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-346,6 +346,36 @@ However, the CNN Combi Extra Conv model performed the best (marginally). The sur\n \n Now that we've found an architecture that works best, we wanted to see how far we could push it. If we took this same architecture and added additional nodes to the layers, how much better could performance become? In this section, we will explore just how good we can get the model by increasing its size further.\n \n+We increased the number of nodes at all layers of our best-performing model, to create a model with a huge 123,416,729 learnable parameters, to see how far we could push the model. As you can see, it reached a very low loss number compared to our other models while training:\n+\n+![XL Model Training Loss](./images/xl_model_loss.png)\n+\n+Here's how it performed on our test dataset compared to the other models:\n+\n+| Model | % puzzles correct (single guess) | % puzzles correct (iterative guesses) | % numbers correct (iterative guesses) |\n+| ---------------------------- | ------------------------------------ | ----------------------------------------- | ----------------------------------------- |\n+| MLP | 0.0 | 1.3 | 68.7 |\n+| CNN stride 3 | 24.7 | 35.5 | 83.3 |\n+| CNN combi extra conv | 52.2 | 70.6 | 92.6 |\n+| **CNN combi extra conv XL** | **65.6** | **96.1** | **96.2** |\n+\n+It is better again, especially when iteratively guessing the puzzles. This brought it up to an incredible 96.1% of all puzzles completed successfully. We then broke down the results by puzzle difficulty, and even on the very hardest sudoku puzzles (with 64 blanks/just 17 clues), our model was getting almost 60% of them correct:\n+\n+![alt text](./images/large_model_puzzles_correct.png)\n+\n+**TODO:** The model performed terribly on the other datasets and we don't understand why - should we talk about this or is it not very exciting since we have no insight into what's 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-103,42 +107,79 @@ training_data, validation_data = random_split(dataset, [0.8, 0.2], generator=gen\n \n We can then use pytorch's `random_split` function to split the dataset into our training and validation sets, and we'll later use a `DataLoader` to get the batches of data for our model within the training and validation loops.\n \n-## Model Architectures\n-\n-We explored two different model architectures in our quest to solve sudoku with neural networks.\n+## Models\n \n-### Multilayer Perceptron (MLP)\n+We explored two different base model architectures in our quest to solve sudoku with neural networks.\n \n-The most recognisable neural network. The MLP consists of at least three layers: input, hidden, and output. All neurons are connected to all the rest in the layer ahead of them. The weights of the neurons' connections are altered throughout the learning process via backpropagation in order to allow the network to learn based on input data.\n+### Initial Model: Multilayer Perceptron (MLP)\n \n-Our first model consisted of an MLP with three hidden linear layers, interspersed with non-linear activation functions in the form of rectified linear units (ReLUs). This model performed...\n+The MLP is the most recognisable neural network. The MLP consists of at least three layers: input, hidden, and output. All neurons are connected to all the rest in the layer ahead of them. The weights of the neurons' connections are altered throughout the learning process via backpropagation in order to allow the network to learn based on input data.\n \n
\n-
\n+
\n
\n \n-### Convolutional Neural Network (CNN)\n+Our first model consisted of an MLP with three linear layers, including one hidden layer. These layers are interspersed with non-linear activation functions in the form of rectified linear units (ReLUs). You can see this model defined in pytorch as follows:\n \n-A CNN uses convolutions over tensors to facilitate machine learning. The kernel moves over...\n+```python\n+class MLP(nn.Module):\n+ def __init__(self):\n+ super().__init__()\n+ self.flatten = nn.Flatten()\n+ self.unflatten = nn.Unflatten(1, (81, 9))\n+ \n+ self.linear_relu_stack = nn.Sequential(\n+ nn.Linear(729, 100),\n+ nn.ReLU(),\n+ nn.Linear(100, 100),\n+ nn.ReLU(),\n+ nn.Linear(100, 729),\n+ )\n+\n+ def forward(self, x):\n+ x = self.flatten(x)\n+ logits = self.linear_relu_stack(x)\n+ return self.unflatten(logits)\n+```\n \n-Explanation of kernels and incorporating rules.\n+We also created a function that counts the number of parameters in a particular model. This is a good baseline to understand the model's capability for learning. Too few parameters and it may not have enough learning capacity to learn the complexities of what we're training it on. Too many parameters and the model can become difficult to train and is more susceptible to memorisation - learning specific solutions rather than generalising appropriately.\n \n-\n+The `MLP` model we defined above has 156,729 learnable parameters, which we will use as a baseline to compare to future models.\n \n-## Loss Function\n+### Training\n \n-\n-
\n-
\n-
\n+We generally trained our models on the 4m Sudoku puzzles for two epochs, since the learning of most models plateaued by this point. Later, some of our larger models required more epochs as they trained much slower, but where this happened we will mention it.\n+\n+We shuffled the training data at the end of each epoch to ensure that the model was seeing a different ordering of puzzles in the next epoch, and we also tested the model against validation data which it had never seen to ensure the model was not overfitting, or memorising, the training data.\n+\n+You can see here how our first model trained:\n+\n+![MLP model training loss](./images/mlp_model_training.png)\n+\n+### Testing our models\n+\n+While training the model we capture the loss which helps us train the model, but this loss number doesn't really mean much to us humans. We decided that there were two metrics that we'd be interested in also looking at, to compare model performance:\n+\n+1. On average, how many numbers the model accurately guessed vs. the solution\n+2. What percentage of puzzles the model can solve 100% correctly (no incorrect numbers whatsoever)\n+\n+We planned to train our models against our standard loss calculations, and then once trained, verify the performance using these two metrics. We would run the trained model against the validation dataset to ensure it had never seen any of the puzzles before.\n+\n+We also read about an interesting technique to improve model performance in sudoku from a GitHub repository called [Can Convolutional Neural Networks Crack Sudoku Puzzles?](https://github.com/Kyubyong/sudoku), where they only take the single number the model is most sure about, update the input with this number and then feed this updated model back into the model, until the puzzle is completely filled out. We decided to also measure the model performance when used this way as well, which we will refer to as \"iterative guesses\" in the performance tables throughout this blog.\n+\n+So how did our `MLP` model do? Well, after being trained on over 6 million sudoku puzzles, we put it to the test and you can see the results in the table 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-103,42 +107,79 @@ training_data, validation_data = random_split(dataset, [0.8, 0.2], generator=gen\n \n We can then use pytorch's `random_split` function to split the dataset into our training and validation sets, and we'll later use a `DataLoader` to get the batches of data for our model within the training and validation loops.\n \n-## Model Architectures\n-\n-We explored two different model architectures in our quest to solve sudoku with neural networks.\n+## Models\n \n-### Multilayer Perceptron (MLP)\n+We explored two different base model architectures in our quest to solve sudoku with neural networks.\n \n-The most recognisable neural network. The MLP consists of at least three layers: input, hidden, and output. All neurons are connected to all the rest in the layer ahead of them. The weights of the neurons' connections are altered throughout the learning process via backpropagation in order to allow the network to learn based on input data.\n+### Initial Model: Multilayer Perceptron (MLP)\n \n-Our first model consisted of an MLP with three hidden linear layers, interspersed with non-linear activation functions in the form of rectified linear units (ReLUs). This model performed...\n+The MLP is the most recognisable neural network. The MLP consists of at least three layers: input, hidden, and output. All neurons are connected to all the rest in the layer ahead of them. The weights of the neurons' connections are altered throughout the learning process via backpropagation in order to allow the network to learn based on input data.\n \n \n-
\n+
\n
\n \n-### Convolutional Neural Network (CNN)\n+Our first model consisted of an MLP with three linear layers, including one hidden layer. These layers are interspersed with non-linear activation functions in the form of rectified linear units (ReLUs). You can see this model defined in pytorch as follows:\n \n-A CNN uses convolutions over tensors to facilitate machine learning. The kernel moves over...\n+```python\n+class MLP(nn.Module):\n+ def __init__(self):\n+ super().__init__()\n+ self.flatten = nn.Flatten()\n+ self.unflatten = nn.Unflatten(1, (81, 9))\n+ \n+ self.linear_relu_stack = nn.Sequential(\n+ nn.Linear(729, 100),\n+ nn.ReLU(),\n+ nn.Linear(100, 100),\n+ nn.ReLU(),\n+ nn.Linear(100, 729),\n+ )\n+\n+ def forward(self, x):\n+ x = self.flatten(x)\n+ logits = self.linear_relu_stack(x)\n+ return self.unflatten(logits)\n+```\n \n-Explanation of kernels and incorporating rules.\n+We also created a function that counts the number of parameters in a particular model. This is a good baseline to understand the model's capability for learning. Too few parameters and it may not have enough learning capacity to learn the complexities of what we're training it on. Too many parameters and the model can become difficult to train and is more susceptible to memorisation - learning specific solutions rather than generalising appropriately.\n \n-\n+The `MLP` model we defined above has 156,729 learnable parameters, which we will use as a baseline to compare to future models.\n \n-## Loss Function\n+### Training\n \n-\n-
\n-
\n-
\n+We generally trained our models on the 4m Sudoku puzzles for two epochs, since the learning of most models plateaued by this point. Later, some of our larger models required more epochs as they trained much slower, but where this happened we will mention it.\n+\n+We shuffled the training data at the end of each epoch to ensure that the model was seeing a different ordering of puzzles in the next epoch, and we also tested the model against validation data which it had never seen to ensure the model was not overfitting, or memorising, the training data.\n+\n+You can see here how our first model trained:\n+\n+![MLP model training loss](./images/mlp_model_training.png)\n+\n+### Testing our models\n+\n+While training the model we capture the loss which helps us train the model, but this loss number doesn't really mean much to us humans. We decided that there were two metrics that we'd be interested in also looking at, to compare model performance:\n+\n+1. On average, how many numbers the model accurately guessed vs. the solution\n+2. What percentage of puzzles the model can solve 100% correctly (no incorrect numbers whatsoever)\n+\n+We planned to train our models against our standard loss calculations, and then once trained, verify the performance using these two metrics. We would run the trained model against the validation dataset to ensure it had never seen any of the puzzles before.\n+\n+We also read about an interesting technique to improve model performance in sudoku from a GitHub repository called [Can Convolutional Neural Networks Crack Sudoku Puzzles?](https://github.com/Kyubyong/sudoku), where they only take the single number the model is most sure about, update the input with this number and then feed this updated model back into the model, until the puzzle is completely filled out. We decided to also measure the model performance when used this way as well, which we will refer to as \"iterative guesses\" in the performance tables throughout this blog.\n+\n+So how did our `MLP` model do? Well, after being trained on over 6 million sudoku puzzles, we put it to the test and you can see the results in the table 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-249,14 +249,20 @@ How accurate? Compare to different implementations both AI and programmatic ones\n \n We have learnt a great deal throughout this journey to solving sudoku puzzles with neural networks. We discovered how different architectures are suited to different tasks, how to apply improvement techniques to poorly performing base models, and how to work with datasets to train models for the task at hand.\n \n-We have also learnt (confirmed?) that neural networks are not the best way to solve sudoku puzzles. There are numerous drawbacks including:\n+We have also learnt (confirmed?) that neural networks are not the best tools to solve sudoku puzzles. There are drawbacks aplenty including:\n \n - Poor accuracy, especially on puzzles with a great number of blanks\n-- Solving different size puzzles requires re-training\n-- Model files take up significant storage\n+- Solving different size puzzles (for example 4x4 or 12x9) requires architecture tweaks and retraining\n+- The model parameters take up more storage than the lines of code of a written solver do (though the models are very small in the realm of neural networks)\n \n On top of all this, algorithmic solvers already exist which have 100% accuracy - and they can often tell when a sudoku has no solution, something which our AI has no concept of. Additionally, these programmatic solvers are able to determine multiple solutions to sudokus which do not have unique solutions - our AI is not able to output multiple solutions to the same puzzle, it is deterministic once trained.\n \n-Despite its many shortcomings, one thing we should not expect of an AI sudoku solver is that it be infallible. It may be thought of not as code but as a small brain, distilled for the sole purpose of solving sudoku puzzles. People make mistakes on sudokus all the time - being tough on this AI, which figures out possible solutions to millions of puzzles in seconds, would be unfair.\n+There are also many positive aspects of solving sudoku puzzles with neural networks such as:\n+\n+- No need to write code which solves by constraints or deduction, we built and trained an initial model within half an hour\n+- Puzzles need not be logically soluble, the AI solver may find solutions to sudokus which deductive programmatic solvers could never work out","path":"blog/sudoko_blog_structure.md","commit_id":"f1d9cd515cad7784695987e8dc266521bcd80509","original_commit_id":"f1d9cd515cad7784695987e8dc266521bcd80509","user":{"login":"JonnySpruce","id":30812276,"node_id":"MDQ6VXNlcjMwODEyMjc2","avatar_url":"https://avatars.githubusercontent.com/u/30812276?v=4","gravatar_id":"","url":"https://api.github.com/users/JonnySpruce","html_url":"https://github.com/JonnySpruce","followers_url":"https://api.github.com/users/JonnySpruce/followers","following_url":"https://api.github.com/users/JonnySpruce/following{/other_user}","gists_url":"https://api.github.com/users/JonnySpruce/gists{/gist_id}","starred_url":"https://api.github.com/users/JonnySpruce/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/JonnySpruce/subscriptions","organizations_url":"https://api.github.com/users/JonnySpruce/orgs","repos_url":"https://api.github.com/users/JonnySpruce/repos","events_url":"https://api.github.com/users/JonnySpruce/events{/privacy}","received_events_url":"https://api.github.com/users/JonnySpruce/received_events","type":"User","site_admin":false},"body":"Not sure the dissolving properties of the puzzle has much of an impact on the performance of the programmatic solvers ;)\r\n\r\n```suggestion\r\n- Puzzles need not be logically solvable, the AI solver may find solutions to sudokus which deductive programmatic solvers could never work out\r\n```","created_at":"2024-02-14T10:28:41Z","updated_at":"2024-02-14T10:29:30Z","html_url":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10#discussion_r1489246246","pull_request_url":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/10","author_association":"OWNER","_links":{"self":{"href":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/comments/1489246246"},"html":{"href":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10#discussion_r1489246246"},"pull_request":{"href":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/10"}},"reactions":{"url":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/comments/1489246246/reactions","total_count":0,"+1":0,"-1":0,"laugh":0,"hooray":0,"confused":0,"heart":0,"rocket":0,"eyes":0},"start_line":null,"original_start_line":null,"start_side":null,"line":263,"original_line":263,"side":"RIGHT","original_position":19,"position":19,"subject_type":"line"},"pull_request":{"url":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/10","id":1723791517,"node_id":"PR_kwDOLLACAc5mvvid","html_url":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10","diff_url":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10.diff","patch_url":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10.patch","issue_url":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/issues/10","number":10,"state":"open","locked":false,"title":"Conclusion First 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Compare to different implementations both AI and programmatic ones\n \n ## Conclusion\n \n-Is using neural networks to solve sudoku a good idea? What did we learn from this task?\n+We have learnt a great deal throughout this journey to solving sudoku puzzles with neural networks. We discovered how different architectures are suited to different tasks, how to apply improvement techniques to poorly performing base models, and how to work with datasets to train models for the task at hand.\n+\n+We have also learnt (confirmed?) that neural networks are not the best way to solve sudoku puzzles. There are numerous drawbacks including:\n+\n+- Poor accuracy, especially on puzzles with a great number of blanks\n+- Solving different size puzzles requires re-training","path":"blog/sudoko_blog_structure.md","commit_id":"50aa34d25bf0618a5154a1fe1c3b0e07a2a542bf","original_commit_id":"50aa34d25bf0618a5154a1fe1c3b0e07a2a542bf","user":{"login":"JonnySpruce","id":30812276,"node_id":"MDQ6VXNlcjMwODEyMjc2","avatar_url":"https://avatars.githubusercontent.com/u/30812276?v=4","gravatar_id":"","url":"https://api.github.com/users/JonnySpruce","html_url":"https://github.com/JonnySpruce","followers_url":"https://api.github.com/users/JonnySpruce/followers","following_url":"https://api.github.com/users/JonnySpruce/following{/other_user}","gists_url":"https://api.github.com/users/JonnySpruce/gists{/gist_id}","starred_url":"https://api.github.com/users/JonnySpruce/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/JonnySpruce/subscriptions","organizations_url":"https://api.github.com/users/JonnySpruce/orgs","repos_url":"https://api.github.com/users/JonnySpruce/repos","events_url":"https://api.github.com/users/JonnySpruce/events{/privacy}","received_events_url":"https://api.github.com/users/JonnySpruce/received_events","type":"User","site_admin":false},"body":"Ah yes that's true, the architecture would have to be tweaked too so yes you're right - is that something which code solvers can handle typically? I think we can keep it in if so but just clarify what you mean by size maybe?","created_at":"2024-02-13T14:00:27Z","updated_at":"2024-02-13T14:00:27Z","html_url":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10#discussion_r1487911052","pull_request_url":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/10","author_association":"OWNER","_links":{"self":{"href":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/comments/1487911052"},"html":{"href":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10#discussion_r1487911052"},"pull_request":{"href":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/10"}},"reactions":{"url":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/comments/1487911052/reactions","total_count":0,"+1":0,"-1":0,"laugh":0,"hooray":0,"confused":0,"heart":0,"rocket":0,"eyes":0},"start_line":null,"original_start_line":null,"start_side":null,"line":255,"original_line":255,"side":"RIGHT","in_reply_to_id":1487892030,"original_position":10,"position":10,"subject_type":"line"},"pull_request":{"url":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/10","id":1723791517,"node_id":"PR_kwDOLLACAc5mvvid","html_url":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10","diff_url":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10.diff","patch_url":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10.patch","issue_url":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/issues/10","number":10,"state":"open","locked":false,"title":"Conclusion 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-247,4 +247,16 @@ How accurate? Compare to different implementations both AI and programmatic ones\n \n ## Conclusion\n \n-Is using neural networks to solve sudoku a good idea? What did we learn from this task?\n+We have learnt a great deal throughout this journey to solving sudoku puzzles with neural networks. We discovered how different architectures are suited to different tasks, how to apply improvement techniques to poorly performing base models, and how to work with datasets to train models for the task at hand.\n+\n+We have also learnt (confirmed?) that neural networks are not the best way to solve sudoku puzzles. There are numerous drawbacks including:\n+\n+- Poor accuracy, especially on puzzles with a great number of blanks\n+- Solving different size puzzles requires re-training\n+- Model files take up significant storage","path":"blog/sudoko_blog_structure.md","commit_id":"50aa34d25bf0618a5154a1fe1c3b0e07a2a542bf","original_commit_id":"50aa34d25bf0618a5154a1fe1c3b0e07a2a542bf","user":{"login":"JonnySpruce","id":30812276,"node_id":"MDQ6VXNlcjMwODEyMjc2","avatar_url":"https://avatars.githubusercontent.com/u/30812276?v=4","gravatar_id":"","url":"https://api.github.com/users/JonnySpruce","html_url":"https://github.com/JonnySpruce","followers_url":"https://api.github.com/users/JonnySpruce/followers","following_url":"https://api.github.com/users/JonnySpruce/following{/other_user}","gists_url":"https://api.github.com/users/JonnySpruce/gists{/gist_id}","starred_url":"https://api.github.com/users/JonnySpruce/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/JonnySpruce/subscriptions","organizations_url":"https://api.github.com/users/JonnySpruce/orgs","repos_url":"https://api.github.com/users/JonnySpruce/repos","events_url":"https://api.github.com/users/JonnySpruce/events{/privacy}","received_events_url":"https://api.github.com/users/JonnySpruce/received_events","type":"User","site_admin":false},"body":"I'd say it's significant compared to lines of code but our biggest models are ~40MB, so not very large really.","created_at":"2024-02-13T13:50:46Z","updated_at":"2024-02-13T13:52:16Z","html_url":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10#discussion_r1487893422","pull_request_url":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/10","author_association":"OWNER","_links":{"self":{"href":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/comments/1487893422"},"html":{"href":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10#discussion_r1487893422"},"pull_request":{"href":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/10"}},"reactions":{"url":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/comments/1487893422/reactions","total_count":0,"+1":0,"-1":0,"laugh":0,"hooray":0,"confused":0,"heart":0,"rocket":0,"eyes":0},"start_line":null,"original_start_line":null,"start_side":null,"line":256,"original_line":256,"side":"RIGHT","original_position":11,"position":11,"subject_type":"line"},"pull_request":{"url":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/10","id":1723791517,"node_id":"PR_kwDOLLACAc5mvvid","html_url":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10","diff_url":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10.diff","patch_url":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10.patch","issue_url":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/issues/10","number":10,"state":"open","locked":false,"title":"Conclusion 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-247,4 +247,16 @@ How accurate? Compare to different implementations both AI and programmatic ones\n \n ## Conclusion\n \n-Is using neural networks to solve sudoku a good idea? What did we learn from this task?\n+We have learnt a great deal throughout this journey to solving sudoku puzzles with neural networks. We discovered how different architectures are suited to different tasks, how to apply improvement techniques to poorly performing base models, and how to work with datasets to train models for the task at hand.\n+\n+We have also learnt (confirmed?) that neural networks are not the best way to solve sudoku puzzles. There are numerous drawbacks including:\n+\n+- Poor accuracy, especially on puzzles with a great number of blanks\n+- Solving different size puzzles requires re-training\n+- Model files take up significant storage\n+","path":"blog/sudoko_blog_structure.md","commit_id":"50aa34d25bf0618a5154a1fe1c3b0e07a2a542bf","original_commit_id":"50aa34d25bf0618a5154a1fe1c3b0e07a2a542bf","user":{"login":"JonnySpruce","id":30812276,"node_id":"MDQ6VXNlcjMwODEyMjc2","avatar_url":"https://avatars.githubusercontent.com/u/30812276?v=4","gravatar_id":"","url":"https://api.github.com/users/JonnySpruce","html_url":"https://github.com/JonnySpruce","followers_url":"https://api.github.com/users/JonnySpruce/followers","following_url":"https://api.github.com/users/JonnySpruce/following{/other_user}","gists_url":"https://api.github.com/users/JonnySpruce/gists{/gist_id}","starred_url":"https://api.github.com/users/JonnySpruce/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/JonnySpruce/subscriptions","organizations_url":"https://api.github.com/users/JonnySpruce/orgs","repos_url":"https://api.github.com/users/JonnySpruce/repos","events_url":"https://api.github.com/users/JonnySpruce/events{/privacy}","received_events_url":"https://api.github.com/users/JonnySpruce/received_events","type":"User","site_admin":false},"body":"Could you add some positives as well? E.g. you don't have to write the code which can solve it, it just figures it out? (in ~30 minutes we had pretty good results for the dataset)","created_at":"2024-02-13T13:51:28Z","updated_at":"2024-02-13T13:52:16Z","html_url":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10#discussion_r1487894498","pull_request_url":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/10","author_association":"OWNER","_links":{"self":{"href":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/comments/1487894498"},"html":{"href":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10#discussion_r1487894498"},"pull_request":{"href":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/10"}},"reactions":{"url":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/comments/1487894498/reactions","total_count":0,"+1":0,"-1":0,"laugh":0,"hooray":0,"confused":0,"heart":0,"rocket":0,"eyes":0},"start_line":null,"original_start_line":null,"start_side":null,"line":257,"original_line":257,"side":"RIGHT","original_position":12,"position":12,"subject_type":"line"},"pull_request":{"url":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/pulls/10","id":1723791517,"node_id":"PR_kwDOLLACAc5mvvid","html_url":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10","diff_url":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10.diff","patch_url":"https://github.com/JonnySpruce/ml-sudoku-solver/pull/10.patch","issue_url":"https://api.github.com/repos/JonnySpruce/ml-sudoku-solver/issues/10","number":10,"state":"open","locked":false,"title":"Conclusion 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