance_loss(model, parameters=None):\n",
" if parameters is None:\n",
" p = Parameters()\n",
" else:\n",
" p = parameters\n",
"\n",
" latent = model.encoder\n",
"\n",
" # we will come back to this later\n",
" dist_loss = sigmoid_loss(p)\n",
"\n",
" def distance_loss_func(y_true, y_pred):\n",
" y_pred = latent(y_true)\n",
" \n",
" # functional model gives a tuple\n",
" if isinstance(y_true, tuple):\n",
" y_true = tf.concat(y_true[:3], axis=1)\n",
" if p.distance_cost_scale is not None:\n",
" dist_cost = dist_loss(y_true, y_pred)\n",
" if p.distance_cost_scale != 0:\n",
" dist_cost *= p.distance_cost_scale\n",
" else:\n",
" dist_cost = 0.0\n",
" return dist_cost\n",
" return distance_loss_func\n",
"```\n",
"\n",
"With the information from the autoencoder loss, we can easily understand this loss function. In the outer function, the same handling of the `parameters` argument is done. Inside the inner function this object's `p.distance_cost_scale` attribute is used. Furthermore, the encoder sub-model is extracted from the `model` argument via the line `latent = model.encoder` and the encoder output (here called `y_pred`) is generated from calling this sub-model (`latent(y_true)`) in the inner function. The last line of the outer function (`dist_loss = sigmoid_loss(p)`) uses another closure which you can see below.\n",
"\n",
"```python\n",
"def sigmoid_loss(parameters):\n",
" if parameters is None:\n",
" p = Parameters()\n",
" else:\n",
" p = parameters\n",
" periodicity = p.periodicity\n",
" dist_sig_parameters = p.dist_sig_parameters\n",
" def sigmoid_loss_func(y_true: tf.Tensor, y_pred: tf.Tensor) -> tf.Tensor:\n",
" r_h = y_true\n",
" r_l = y_pred\n",
" if periodicity == float(\"inf\"):\n",
" dist_h = pairwise_dist(r_h)\n",
" else:\n",
" dist_h = pairwise_dist_periodic(r_h, periodicity)\n",
" dist_l = pairwise_dist(r_l)\n",
"\n",
" sig_h = sigmoid(*dist_sig_parameters[:3])(dist_h)\n",
" sig_l = sigmoid(*dist_sig_parameters[3:])(dist_l)\n",
"\n",
" cost = tf.reduce_mean(tf.square(sig_h - sig_l))\n",
" return cost\n",
"\n",
" return sigmoid_loss_func\n",
"```\n",
"\n",
"This function implements the sigmoid scaled multi-dimensional scaling described in the original sketch-map paper [[1]](#cite-sketchmap). The `periodicity` and the user-specified `dist_sig_parameters` are used inside the inner function."
]
},
{
"cell_type": "markdown",
"id": "8d5ade49-a728-4fea-a570-dc394d0179c0",
"metadata": {},
"source": [
"\n",
"\n",
"## Custom cost functions\n",
"\n",
"We can now try to write custom loss functions and also compare how they affect the training of the EncoderMap network. We will compare the EncoderMap network.\n",
"\n",
"### Triplet cost (contrastive learning)\n",
"\n",
"Thanks to Olivier Moindrot for his blog post on https://omoindrot.github.io/triplet-loss\n",
"\n",
"Contrastive learning is a technique in the field of machine learning leveraging neural networks to create high quality low-dimensional embeddings from high-dimensional data. The learning can be self- or semi-supervised. A cost function often implemented in contrastive learning is the *triplet loss*. In contrast to EncoderMap's distance cost, where pairwise distances between high-dimensional input and low-dimensional latent space are compared, the *triplet loss* uses triplets of points in the embedding to arrivwe at a cost scalar.\n",
"\n",
"A key difference between triplet loss and EncoderMap is the presence of labels (sometimes called classes in machine learning lingo). Take images of fruits as high-dimensional inputs. Let's say we have pictures of bananas, oranges, and apples. We want to define a loss function so that similar labels are pushed closely together in the embedding, while the different labels are pushed further apart.\n",
"\n",
"We provide the network with triplets of the inputs. These triplets are selected from the labelled train data so that we provide from the train data.\n",
"\n",
"- An anchor.\n",
"- A positive of the same class as anchor.\n",
"- A negative of a different class.\n",
"\n",
"The loss of a triplet $(a, p, n)$ can be calculated as:\n",
"\n",
"\\begin{equation}\n",
"C_{\\mathrm{triplet}} = \\text{max}\\left( d(a, p) - d(a, n) + m, 0 \\right)\n",
"\\end{equation}\n",
"\n",
"where $m$ is the so-called *margin*. A hyperparameter. While EncoderMap lacks labels that could be used for this definition of a triplet loss, we can use distances between triplets from the input and the latent space for a new loss function."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "97bbe357-3553-4489-9d90-cdaa4508b25d",
"metadata": {
"execution": {
"iopub.execute_input": "2025-06-19T23:04:47.194166Z",
"iopub.status.busy": "2025-06-19T23:04:47.194038Z",
"iopub.status.idle": "2025-06-19T23:04:47.221038Z",
"shell.execute_reply": "2025-06-19T23:04:47.220547Z"
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},
"outputs": [],
"source": [
"from encodermap.misc.distances import pairwise_dist\n",
"\n",
"def triplet_loss(model, parameters, margin=0.2):\n",
" \"\"\"Triplet loss outer function. Takes model and parameters. Parameters is only here for demonstration purpoes.\n",
" It is not actually needed in the closure.\n",
"\n",
" Thanks to Olivier Moindrot.\n",
"\n",
" \"\"\"\n",
" # use the models encoder part to create low-dimensional data\n",
" latent = model.encoder\n",
"\n",
" def triplet_loss_fn(y_true, y_pred=None):\n",
" \"\"\"Triplet loss inner function. Takes y_true and y_pred. y_pred will not be used. y_true will be used to get\n",
" the latent space of the autoencoder.\n",
"\n",
" \"\"\"\n",
" # get latent output\n",
" lowd = latent(y_true)\n",
"\n",
" # Get the pairwise distance matrix\n",
" lowd_pairwise_dist = pairwise_dist(lowd, squared=False)\n",
" highd_pairwise_dist = pairwise_dist(y_true, squared=False)\n",
"\n",
" lowd_anchor_positive_dist = tf.expand_dims(lowd_pairwise_dist, 2)\n",
" lowd_anchor_negative_dist = tf.expand_dims(lowd_pairwise_dist, 1)\n",
" highd_anchor_positive_dist = tf.expand_dims(highd_pairwise_dist, 2)\n",
" highd_anchor_negative_dist = tf.expand_dims(highd_pairwise_dist, 1)\n",
"\n",
" # Compute a 3D tensor of size (batch_size, batch_size, batch_size)\n",
" # triplet_loss[i, j, k] will contain the triplet loss of anchor=i, positive=j, negative=k\n",
" # Uses broadcasting where the 1st argument has shape (batch_size, batch_size, 1)\n",
" # and the 2nd (batch_size, 1, batch_size)\n",
" lowd_triplet_loss = lowd_anchor_positive_dist - lowd_anchor_negative_dist + margin\n",
" highd_triplet_loss = highd_anchor_positive_dist - highd_anchor_negative_dist + margin\n",
"\n",
" # return cost\n",
" return tf.reduce_mean(tf.abs(lowd_triplet_loss - highd_triplet_loss))\n",
"\n",
" # return inner function\n",
" return triplet_loss_fn"
]
},
{
"cell_type": "markdown",
"id": "34d64fed-37fc-4575-9ca7-ab9405273652",
"metadata": {},
"source": [
"As usual, we create an instance of `EncoderMap`. For this instance, we will use the cube example data. This time, we set the `distance_cost_scale` to 0, to not have the sigmoid weighted pairwise distance cost interfere with our triplet cost function."
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "a819902f-04b9-4540-91bc-0f8797ad3ab3",
"metadata": {
"execution": {
"iopub.execute_input": "2025-06-19T23:04:47.222584Z",
"iopub.status.busy": "2025-06-19T23:04:47.222462Z",
"iopub.status.idle": "2025-06-19T23:04:47.328323Z",
"shell.execute_reply": "2025-06-19T23:04:47.327814Z"
}
},
"outputs": [],
"source": [
"high_d_data, ids = em.misc.create_n_cube()\n",
"parameters = em.Parameters(\n",
" tensorboard=False,\n",
" distance_cost_scale=0,\n",
" n_steps=100,\n",
")\n",
"emap_triplet = em.EncoderMap(\n",
" parameters=parameters,\n",
" train_data=high_d_data,\n",
" read_only=True,\n",
")"
]
},
{
"cell_type": "markdown",
"id": "a4441aff-1374-4a67-b7b1-bfe748e4d37d",
"metadata": {},
"source": [
"Add the loss"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "f34ab6a1-7910-46e0-aae6-30842c72614a",
"metadata": {
"execution": {
"iopub.execute_input": "2025-06-19T23:04:47.330236Z",
"iopub.status.busy": "2025-06-19T23:04:47.330047Z",
"iopub.status.idle": "2025-06-19T23:04:47.355956Z",
"shell.execute_reply": "2025-06-19T23:04:47.355500Z"
}
},
"outputs": [],
"source": [
"emap_triplet.add_loss(triplet_loss)"
]
},
{
"cell_type": "markdown",
"id": "a959b8a5-b18d-46b0-b2e2-64d990dc7c8d",
"metadata": {},
"source": [
"#### Train"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "371da93d-7704-43c5-a1af-e3449a9ff92b",
"metadata": {
"execution": {
"iopub.execute_input": "2025-06-19T23:04:47.357479Z",
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"shell.execute_reply": "2025-06-19T23:04:54.674506Z"
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"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
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"\n",
"\n",
"### Adding a unit circle cost\n",
"\n",
"In this example, we will do something silly. We will replace EncoderMap's `center_cost` with a loss that tries to push the low-dimensional points into a unit circle. For a unit circle the following equation holds true:\n",
"\n",
"\\begin{align}\n",
"x^2 + y^2 &= 1\\\\\n",
"x^2 + y^2 - 1 &= 0\n",
"\\end{align}\n",
"\n",
"Let us first plot a unit circle with matplotlib."
]
},
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"id": "5ab8ffd2",
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},
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""
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"source": [
"def distance_to_unit_circle_2D(x, y):\n",
" return np.abs((np.square(x) + np.square(y)) - 1)\n",
"\n",
"xx = np.linspace(-2, 2, 250)\n",
"yy = np.linspace(-2, 2, 250)\n",
"grid = np.meshgrid(xx, yy)\n",
"z = distance_to_unit_circle_2D(*grid)\n",
"\n",
"px.imshow(z, height=500, width=500)"
]
},
{
"cell_type": "markdown",
"id": "7be15a9f-1320-4afc-8a52-171e22af4739",
"metadata": {},
"source": [
"The loss function can be written with a closure like so:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "9424eafd",
"metadata": {
"execution": {
"iopub.execute_input": "2025-06-19T23:04:55.019248Z",
"iopub.status.busy": "2025-06-19T23:04:55.019064Z",
"iopub.status.idle": "2025-06-19T23:04:55.050734Z",
"shell.execute_reply": "2025-06-19T23:04:55.050196Z"
}
},
"outputs": [],
"source": [
"def circle_loss(model, parameters):\n",
" \"\"\"Circle loss outer function. Takes model and parameters. Parameters is only here for demonstration purpoes.\n",
" It is not actually needed in the closure.\n",
"\n",
" \"\"\"\n",
" # use the models encoder part to create low-dimensional data\n",
" latent = model.encoder\n",
"\n",
" def circle_loss_fn(y_true, y_pred=None):\n",
" \"\"\"Circle loss inner function. Takes y_true and y_pred. y_pred will not be used. y_true will be used to get\n",
" the latent space of the autoencoder.\n",
"\n",
" \"\"\"\n",
" # get latent output\n",
" lowd = latent(y_true)\n",
"\n",
" # get circle cost\n",
" circle_cost = tf.reduce_mean(tf.abs(tf.reduce_sum(tf.square(lowd), axis=0) - 1))\n",
"\n",
" # bump up the cost to make it stronger than the other contributions\n",
" circle_cost *= 5\n",
"\n",
" # write to tensorboard\n",
" tf.summary.scalar('Circle Cost', circle_cost)\n",
"\n",
" # return circle cost\n",
" return circle_cost\n",
"\n",
" # return inner function\n",
" return circle_loss_fn"
]
},
{
"cell_type": "markdown",
"id": "35da01e7",
"metadata": {},
"source": [
"#### Include the loss function in EncoderMap\n",
"\n",
"**First:** Let us load the dihedral data from `../notebooks_easy` and define some Parameters. For the parameters we will set the `center_cost_scale` to be 0 as to not interfere with our new circle cost."
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "90dc660e",
"metadata": {
"execution": {
"iopub.execute_input": "2025-06-19T23:04:55.052467Z",
"iopub.status.busy": "2025-06-19T23:04:55.052303Z",
"iopub.status.idle": "2025-06-19T23:04:55.090334Z",
"shell.execute_reply": "2025-06-19T23:04:55.089819Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(10001, 12) (10001,)\n",
"(10001, 13)\n"
]
}
],
"source": [
"df = pd.read_csv('asp7.csv')\n",
"dihedrals = df.iloc[:,:-1].values.astype(np.float32)\n",
"cluster_ids = df.iloc[:,-1].values\n",
"print(dihedrals.shape, cluster_ids.shape)\n",
"print(df.shape)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "9cf5d3cf",
"metadata": {
"execution": {
"iopub.execute_input": "2025-06-19T23:04:55.092115Z",
"iopub.status.busy": "2025-06-19T23:04:55.091962Z",
"iopub.status.idle": "2025-06-19T23:04:55.129490Z",
"shell.execute_reply": "2025-06-19T23:04:55.128911Z"
}
},
"outputs": [],
"source": [
"parameters = em.Parameters(\n",
" tensorboard=True,\n",
" center_cost_scale=0,\n",
" n_steps=400,\n",
" periodicity=2*np.pi,\n",
" main_path=em.misc.run_path('runs/custom_losses')\n",
")"
]
},
{
"cell_type": "markdown",
"id": "481468d2",
"metadata": {},
"source": [
"Now we can instaniate the `EncoderMap` class. For visualization purposes we will also make tensorboard write images."
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "1d2300f8",
"metadata": {
"execution": {
"iopub.execute_input": "2025-06-19T23:04:55.131358Z",
"iopub.status.busy": "2025-06-19T23:04:55.131173Z",
"iopub.status.idle": "2025-06-19T23:04:55.361902Z",
"shell.execute_reply": "2025-06-19T23:04:55.361519Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Output files are saved to runs/custom_losses/run1 as defined in 'main_path' in the parameters.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saved a text-summary of the model and an image in runs/custom_losses/run1, as specified in 'main_path' in the parameters.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Logging images with (10001, 12)-shaped data every 1 epochs to Tensorboard at runs/custom_losses/run1\n"
]
}
],
"source": [
"e_map = em.EncoderMap(parameters, dihedrals)\n",
"e_map.add_images_to_tensorboard(dihedrals, image_step=1, save_to_disk=True)"
]
},
{
"cell_type": "markdown",
"id": "0bc2ac47",
"metadata": {},
"source": [
"We can now tell the `EncoderMap` instance to add our new loss."
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "3722415a",
"metadata": {
"execution": {
"iopub.execute_input": "2025-06-19T23:04:55.363556Z",
"iopub.status.busy": "2025-06-19T23:04:55.363423Z",
"iopub.status.idle": "2025-06-19T23:04:55.389546Z",
"shell.execute_reply": "2025-06-19T23:04:55.389177Z"
}
},
"outputs": [],
"source": [
"e_map.add_loss(circle_loss)"
]
},
{
"cell_type": "markdown",
"id": "ce54855a",
"metadata": {},
"source": [
"Now we add this loss to `EncoderMap`'s losses"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "0d4c51ba",
"metadata": {
"execution": {
"iopub.execute_input": "2025-06-19T23:04:55.391218Z",
"iopub.status.busy": "2025-06-19T23:04:55.391082Z",
"iopub.status.idle": "2025-06-19T23:04:55.416686Z",
"shell.execute_reply": "2025-06-19T23:04:55.416344Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[.auto_loss_func at 0x73144456d5a0>, .regularization_loss_func at 0x73144455ca60>, .center_loss_func at 0x73144455feb0>, .distance_loss_func at 0x73144455c0d0>, .circle_loss_fn at 0x731454069510>]\n"
]
}
],
"source": [
"print(e_map.loss)"
]
},
{
"cell_type": "markdown",
"id": "6138c276",
"metadata": {},
"source": [
"### Train\n",
"\n",
"Also make sure to execute tensorboard in the correct directory:\n",
"\n",
"```bash\n",
"$ tensorboard --logdir . --reload_multifile True\n",
"```\n",
"\n",
"If you're on Google colab, you can use tensorboard, by activating the tensorboard extension:"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "2ed7bb5a",
"metadata": {
"execution": {
"iopub.execute_input": "2025-06-19T23:04:55.418290Z",
"iopub.status.busy": "2025-06-19T23:04:55.418161Z",
"iopub.status.idle": "2025-06-19T23:04:55.443180Z",
"shell.execute_reply": "2025-06-19T23:04:55.442810Z"
}
},
"outputs": [],
"source": [
"# %load_ext tensorboard\n",
"# %tensorboard --logdir ."
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "de5b4e8f",
"metadata": {
"execution": {
"iopub.execute_input": "2025-06-19T23:04:55.444860Z",
"iopub.status.busy": "2025-06-19T23:04:55.444719Z",
"iopub.status.idle": "2025-06-19T23:06:46.100703Z",
"shell.execute_reply": "2025-06-19T23:06:46.100158Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\r",
" 0%| | 0/400 [00:00"
]
},
{
"cell_type": "markdown",
"id": "74cd1d4c-f4c6-42f5-8b6b-9624f4fbcded",
"metadata": {},
"source": [
"## Loading logs into jupyter notebook\n",
"\n",
"Last but not least, we will have a look at how we could retrieve the images and logs from TensorBoard. This is not trivial, as the `tfevent` files, that TensorFlow writes are so-called protobuf files (for protocol buffers, a data serialization format developed by Google)."
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "d8d8e16f-330d-42e3-946e-fc7afaab7dc8",
"metadata": {
"execution": {
"iopub.execute_input": "2025-06-19T23:06:46.102489Z",
"iopub.status.busy": "2025-06-19T23:06:46.102266Z",
"iopub.status.idle": "2025-06-19T23:06:46.279935Z",
"shell.execute_reply": "2025-06-19T23:06:46.279376Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"events.out.tfevents.1735476821.Marlin.415482.6.v2\r\n",
"events.out.tfevents.1735476821.Marlin.415482.7.v2\r\n"
]
}
],
"source": [
"ls runs/custom_losses/run0/train"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "d0ab333c-1d41-4d8a-88ba-e7275dbb90f0",
"metadata": {
"execution": {
"iopub.execute_input": "2025-06-19T23:06:46.281738Z",
"iopub.status.busy": "2025-06-19T23:06:46.281586Z",
"iopub.status.idle": "2025-06-19T23:06:46.428216Z",
"shell.execute_reply": "2025-06-19T23:06:46.427784Z"
}
},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
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",
"type": "image",
"xaxis": "x",
"yaxis": "y"
},
{
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",
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"xaxis": "x2",
"yaxis": "y2"
},
{
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""
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"source": [
"from tensorflow.python.summary.summary_iterator import summary_iterator\n",
"from io import BytesIO\n",
"from plotly.subplots import make_subplots\n",
"import base64\n",
"from pathlib import Path\n",
"\n",
"records_files = list(\n",
" Path(parameters.main_path).rglob(\"*tfevents*\")\n",
")\n",
"\n",
"prefix = \"data:image/png;base64,\"\n",
"\n",
"visited_tags = {}\n",
"image_steps = [0, 68, 399]\n",
"images_at_steps = {}\n",
"\n",
"for records_file in records_files:\n",
" visited_tags[records_file] = set()\n",
" for i, summary in enumerate(summary_iterator(str(records_file))):\n",
" for j, v in enumerate(summary.summary.value):\n",
" visited_tags[records_file].add(v.tag)\n",
" if v.tag == \"Latent Output/Latent Density\":\n",
" b = tf.make_ndarray(v.tensor)[-1]\n",
" stream = BytesIO(b)\n",
" base64_string = prefix + base64.b64encode(stream.getvalue()).decode(\"utf-8\")\n",
" images_at_steps[summary.step] = base64_string\n",
"\n",
"fig = make_subplots(cols=3, rows=1, subplot_titles=[\"step 0\", \"step 12\", \"step 67\"])\n",
"fig.add_trace(\n",
" go.Image(source=images_at_steps[0]), col=1, row=1,\n",
")\n",
"fig.add_trace(\n",
" go.Image(source=images_at_steps[12]), col=2, row=1,\n",
")\n",
"fig.add_trace(\n",
" go.Image(source=images_at_steps[67]), col=3, row=1,\n",
")"
]
},
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"source": [
"## Conclusion\n",
"\n",
"Using the closure method, you can easily add new loss functions to EncoderMap."
]
},
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"source": [
"## References\n",
"\n",
"\n",
"\n",
"```\n",
"@article{ceriotti2011simplifying,\n",
" title={Simplifying the representation of complex free-energy landscapes using sketch-map},\n",
" author={Ceriotti, Michele and Tribello, Gareth A and Parrinello, Michele},\n",
" journal={Proceedings of the National Academy of Sciences},\n",
" volume={108},\n",
" number={32},\n",
" pages={13023--13028},\n",
" year={2011},\n",
" publisher={National Acad Sciences}\n",
"}\n",
"```\n",
"\n",
"\n",
"\n",
"```\n",
"@article{sawade2023combining,\n",
" title={Combining molecular dynamics simulations and scoring method to computationally model ubiquitylated linker histones in chromatosomes},\n",
" author={Sawade, Kevin and Marx, Andreas and Peter, Christine and Kukharenko, Oleksandra},\n",
" journal={PLoS Computational Biology},\n",
" volume={19},\n",
" number={8},\n",
" pages={e1010531},\n",
" year={2023},\n",
" publisher={Public Library of Science San Francisco, CA USA}\n",
"}\n",
"```\n",
"\n",
"\n",
"```\n",
"@article{franke2023visualizing,\n",
" title={Visualizing the residue interaction landscape of proteins by temporal network embedding},\n",
" author={Franke, Leon and Peter, Christine},\n",
" journal={Journal of Chemical Theory and Computation},\n",
" volume={19},\n",
" number={10},\n",
" pages={2985--2995},\n",
" year={2023},\n",
" publisher={ACS Publications}\n",
"}\n",
"```"
]
}
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