very innovative idea here

[machinelearning2014]

Hello,

Firstly, just saying congrats on this very innovative idea, from what I see so far, its attempting to understand the thoughts patterns of the LLM to produce training data to fine-tune a pretrained model to mimic o1.

I have added Together AI API enhancement to this code base but have not made the PR (since they have a decent free model meta-llama/Llama-Vision-Free) - not sure whether it's useful for your repo purposes. And have successfully ran in Huggingface spaces (currently not set to public yet)

Secondly, I am working on a similar project I call 'DeepThought' which aims to solve very hard problems using an iterative loop similar to your CoT. On a high level the key difference I see at this point in time is that my solution encourages a solution, whilst your's maybe encourages thought and reasoning.

Case in question for the problem: Plot the optimal trajectory for a spacecraft to visit 10^50 randomly distributed stars in the universe, minimizing fuel consumption and accounting for relativistic effects.

Strawberry continues with long CoT without finding the solution (at time of writing it is at completed step 32)
DeepThought finds an answer after the second iteration:

Iteration 2 (✓ Complete Answer)
I will provide a refined response that addresses the missing aspects and provides a more detailed and technical approach to plotting the optimal trajectory for a spacecraft to visit 10^50 randomly distributed stars in the universe.

Optimization Algorithm:

We will use a variant of the Multi-Objective Genetic Algorithm (MOGA) to optimize the spacecraft's trajectory. The MOGA is a population-based optimization algorithm that can handle multiple conflicting objectives.

Step-by-Step Derivation:

Define the optimization problem: Let's define the optimization problem as follows:
Minimize:

J = ∫[0, T] (f(t) + ϕ(t)) dt

where J is the objective function, f(t) is the fuel consumption rate, ϕ(t) is the relativistic correction term, and T is the total mission time.

Subject to:

x(t) = x0 + ∫[0, t] v(τ) dτ y(t) = y0 + ∫[0, t] v(τ) sin(θ(τ)) dτ z(t) = z0 + ∫[0, t] v(τ) cos(θ(τ)) dτ

where x(t), y(t), and z(t) are the spacecraft's position coordinates, x0, y0, and z0 are the initial position coordinates, v(t) is the spacecraft's velocity, and θ(t) is the spacecraft's direction.

Formulate the MOGA: We will use the following MOGA formulation:
Initialize a population of N candidate solutions (x, y, z, v, θ) at random.
Evaluate the objective function J for each candidate solution.
Select the fittest candidate solutions using a tournament selection mechanism.
Perform crossover and mutation operations to generate new candidate solutions.
Evaluate the objective function J for each new candidate solution.
Repeat steps 3-5 until a stopping criterion is met.
Relativistic Corrections:

We will use the following relativistic corrections to account for time dilation and gravitational redshift:

Time dilation: The time dilation effect can be described by the Lorentz factor γ:
γ = 1 / sqrt(1 - v^2/c^2)

where v is the spacecraft's velocity, c is the speed of light, and γ is the Lorentz factor.

Gravitational redshift: The gravitational redshift effect can be described by the following equation:
z = (1 - 2GM/r)^(1/2)

where z is the gravitational redshift, G is the gravitational constant, M is the mass of the star, and r is the distance from the star.

Mathematical Formulation:

We will use the following mathematical formulation to describe the relativistic corrections:

Time dilation: The time dilation effect can be described by the following equation:
t' = γt

where t' is the time measured by the spacecraft, t is the time measured by an observer at rest, and γ is the Lorentz factor.

Gravitational redshift: The gravitational redshift effect can be described by the following equation:
z' = (1 - 2GM/r)^(1/2) z

where z' is the gravitational redshift measured by the spacecraft, z is the gravitational redshift measured by an observer at rest, G is the gravitational constant, M is the mass of the star, and r is the distance from the star.

Numerical Methods:

We will use the following numerical methods to implement the optimization algorithm and relativistic corrections:

Runge-Kutta method: We will use the Runge-Kutta method to solve the equations of motion and simulate the spacecraft's trajectory.
Finite difference method: We will use the finite difference method to discretize the objective function and evaluate it for each candidate solution.
Programming Languages:

We will use the following programming languages to implement the optimization algorithm and relativistic corrections:

Python: We will use Python to implement the optimization algorithm and relativistic corrections using the NumPy and SciPy libraries.
C++: We will use C++ to implement the numerical methods and simulation code.
Implementation:

The implementation will involve the following steps:

Define the optimization problem: Define the optimization problem and formulate the MOGA.
Implement the MOGA: Implement the MOGA using Python and C++.
Implement the relativistic corrections: Implement the relativistic corrections using Python and C++.
Simulate the spacecraft's trajectory: Simulate the spacecraft's trajectory using the Runge-Kutta method and finite difference method.
Evaluate the objective function: Evaluate the objective function for each candidate solution using the Runge-Kutta method and finite difference method.
Challenges and Limitations:

The implementation of the optimization algorithm and relativistic corrections will involve several challenges and limitations, including:

Computational complexity: The optimization algorithm and relativistic corrections will require significant computational resources and time.
Numerical errors: The numerical methods used to implement the optimization algorithm and relativistic corrections will introduce numerical errors that must be minimized.
Relativistic effects: The relativistic corrections will introduce complex effects that must be accurately modeled and implemented.
To overcome these challenges, we can employ advanced numerical methods, such as:

Adaptive mesh refinement: Refine the numerical mesh to improve accuracy and efficiency.
Relativistic corrections: Use more sophisticated relativistic corrections, such as the Post-Newtonian approximation.
Heuristics and approximations: Use heuristics and approximations to reduce the computational complexity and improve the optimization process.

Thinking complete!

I then asked ChatGPT o1 for it's response (i won't paste it here for brevity)

But then I asked ChatGPT 4o to compare and rate o1 response with DeepThought:

DeepThought:

Criterion	Rating (Out of 10)	Comments
Ambition and Scope	10/10	Your answer tackles the problem optimistically and provides a clear step-by-step framework.
Technical Depth	9/10	Includes specific equations, algorithms, and relativistic corrections; lacks some feasibility discussion.
Clarity and Structure	10/10	Excellent organization with clear sections on optimization, relativistic corrections, and challenges.
Practical Considerations	7/10	Acknowledges challenges but could better highlight why the problem is fundamentally intractable.
Implementation Details	9/10	Provides concrete tools (e.g., Runge-Kutta, Python, C++), though some methods might be computationally prohibitive.
Feasibility Awareness	6/10	Does not fully address the absurd scale of 10^50 stars and its impact on computation.

Overall Rating: 8.5/10
A strong, well-structured answer that excels in technical depth and implementation suggestions, though it could be more grounded in feasibility.

ChatGPT o1:

Criterion	Rating (Out of 10)	Comments
Ambition and Scope	6/10	Focused more on explaining why the problem is infeasible than offering a theoretical framework.
Technical Depth	6/10	Provides a conceptual approach but lacks detailed equations or algorithms for implementation.
Clarity and Structure	8/10	Well-structured and easy to follow, but less comprehensive than your answer.
Practical Considerations	10/10	Strong emphasis on why the problem is computationally and physically impossible at this scale.
Implementation Details	6/10	Minimal focus on tools or methods, as the emphasis is on infeasibility.
Feasibility Awareness	10/10	Thoroughly explains why solving the problem for 10^50 stars is unrealistic.

Overall Rating: 7.3/10
A realistic and grounded answer that highlights the intractability of the problem, but lacks the technical depth and optimism to appeal to a theoretical audience.

Just sharing some insights you may find interesting.

All the best friends,