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0:00:01\r\u001b[K |██████████████████████████▊ | 71 kB 4.5 MB/s eta 0:00:01\r\u001b[K |██████████████████████████████▌ | 81 kB 5.1 MB/s eta 0:00:01\r\u001b[K |████████████████████████████████| 85 kB 2.4 MB/s \n","\u001b[?25h"]}]},{"cell_type":"code","metadata":{"id":"ZbRt7EjfcJaF"},"source":["import os\n","import pprint\n","import tempfile\n","import matplotlib.pyplot as plt\n","from typing import Dict, Text\n","\n","import numpy as np\n","import tensorflow as tf\n","import tensorflow_datasets as tfds\n","from typing import Dict, Text\n","import pandas as pd\n","import numpy as np\n","\n","import tensorflow as tf\n","\n","import tensorflow_datasets as tfds\n","import tensorflow_recommenders as tfrs\n","\n","plt.style.use('ggplot')"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"gylBpOf-cNIY"},"source":["## Data Loading and Processing"]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":267,"referenced_widgets":["b3da79a48a094d8c958e7129cc382d84","f36e9d18e2ba4585b99f690165f286a9","b65f4b68cb2d46ef8af1171f56a735cd","bc3ecb0781f64b8781a58f93dff15c7d","5d837e6e699a4a7fad4f2b3821e79bef","c095cd98b9b34f96bd2c28f642817c9e","c56a52e80c6845d6ae040b23fd913430","8b8431b9d12040adbfa9d316c479a135","d30d3a3632ee4d8197a6add33a556116","10a3904ff91845a39d69f178ab545e3a","47b8edd09b614ed7b804ef350b72f965","63f53f8fe7ee4a26809973771a00b943","235a49347bf1437d8c7ea398e7d057a2","8122a3abc48747dca3f2abdb16e3e2d3","46dbf8f5e0da434aa0204e08224bc622","2aeac4580c8a4aae98d0604eec9effce","08e66ba5c5384af3881f0da705cf212a","374f61b8a05f4a3a84574ce3247d4b6e","0b849873407b47ddbc6501851c0b6b57","8b875e2b42854ca096973ae740c35432","af9a2906804f461babea1afd462e3a5e","02fc038820eb4966acf7d04bfe836ccd","fcf7aa1b4f764989978f32653d21a9ca","676e9ba66e4d4775a632306405c734b7","2f81eccc782d44b5ba4cd4ecf0c1df6a","4d90cf9969344ed69447ae3734ae6432","6dc951a1a8ac47c5b5ea1a2403a087c0","d478847f212c46318c4ff89dc3c74252","364457da9e1b4b6abcb99f33a8b98b50","40b8b02b95214b5f8ccee2e7963735d5","61639a72e8db47fcb8caa067e71a7d70","e3ad859339504c9fa04fa1c739c6ab51","8feeb2a22c674c8381850356f6ab49ec","e3b3d295120b43f6819ca0c94180d82d","a8d8e6214206448c9560501f65055b9c","17fab15742594801ba96d8be615de281","1a86e763e52245af9eaa1de718f14b54","02ef19d9603c4a8fad07f7156a109838","fd6d349938e0444699a302c341655f98","f59320ac3e2c451fba6048c87d8b3a8f","7015c48ce05442218d5f5f481cc2e60b","78ff6e33c45e4e959ba6d80af0916cfe","ca6fab2736644982bed7bc12cd62d393","ef44aad5a7a3440592782c0014557b9d","484347b925f043d9b82d7e876770bf93","00815be440a447b7979daf398f89e080","cfee3d538bbb4a5f9979be4d6efdf0c3","31f6b8d0492c49c0bc2e2e62768393e4","d28c889ef4d247598f2e6942198894d2","55d276166b3e49c890e06169cba5dd2f","9d33f08184154e3bb4b654797dd23651","8582137856184efa8f19ff15c772db4c","44b59b99a12149ea9525d069e9065f1e","eaf7abf508374eb6a6dcfd5745994b77","ae5057290dbc4b8695915241fa547b11"]},"id":"DbiQMqTqcRxx","executionInfo":{"status":"ok","timestamp":1636021760410,"user_tz":-330,"elapsed":891970,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"eb73ab77-9fdf-485a-cd16-99380022cad0"},"source":["# Ratings data.\n","ratings = tfds.load(\"movielens/1m-ratings\", split=\"train\", shuffle_files=True)"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["\u001b[1mDownloading and preparing dataset movielens/1m-ratings/0.1.0 (download: 5.64 MiB, generated: 308.42 MiB, total: 314.06 MiB) to /root/tensorflow_datasets/movielens/1m-ratings/0.1.0...\u001b[0m\n"]},{"output_type":"display_data","data":{"application/vnd.jupyter.widget-view+json":{"model_id":"b3da79a48a094d8c958e7129cc382d84","version_minor":0,"version_major":2},"text/plain":["Dl Completed...: 0 url [00:00, ? url/s]"]},"metadata":{}},{"output_type":"display_data","data":{"application/vnd.jupyter.widget-view+json":{"model_id":"63f53f8fe7ee4a26809973771a00b943","version_minor":0,"version_major":2},"text/plain":["Dl Size...: 0 MiB [00:00, ? MiB/s]"]},"metadata":{}},{"output_type":"display_data","data":{"application/vnd.jupyter.widget-view+json":{"model_id":"fcf7aa1b4f764989978f32653d21a9ca","version_minor":0,"version_major":2},"text/plain":["Extraction completed...: 0 file [00:00, ? file/s]"]},"metadata":{}},{"output_type":"stream","name":"stdout","text":["\n","\n","\n"]},{"output_type":"display_data","data":{"application/vnd.jupyter.widget-view+json":{"model_id":"e3b3d295120b43f6819ca0c94180d82d","version_minor":0,"version_major":2},"text/plain":["0 examples [00:00, ? examples/s]"]},"metadata":{}},{"output_type":"stream","name":"stdout","text":["Shuffling and writing examples to /root/tensorflow_datasets/movielens/1m-ratings/0.1.0.incomplete7B5QAC/movielens-train.tfrecord\n"]},{"output_type":"display_data","data":{"application/vnd.jupyter.widget-view+json":{"model_id":"484347b925f043d9b82d7e876770bf93","version_minor":0,"version_major":2},"text/plain":[" 0%| | 0/1000209 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\n","text/plain":["
"]},"metadata":{}}]},{"cell_type":"markdown","metadata":{"id":"X4o-6uVyczF0"},"source":["One of the nice things about DCN is that you can visualize the weights from the cross network and see if it has successfully learned the important feature process. As shown above, the stronger the interaction between two features is. In this case, the feature cross of user ID and movie ID is of great importance.\n","\n"]},{"cell_type":"markdown","metadata":{"id":"ajpGin5eczS4"},"source":["To reduce the training and serving cost, we leverage low-rank techniques to approximate the DCN weight matrices. The rank is passed in through argument projection_dim; a smaller projection_dim results in a lower cost. Note that projection_dim needs to be smaller than (input size)/2 to reduce the cost. In practice, we've observed using low-rank DCN with rank (input size)/4 consistently preserved the accuracy of a full-rank DCN."]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"FX9VgWV7c43D","executionInfo":{"status":"ok","timestamp":1636022703245,"user_tz":-330,"elapsed":154417,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"748031af-c360-4a2f-cf06-04e859ff545d"},"source":["dcn_lr_result = run_models(use_cross_layer=True,\n"," projection_dim=20,\n"," deep_layer_sizes=[192, 192])"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["123/123 [==============================] - 2s 13ms/step - RMSE: 0.8877 - loss: 0.7886 - regularization_loss: 0.0000e+00 - total_loss: 0.7886\n","123/123 [==============================] - 2s 14ms/step - RMSE: 0.8915 - loss: 0.7957 - regularization_loss: 0.0000e+00 - total_loss: 0.7957\n","123/123 [==============================] - 2s 12ms/step - RMSE: 0.8902 - loss: 0.7931 - regularization_loss: 0.0000e+00 - total_loss: 0.7931\n","123/123 [==============================] - 2s 12ms/step - RMSE: 0.8876 - loss: 0.7884 - regularization_loss: 0.0000e+00 - total_loss: 0.7884\n","123/123 [==============================] - 2s 14ms/step - RMSE: 0.8878 - loss: 0.7892 - regularization_loss: 0.0000e+00 - total_loss: 0.7892\n"]}]},{"cell_type":"markdown","metadata":{"id":"ptrXkbVVc7Wz"},"source":["We train a same-sized DNN model as a reference."]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"StIN236bc9HN","executionInfo":{"status":"ok","timestamp":1636022883046,"user_tz":-330,"elapsed":179827,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"5451949e-dbc1-43fc-d151-fa2a0cd6e632"},"source":["dnn_result = run_models(use_cross_layer=False,\n"," deep_layer_sizes=[192, 192, 192])"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["123/123 [==============================] - 2s 16ms/step - RMSE: 0.8995 - loss: 0.8101 - regularization_loss: 0.0000e+00 - total_loss: 0.8101\n","123/123 [==============================] - 2s 16ms/step - RMSE: 0.8827 - loss: 0.7795 - regularization_loss: 0.0000e+00 - total_loss: 0.7795\n","123/123 [==============================] - 2s 16ms/step - RMSE: 0.8815 - loss: 0.7778 - regularization_loss: 0.0000e+00 - total_loss: 0.7778\n","123/123 [==============================] - 2s 15ms/step - RMSE: 0.9043 - loss: 0.8178 - regularization_loss: 0.0000e+00 - total_loss: 0.8178\n","123/123 [==============================] - 2s 16ms/step - RMSE: 0.9062 - loss: 0.8212 - regularization_loss: 0.0000e+00 - total_loss: 0.8212\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"O8kGoIX7c-4r","executionInfo":{"status":"ok","timestamp":1636022883047,"user_tz":-330,"elapsed":37,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"dca3530a-8c16-4cbd-940e-b25d65e953f3"},"source":["print(\"DCN RMSE mean: {:.4f}, stdv: {:.4f}\".format(dcn_result[\"mean\"], dcn_result[\"stdv\"]))\n","print(\"DCN (low-rank) RMSE mean: {:.4f}, stdv: {:.4f}\".format(dcn_lr_result[\"mean\"], dcn_lr_result[\"stdv\"]))\n","print(\"DNN RMSE mean: {:.4f}, stdv: {:.4f}\".format(dnn_result[\"mean\"], dnn_result[\"stdv\"]))"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["DCN RMSE mean: 0.8865, stdv: 0.0020\n","DCN (low-rank) RMSE mean: 0.8890, stdv: 0.0016\n","DNN RMSE mean: 0.8948, stdv: 0.0106\n"]}]}]}