messages listlengths 2 2 | topic stringclasses 4
values | difficulty stringclasses 3
values |
|---|---|---|
[
{
"role": "user",
"content": "Create an educational manim animation explaining SVD. Show the original matrix, the factorization, and the progressive reconstruction by adding rank-1 terms. Include a bar chart of singular values."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_... | linear_algebra | hard |
[
{
"role": "user",
"content": "Create a manim animation of a 3-state Markov chain showing state transitions and the probability distribution evolving toward the stationary distribution over 8 iterations."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: PLAN:\n1. Setu... | probability_stats | easy |
[
{
"role": "user",
"content": "Create an educational manim animation explaining how neural networks learn. Show forward pass (blue flow), loss computation, and backward pass (red gradient flow) on a 3-4-2 fully connected network."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem... | ml_ai | medium |
[
{
"role": "user",
"content": "Create a manim animation showing Bayesian updating with a Beta(1,1) prior and 5 Bernoulli observations. Animate the posterior shifting after each observation."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: The user wants a manim anima... | probability_stats | medium |
[
{
"role": "user",
"content": "Write a manim Scene called SVDDecomposition that breaks down SVD into a sum of rank-1 matrices. Show each component, accumulate them into a partial reconstruction, and compare with the original."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_ana... | linear_algebra | medium |
[
{
"role": "user",
"content": "Create a manim animation showing Riemann sums converging to the true integral of f(x) = x^2 on [0, 2]. Start with dx=1, then refine through 0.5, 0.25, and 0.1, showing the error decreasing at each step."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [pro... | calculus | medium |
[
{
"role": "user",
"content": "Create an educational manim animation explaining Fourier series. Show how a sum of sine waves can approximate a square wave, with each added harmonic bringing the approximation closer to the target."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem... | calculus | medium |
[
{
"role": "user",
"content": "Create a manim animation showing Fourier series approximation of a square wave. Start with 1 harmonic, then add 2 more at each step (up to 9 harmonics), showing the curve converging to the square wave."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [prob... | calculus | hard |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing Fourier series convergence. Display the target square wave, then progressively add harmonics (1, 3, 5, 7, 9) and show the approximation improving. Mention the Gibbs phenomenon."
},
{
"role": "assistant",
"content": "<reasoning... | calculus | medium |
[
{
"role": "user",
"content": "Write a manim Scene called BayesianUpdate that demonstrates how a Beta prior gets updated by Bernoulli observations. Show the curve evolving and label the final posterior mode."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: What is th... | probability_stats | hard |
[
{
"role": "user",
"content": "Animate K-means clustering in manim. Initialize 30 random points and 3 centroids, then show 5 iterations of the assign-update cycle with centroids moving and points changing color to match their cluster."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [pr... | ml_ai | medium |
[
{
"role": "user",
"content": "Write a manim Scene called SVDDecomposition that breaks down SVD into a sum of rank-1 matrices. Show each component, accumulate them into a partial reconstruction, and compare with the original."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_ana... | linear_algebra | hard |
[
{
"role": "user",
"content": "Create a manim animation visualizing SVD decomposition. Show a matrix M = U S V^T being reconstructed as a sum of rank-1 matrices sigma_i u_i v_i^T, with each component added one at a time."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis... | linear_algebra | hard |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing Markov chain convergence. Show the state graph with labeled transition probabilities, and a bar chart of the state distribution evolving toward steady state."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_... | probability_stats | hard |
[
{
"role": "user",
"content": "Create a manim animation visualizing SVD decomposition. Show a matrix M = U S V^T being reconstructed as a sum of rank-1 matrices sigma_i u_i v_i^T, with each component added one at a time."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis... | linear_algebra | medium |
[
{
"role": "user",
"content": "Create a manim animation visualizing the attention mechanism. Show Q, K, V matrices, compute QK^T / sqrt(d_k), apply softmax row-wise with a heatmap, and multiply by V to get the output."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: ... | ml_ai | medium |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing backpropagation. Show a 3-4-2 network, animate forward activations flowing left to right, display the loss, then animate gradients flowing backward in red."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_an... | ml_ai | medium |
[
{
"role": "user",
"content": "Animate gradient descent on a quadratic loss in manim. I want to see: axes, the curve f(x)=x^2, a red dot moving downhill, yellow tangent lines at each step, orange gradient arrows, and a final convergence label."
},
{
"role": "assistant",
"content": "<reasoning>\nS... | ml_ai | medium |
[
{
"role": "user",
"content": "Create a manim animation showing Riemann sums converging to the true integral of f(x) = x^2 on [0, 2]. Start with dx=1, then refine through 0.5, 0.25, and 0.1, showing the error decreasing at each step."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [pro... | calculus | medium |
[
{
"role": "user",
"content": "Create a manim animation of K-means clustering on 30 random 2D points with 3 clusters. Show centroid initialization, then iterate: assign points, update centroids, move centroids. Run 5 iterations."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_... | ml_ai | hard |
[
{
"role": "user",
"content": "Write a manim Scene class called GradientDescentFull that visualizes 8 steps of gradient descent on x^2 with learning rate 0.15, showing tangent lines, gradient arrows, and tracking each iterate with labels."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1... | ml_ai | hard |
[
{
"role": "user",
"content": "Write a manim Scene called KMeansConvergence that demonstrates K-means clustering. Use 30 points, 3 centroids (marked as X-shapes), and animate 5 iterations with assignment lines and color-coded clusters."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [p... | ml_ai | medium |
[
{
"role": "user",
"content": "Create a manim animation of K-means clustering on 30 random 2D points with 3 clusters. Show centroid initialization, then iterate: assign points, update centroids, move centroids. Run 5 iterations."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_... | ml_ai | medium |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing Markov chain convergence. Show the state graph with labeled transition probabilities, and a bar chart of the state distribution evolving toward steady state."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_... | probability_stats | medium |
[
{
"role": "user",
"content": "Create an educational manim animation explaining transformer attention. Visualize each matrix operation with proper labels and use a color-coded heatmap for the softmax weights."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: The user ... | ml_ai | easy |
[
{
"role": "user",
"content": "Animate Bayesian updating in manim. Use a Beta(1,1) prior and update with observations [H, H, T, H, H]. Show the posterior curve shifting and sharpening with each new data point."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: What is ... | probability_stats | easy |
[
{
"role": "user",
"content": "Animate the attention mechanism in manim. Show each step: QK^T, scaling by 1/sqrt(d_k), softmax row-wise (as a color heatmap), and the final matrix multiplication with V."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: Goal: animate Q,... | ml_ai | easy |
[
{
"role": "user",
"content": "Animate Fourier series approximation in manim. Use the standard square wave Fourier series, and visualize how adding more harmonics improves the approximation."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: The user wants a manim anim... | calculus | easy |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing the limit definition of the integral. Show Riemann sums with progressively smaller dx, alongside a bar chart of the approximation error converging to zero."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_an... | calculus | hard |
[
{
"role": "user",
"content": "Create a manim animation visualizing the attention mechanism. Show Q, K, V matrices, compute QK^T / sqrt(d_k), apply softmax row-wise with a heatmap, and multiply by V to get the output."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: ... | ml_ai | hard |
[
{
"role": "user",
"content": "Animate Bayesian updating in manim. Use a Beta(1,1) prior and update with observations [H, H, T, H, H]. Show the posterior curve shifting and sharpening with each new data point."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: What is ... | probability_stats | easy |
[
{
"role": "user",
"content": "Create an educational manim animation explaining K-means. Show the iterative process: assign points to nearest centroid, recompute centroids, repeat until convergence. Use distinct colors for each cluster."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [... | ml_ai | hard |
[
{
"role": "user",
"content": "Write a manim Scene called RiemannConvergence that demonstrates how Riemann sums approach the definite integral as the partition gets finer. Include a side-by-side error chart."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: The user w... | calculus | medium |
[
{
"role": "user",
"content": "Write a manim Scene called FourierApproximation that demonstrates Fourier series convergence to a square wave. Show 5 stages of approximation (1, 3, 5, 7, 9 harmonics) with smooth transitions."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analy... | calculus | hard |
[
{
"role": "user",
"content": "Create an educational manim animation explaining K-means. Show the iterative process: assign points to nearest centroid, recompute centroids, repeat until convergence. Use distinct colors for each cluster."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [... | ml_ai | easy |
[
{
"role": "user",
"content": "Animate a 3-state Markov chain in manim. Display the directed graph with edges labeled by transition probabilities, and animate the state distribution converging to the stationary distribution."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_anal... | probability_stats | medium |
[
{
"role": "user",
"content": "Create a manim animation showing Riemann sums converging to the true integral of f(x) = x^2 on [0, 2]. Start with dx=1, then refine through 0.5, 0.25, and 0.1, showing the error decreasing at each step."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [pro... | calculus | easy |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing Markov chain convergence. Show the state graph with labeled transition probabilities, and a bar chart of the state distribution evolving toward steady state."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_... | probability_stats | hard |
[
{
"role": "user",
"content": "Create a manim animation of K-means clustering on 30 random 2D points with 3 clusters. Show centroid initialization, then iterate: assign points, update centroids, move centroids. Run 5 iterations."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_... | ml_ai | medium |
[
{
"role": "user",
"content": "Animate a neural network forward and backward pass in manim. Use ShowPassingFlash to show activations flowing through edges. The forward pass should be blue, the backward pass red."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: What i... | ml_ai | hard |
[
{
"role": "user",
"content": "Create a manim animation showing Bayesian updating with a Beta(1,1) prior and 5 Bernoulli observations. Animate the posterior shifting after each observation."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: PLAN:\n1. Setup phase: axes ... | probability_stats | medium |
[
{
"role": "user",
"content": "Write a manim Scene class called GradientDescentFull that visualizes 8 steps of gradient descent on x^2 with learning rate 0.15, showing tangent lines, gradient arrows, and tracking each iterate with labels."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1... | ml_ai | hard |
[
{
"role": "user",
"content": "Write a manim Scene called NeuralNetworkFlow that demonstrates both forward propagation and backpropagation. Show the network topology, animate the signal flow in both directions, and label each layer."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [prob... | ml_ai | easy |
[
{
"role": "user",
"content": "Animate the attention mechanism in manim. Show each step: QK^T, scaling by 1/sqrt(d_k), softmax row-wise (as a color heatmap), and the final matrix multiplication with V."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: Goal: animate Q,... | ml_ai | medium |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing sequential Bayesian inference. Start with a uniform prior, observe 5 coin flips (4 heads, 1 tail), and show the posterior Beta distribution updating after each flip."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [... | probability_stats | easy |
[
{
"role": "user",
"content": "Build a complex manim Scene that demonstrates gradient descent. Include the function plot, an optimization path with 8 iterations, tangent lines showing local slope, and labeled step values."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysi... | ml_ai | medium |
[
{
"role": "user",
"content": "Create a manim animation showing a linear transformation applied to the unit circle. Highlight the eigenvectors and demonstrate how they only stretch (don't rotate) under the transformation. Use matrix [[2,1],[1,3]]."
},
{
"role": "assistant",
"content": "<reasoning... | linear_algebra | hard |
[
{
"role": "user",
"content": "Animate the convergence of Riemann sums to the integral of x^2 from 0 to 2 in manim. Use dx values of 1, 0.5, 0.25, and 0.1, and display the true integral value (8/3) for comparison."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: What... | calculus | medium |
[
{
"role": "user",
"content": "Animate Bayesian updating in manim. Use a Beta(1,1) prior and update with observations [H, H, T, H, H]. Show the posterior curve shifting and sharpening with each new data point."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: What is ... | probability_stats | hard |
[
{
"role": "user",
"content": "Animate a neural network forward and backward pass in manim. Use ShowPassingFlash to show activations flowing through edges. The forward pass should be blue, the backward pass red."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: PLAN:\... | ml_ai | hard |
[
{
"role": "user",
"content": "Build a complex manim Scene demonstrating self-attention. Display Q, K, V matrices, animate the score computation, the softmax heatmap, and the final weighted sum producing the output."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: Wh... | ml_ai | easy |
[
{
"role": "user",
"content": "Write a manim Scene called FourierApproximation that demonstrates Fourier series convergence to a square wave. Show 5 stages of approximation (1, 3, 5, 7, 9 harmonics) with smooth transitions."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analy... | calculus | easy |
[
{
"role": "user",
"content": "Write a manim Scene called MarkovSteadyState that demonstrates Markov chain convergence to stationary distribution. Include a graph and a dynamic bar chart that updates over 8 iterations."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]:... | probability_stats | hard |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing the limit definition of the integral. Show Riemann sums with progressively smaller dx, alongside a bar chart of the approximation error converging to zero."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_an... | calculus | hard |
[
{
"role": "user",
"content": "Create an educational manim animation explaining Markov chains. Show a 3-state system with transition probabilities, and visualize how the state distribution converges to the steady state."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]... | probability_stats | hard |
[
{
"role": "user",
"content": "Animate the attention mechanism in manim. Show each step: QK^T, scaling by 1/sqrt(d_k), softmax row-wise (as a color heatmap), and the final matrix multiplication with V."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: The user wants a... | ml_ai | medium |
[
{
"role": "user",
"content": "Create an educational manim animation explaining gradient descent. Show the loss surface, the optimization trajectory, the local gradient direction at each step, and how the algorithm converges to the minimum."
},
{
"role": "assistant",
"content": "<reasoning>\nStep... | ml_ai | medium |
[
{
"role": "user",
"content": "Create a manim animation showing Riemann sums converging to the true integral of f(x) = x^2 on [0, 2]. Start with dx=1, then refine through 0.5, 0.25, and 0.1, showing the error decreasing at each step."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [pro... | calculus | medium |
[
{
"role": "user",
"content": "Build a complex manim Scene demonstrating self-attention. Display Q, K, V matrices, animate the score computation, the softmax heatmap, and the final weighted sum producing the output."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: Wh... | ml_ai | medium |
[
{
"role": "user",
"content": "Write a manim Scene called AttentionVisualization that breaks down the attention computation into 4 animated steps: score matrix, scaling, softmax heatmap, and output via V multiplication."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]... | ml_ai | medium |
[
{
"role": "user",
"content": "Create a manim animation showing a linear transformation applied to the unit circle. Highlight the eigenvectors and demonstrate how they only stretch (don't rotate) under the transformation. Use matrix [[2,1],[1,3]]."
},
{
"role": "assistant",
"content": "<reasoning... | linear_algebra | hard |
[
{
"role": "user",
"content": "Create a manim animation visualizing SVD decomposition. Show a matrix M = U S V^T being reconstructed as a sum of rank-1 matrices sigma_i u_i v_i^T, with each component added one at a time."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis... | linear_algebra | hard |
[
{
"role": "user",
"content": "Animate K-means clustering in manim. Initialize 30 random points and 3 centroids, then show 5 iterations of the assign-update cycle with centroids moving and points changing color to match their cluster."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [pr... | ml_ai | easy |
[
{
"role": "user",
"content": "Create an educational manim animation explaining Fourier series. Show how a sum of sine waves can approximate a square wave, with each added harmonic bringing the approximation closer to the target."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem... | calculus | medium |
[
{
"role": "user",
"content": "Create an educational manim animation explaining the fundamental theorem of calculus through Riemann sums. Show the rectangles getting finer and the approximation error shrinking to zero."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]:... | calculus | easy |
[
{
"role": "user",
"content": "Write a manim Scene called BayesianUpdate that demonstrates how a Beta prior gets updated by Bernoulli observations. Show the curve evolving and label the final posterior mode."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: Goal: anim... | probability_stats | easy |
[
{
"role": "user",
"content": "Animate SVD in manim. Display a 4x4 matrix as a heatmap, decompose it as U S V^T, and visualize how the sum of rank-1 outer products reconstructs the original matrix."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: What is the user rea... | linear_algebra | medium |
[
{
"role": "user",
"content": "Create an educational manim animation explaining gradient descent. Show the loss surface, the optimization trajectory, the local gradient direction at each step, and how the algorithm converges to the minimum."
},
{
"role": "assistant",
"content": "<reasoning>\nStep... | ml_ai | medium |
[
{
"role": "user",
"content": "Build a complex manim Scene that demonstrates gradient descent. Include the function plot, an optimization path with 8 iterations, tangent lines showing local slope, and labeled step values."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysi... | ml_ai | easy |
[
{
"role": "user",
"content": "Animate a neural network forward and backward pass in manim. Use ShowPassingFlash to show activations flowing through edges. The forward pass should be blue, the backward pass red."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: Goal: ... | ml_ai | easy |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing eigenvalues and eigenvectors. Show the unit circle, apply a 2x2 transformation matrix, and demonstrate that eigenvectors remain on their span after transformation."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [pr... | linear_algebra | hard |
[
{
"role": "user",
"content": "Animate Fourier series approximation in manim. Use the standard square wave Fourier series, and visualize how adding more harmonics improves the approximation."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: The user wants a manim anim... | calculus | easy |
[
{
"role": "user",
"content": "Write a manim Scene called FourierApproximation that demonstrates Fourier series convergence to a square wave. Show 5 stages of approximation (1, 3, 5, 7, 9 harmonics) with smooth transitions."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analy... | calculus | easy |
[
{
"role": "user",
"content": "Animate a neural network forward and backward pass in manim. Use ShowPassingFlash to show activations flowing through edges. The forward pass should be blue, the backward pass red."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: PLAN:\... | ml_ai | hard |
[
{
"role": "user",
"content": "Animate the concept of eigendecomposition in manim. Show a unit circle being transformed into an ellipse by matrix [[2,1],[1,3]], with eigenvectors highlighted as arrows that don't change direction."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem... | linear_algebra | easy |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing Fourier series convergence. Display the target square wave, then progressively add harmonics (1, 3, 5, 7, 9) and show the approximation improving. Mention the Gibbs phenomenon."
},
{
"role": "assistant",
"content": "<reasoning... | calculus | medium |
[
{
"role": "user",
"content": "Create a manim animation of a 3-state Markov chain showing state transitions and the probability distribution evolving toward the stationary distribution over 8 iterations."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: PLAN:\n1. Setu... | probability_stats | medium |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing Markov chain convergence. Show the state graph with labeled transition probabilities, and a bar chart of the state distribution evolving toward steady state."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_... | probability_stats | easy |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing K-means convergence. Show scattered points, 3 centroid markers, and animate the assignment + update steps over 5 iterations with colored cluster assignments."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_... | ml_ai | hard |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing backpropagation. Show a 3-4-2 network, animate forward activations flowing left to right, display the loss, then animate gradients flowing backward in red."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_an... | ml_ai | medium |
[
{
"role": "user",
"content": "Create an educational manim animation explaining Markov chains. Show a 3-state system with transition probabilities, and visualize how the state distribution converges to the steady state."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]... | probability_stats | easy |
[
{
"role": "user",
"content": "Animate K-means clustering in manim. Initialize 30 random points and 3 centroids, then show 5 iterations of the assign-update cycle with centroids moving and points changing color to match their cluster."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [pr... | ml_ai | easy |
[
{
"role": "user",
"content": "Write a manim Scene called RiemannConvergence that demonstrates how Riemann sums approach the definite integral as the partition gets finer. Include a side-by-side error chart."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: Goal: anim... | calculus | hard |
[
{
"role": "user",
"content": "Animate a neural network forward and backward pass in manim. Use ShowPassingFlash to show activations flowing through edges. The forward pass should be blue, the backward pass red."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: Goal: ... | ml_ai | medium |
[
{
"role": "user",
"content": "Write a manim Scene called MarkovSteadyState that demonstrates Markov chain convergence to stationary distribution. Include a graph and a dynamic bar chart that updates over 8 iterations."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]:... | probability_stats | hard |
[
{
"role": "user",
"content": "Write a manim Scene called SVDDecomposition that breaks down SVD into a sum of rank-1 matrices. Show each component, accumulate them into a partial reconstruction, and compare with the original."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_ana... | linear_algebra | hard |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing Markov chain convergence. Show the state graph with labeled transition probabilities, and a bar chart of the state distribution evolving toward steady state."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_... | probability_stats | medium |
[
{
"role": "user",
"content": "Animate the concept of eigendecomposition in manim. Show a unit circle being transformed into an ellipse by matrix [[2,1],[1,3]], with eigenvectors highlighted as arrows that don't change direction."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem... | linear_algebra | medium |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing K-means convergence. Show scattered points, 3 centroid markers, and animate the assignment + update steps over 5 iterations with colored cluster assignments."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_... | ml_ai | easy |
[
{
"role": "user",
"content": "Create a manim animation showing Riemann sums converging to the true integral of f(x) = x^2 on [0, 2]. Start with dx=1, then refine through 0.5, 0.25, and 0.1, showing the error decreasing at each step."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [pro... | calculus | medium |
[
{
"role": "user",
"content": "Write a manim Scene called KMeansConvergence that demonstrates K-means clustering. Use 30 points, 3 centroids (marked as X-shapes), and animate 5 iterations with assignment lines and color-coded clusters."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [p... | ml_ai | hard |
[
{
"role": "user",
"content": "Create a manim animation of a 3-state Markov chain showing state transitions and the probability distribution evolving toward the stationary distribution over 8 iterations."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: What is the us... | probability_stats | medium |
[
{
"role": "user",
"content": "Create an educational manim animation explaining eigenvectors. Show that under a linear transformation, the unit circle becomes an ellipse but eigenvectors only get scaled — they keep their direction."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [probl... | linear_algebra | hard |
[
{
"role": "user",
"content": "Build a complex manim Scene that demonstrates gradient descent. Include the function plot, an optimization path with 8 iterations, tangent lines showing local slope, and labeled step values."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysi... | ml_ai | hard |
[
{
"role": "user",
"content": "Create a manim animation showing Bayesian updating with a Beta(1,1) prior and 5 Bernoulli observations. Animate the posterior shifting after each observation."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: Goal: animate sequential Bay... | probability_stats | easy |
[
{
"role": "user",
"content": "Write a manim Scene called BayesianUpdate that demonstrates how a Beta prior gets updated by Bernoulli observations. Show the curve evolving and label the final posterior mode."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: Goal: anim... | probability_stats | hard |
[
{
"role": "user",
"content": "Animate SVD in manim. Display a 4x4 matrix as a heatmap, decompose it as U S V^T, and visualize how the sum of rank-1 outer products reconstructs the original matrix."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: Goal: animate SVD de... | linear_algebra | hard |
[
{
"role": "user",
"content": "Create an educational manim animation explaining eigenvectors. Show that under a linear transformation, the unit circle becomes an ellipse but eigenvectors only get scaled — they keep their direction."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [probl... | linear_algebra | easy |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing eigenvalues and eigenvectors. Show the unit circle, apply a 2x2 transformation matrix, and demonstrate that eigenvectors remain on their span after transformation."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [pr... | linear_algebra | easy |
[
{
"role": "user",
"content": "Create a manim animation of a 3-layer neural network (3-4-2) showing the forward pass with activation flow, then the backward pass with gradient flow in red. Include layer labels and a loss display."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem... | ml_ai | hard |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.