Numerical precision | Specialized Binary Metrics | References

Start here | Before changing the method | Change the direction method when | Tune the line search when | Wolfe conditions and c2 | Initial step estimates | Backtracking, constant, and bold-driver steps | Momentum and adaptive learning-rate methods | Nesterov Accelerated Gradient ("NAG") | Momentum schedules and update order | Delta-Bar-Delta learning rates | Adaptive restart | See also

Choose stopping controls | Iteration limit | Function-change tolerances | Gradient tolerances | Step tolerance | Evaluation budgets | When several criteria are active | Failure result | Checking tolerances less often | Best and last results | See also

Define the objective and gradient | Choose a starting point and check the gradient | Run the optimization | Read the termination record | Inspect progress | Where to go next

Stress and its gradient | Validate the gradient | Optimize with separate and combined callbacks | Put the configuration on the map | See also

Why retaining state matters | The stateful lifecycle | Optional observations | A minimal terminal-aware loop | Work safely between steps | Deliberate observations and diagnostics | Hard budgets can deny a requested observation | Checkpoint and resume | Reinitialization starts a new run | See also

Brute Force | Random Projection Forests | Graph Search | n_threads | epsilon | init | Neighbor Graph Input | Neighbor Indices Only | Forest initialization | Preparing the Search Graph | Diversification Probability | Degree Pruning | References

Basic UMAP | Parameters | min_dist | n_neighbors | init | dens_scale | Embedding New Data | Supported Distances | Multi-threading support | Python Comparison | Limitations and Other Issues | Nearest Neighbor Calculation | Spectral Initialization | Supporting Libraries

Comparing Low- and High-Dimensional Nearest Neighbors | Detecting Hubness | k-occurrence in the 2D case | k-occurrence in the 1000D case | k-occurrence as a diagnostic of NND failure | Detecting Poorly Predicted Neighbors | Detecting Problems Early | Improving accuracy | Weight candidates by degree | Use More Neighbors | Use More Candidates | Decrease the convergence tolerance | Merging Multiple Independent Results | Using a Search Graph | Conclusions | References

Building a Space-Partitioning Tree | Building a Random Partition Tree | From Trees to Forests | Build a Forest | Finding Nearest Neighbors | A Small Optimization for the k-Nearest Neighbors | Margin | Filtering a Forest | References

Find the k-nearest neighbors | The Neighbor Graph Format | Build an Index | Querying Data | Parallelism | Available Metrics | Supported Data Types | Parameters | References

Local Join | Other Heuristics | PyNNDescent Modifications | Example | Troubleshooting | Querying New Data | References