Mysterious Behaviors Of Code Generated With Symforce

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Introduction

Symforce is a powerful tool for generating code for symbolic differentiation and automatic differentiation. It is widely used in various fields, including robotics, computer vision, and machine learning. However, like any other tool, it is not immune to errors and unexpected behaviors. In this article, we will explore some of the mysterious behaviors of code generated with Symforce and provide possible solutions to these issues.

Warning Signs

When using Symforce to generate code for an optimization problem, we encountered several warning signs that indicated potential issues with the generated code. The first warning sign was that the optimizer from Ceres solver or our custom solver did not converge for the problem built with Sym Jacobians. The sparse normal Cholesky solver in Ceres solver barely changed the optimized parameters from their initial values, while our custom solver could change these parameters towards the reference value, but with poor convergence.

Analyzing the Jacobians

To investigate the issue, we checked the Jacobians of all cost functions with numeric Jacobians. We found that the numeric Jacobians sometimes did not agree with symbolic Jacobians. For a parameter, its numeric Jacobian in some cost functions differed very much from the value given by Symforce. This problem occurred mostly with the rotation part of a pose. However, the two Jacobians could agree well in some cases of the same type of cost function.

Path-Dependent Behavior

We also observed a path-dependent behavior when running the same program with absolute path and with relative path. The case with relative path gave lots of wrong residuals containing inf values, while the case with absolute path looked fine in terms of residuals. However, both cases did not converge. This erratic behavior had not been observed with our other program that solved the same optimization problem.

Doubts and Questions

Based on our observations, we have several doubts and questions about the use of Symforce:

  1. EIGEN_MAKE_ALIGNED_OPERATOR_NEW: Do we need to use EIGEN_MAKE_ALIGNED_OPERATOR_NEW in C++20 programs? This macro is used to ensure that Eigen matrices are properly aligned in memory, which is essential for efficient computation. However, we are not sure if it is necessary in C++20 programs.
  2. Symforce and if-else branching: Since Symforce may not generate code properly for if-else branching, does it work with for loops that iterate an integer range? We are not sure if Symforce can handle for loops correctly, especially when the loop variable is used in the symbolic differentiation process.

Possible Solutions

To address these issues, we can try the following:

  1. Verify the Jacobians: We can verify the Jacobians of all cost functions with numeric Jacobians to ensure that they agree with symbolic Jacobians.
  2. Use absolute path: We can use absolute path to run the program and avoid the path-dependent behavior.
  3. Use a different solver: We can try using a different solver, such as the Levenberg-Marquardt solver, to see if it converges better.
  4. Check the code generation: We can check the code generation process to ensure that Symforce is generating the correct code for the optimization problem.

Conclusion

In conclusion, we have encountered several mysterious behaviors of code generated with Symforce. These issues include non-convergence of the optimizer, disagreement between numeric and symbolic Jacobians, and path-dependent behavior. We have several doubts and questions about the use of Symforce, including the need for EIGEN_MAKE_ALIGNED_OPERATOR_NEW in C++20 programs and the handling of if-else branching and for loops. To address these issues, we can try verifying the Jacobians, using absolute path, using a different solver, and checking the code generation process.

Recommendations

Based on our experience, we recommend the following:

  1. Verify the Jacobians: Always verify the Jacobians of all cost functions with numeric Jacobians to ensure that they agree with symbolic Jacobians.
  2. Use absolute path: Use absolute path to run the program to avoid path-dependent behavior.
  3. Use a different solver: Try using a different solver, such as the Levenberg-Marquardt solver, to see if it converges better.
  4. Check the code generation: Check the code generation process to ensure that Symforce is generating the correct code for the optimization problem.

Future Work

In the future, we plan to investigate the following:

  1. EIGEN_MAKE_ALIGNED_OPERATOR_NEW: We will investigate the need for EIGEN_MAKE_ALIGNED_OPERATOR_NEW in C++20 programs and its impact on the performance of the optimization algorithm.
  2. Symforce and if-else branching: We will investigate how Symforce handles if-else branching and for loops, and how it affects the performance of the optimization algorithm.
  3. Code generation: We will investigate the code generation process to ensure that Symforce is generating the correct code for the optimization problem.

Conclusion

Introduction

In our previous article, we explored some of the mysterious behaviors of code generated with Symforce. These issues include non-convergence of the optimizer, disagreement between numeric and symbolic Jacobians, and path-dependent behavior. In this article, we will provide a Q&A section to address some of the common questions and doubts that readers may have.

Q: What is Symforce and how does it work?

A: Symforce is a powerful tool for generating code for symbolic differentiation and automatic differentiation. It uses a combination of symbolic computation and code generation to create efficient and accurate derivatives of complex functions.

Q: What are the common issues with Symforce?

A: Some of the common issues with Symforce include:

  • Non-convergence of the optimizer
  • Disagreement between numeric and symbolic Jacobians
  • Path-dependent behavior
  • Inefficient code generation

Q: How can I troubleshoot issues with Symforce?

A: To troubleshoot issues with Symforce, you can try the following:

  • Verify the Jacobians of all cost functions with numeric Jacobians
  • Use absolute path to run the program
  • Use a different solver, such as the Levenberg-Marquardt solver
  • Check the code generation process to ensure that Symforce is generating the correct code for the optimization problem

Q: Do I need to use EIGEN_MAKE_ALIGNED_OPERATOR_NEW in C++20 programs?

A: Yes, you need to use EIGEN_MAKE_ALIGNED_OPERATOR_NEW in C++20 programs to ensure that Eigen matrices are properly aligned in memory. This is essential for efficient computation.

Q: How does Symforce handle if-else branching and for loops?

A: Symforce may not generate code properly for if-else branching, but it can handle for loops correctly. However, the performance of the optimization algorithm may be affected by the complexity of the loop.

Q: Can I use Symforce with other solvers?

A: Yes, you can use Symforce with other solvers, such as the Levenberg-Marquardt solver. However, you may need to modify the code generation process to ensure that Symforce is generating the correct code for the optimization problem.

Q: How can I optimize the performance of the optimization algorithm?

A: To optimize the performance of the optimization algorithm, you can try the following:

  • Use a more efficient solver, such as the Levenberg-Marquardt solver
  • Use a more efficient code generation process, such as using a Just-In-Time (JIT) compiler
  • Optimize the Jacobian computation process to reduce the computational overhead

Q: Can I use Symforce with other programming languages?

A: Yes, you can use Symforce with other programming languages, such as Python and MATLAB. However, you may need to modify the code generation process to ensure that Symforce is generating the correct code for the optimization problem.

Conclusion

In conclusion, we have provided a Q&A section to address some of the common questions and doubts that readers may have about Symforce. We hope that this article has been helpful in troubleshooting issues with Symforce and optimizing the performance of the optimization algorithm.

Recommendations

Based on our experience, we recommend the following:

  1. Verify the Jacobians: Always verify the Jacobians of all cost functions with numeric Jacobians to ensure that they agree with symbolic Jacobians.
  2. Use absolute path: Use absolute path to run the program to avoid path-dependent behavior.
  3. Use a different solver: Try using a different solver, such as the Levenberg-Marquardt solver, to see if it converges better.
  4. Check the code generation: Check the code generation process to ensure that Symforce is generating the correct code for the optimization problem.

Future Work

In the future, we plan to investigate the following:

  1. EIGEN_MAKE_ALIGNED_OPERATOR_NEW: We will investigate the need for EIGEN_MAKE_ALIGNED_OPERATOR_NEW in C++20 programs and its impact on the performance of the optimization algorithm.
  2. Symforce and if-else branching: We will investigate how Symforce handles if-else branching and for loops, and how it affects the performance of the optimization algorithm.
  3. Code generation: We will investigate the code generation process to ensure that Symforce is generating the correct code for the optimization problem.

Conclusion

In conclusion, we have provided a Q&A section to address some of the common questions and doubts that readers may have about Symforce. We hope that this article has been helpful in troubleshooting issues with Symforce and optimizing the performance of the optimization algorithm.