Datasets:
id stringlengths 32 32 | conversations listlengths 2 2 | input stringlengths 44 478 | output stringlengths 3.94k 560k | domain stringclasses 2
values | meta dict |
|---|---|---|---|---|---|
7b666258f82c14c77aa26ef22b70813c | [
{
"from": "human",
"value": "In a two‑player zero‑sum differential game with state x∈ℝ^2, dynamics →ẋ=Ax+Bu+Cv, quadratic cost ∫_0^∞(x^TQx+u^TRu−v^TSv)dt, and seed 718692759 determining the eigenvalues of A, find the Riccati equation whose solution yields the unique saddle‑point feedback strategies?"
},
... | In a two‑player zero‑sum differential game with state x∈ℝ^2, dynamics →ẋ=Ax+Bu+Cv, quadratic cost ∫_0^∞(x^TQx+u^TRu−v^TSv)dt, and seed 718692759 determining the eigenvalues of A, find the Riccati equation whose solution yields the unique saddle‑point feedback strategies? | <think>
The problem asks for the Riccati equation whose solution yields the unique saddle-point feedback strategies for a two-player zero-sum differential game.
The state dynamics are given by $\dot{x} = Ax + Bu + Cv$.
The cost function is $J = \int_0^\infty (x^T Q x + u^T R u - v^T S v) dt$.
This is a standard infinit... | Math | {
"input_tokens": 91,
"output_tokens": 4127,
"teacher_model": "GLM-5.1"
} |
02cb4e992c4287c9eb3b640531018b88 | [
{
"from": "human",
"value": "Consider a finite metric space sampled from a high‑dimensional manifold with unknown curvature; using persistent homology of the Vietoris–Rips filtration, formulate an inverse problem to recover the manifold’s sectional curvature function from the barcode stability under Gaussia... | Consider a finite metric space sampled from a high‑dimensional manifold with unknown curvature; using persistent homology of the Vietoris–Rips filtration, formulate an inverse problem to recover the manifold’s sectional curvature function from the barcode stability under Gaussian noise? | <think>
1. **Deconstruct the Prompt:**
* **Context:** Finite metric space sampled from a high-dimensional manifold with unknown curvature.
* **Tool:** Persistent homology of the Vietoris-Rips (VR) filtration.
* **Task:** Formulate an *inverse problem* to recover the manifold's *sectional curvature fu... | Math | {
"input_tokens": 50,
"output_tokens": 4157,
"teacher_model": "GLM-5.1"
} |
2cabb36eb566e0d5a345b08357f58c1e | [
{
"from": "human",
"value": "For a stochastic differential equation modeling option prices under stochastic volatility, derive the sensitivity of the price to model parameters using adjoint‑based data assimilation, and quantify the resulting uncertainty via polynomial chaos expansion?"
},
{
"from": ... | For a stochastic differential equation modeling option prices under stochastic volatility, derive the sensitivity of the price to model parameters using adjoint‑based data assimilation, and quantify the resulting uncertainty via polynomial chaos expansion? | <think>
1. **Deconstruct the Prompt:**
* **Core Subject:** Stochastic Differential Equation (SDE) modeling option prices under stochastic volatility.
* **Task 1:** Derive the sensitivity of the price to model parameters using adjoint-based data assimilation.
* **Task 2:** Quantify the resulting uncer... | Math | {
"input_tokens": 40,
"output_tokens": 5173,
"teacher_model": "GLM-5.1"
} |
9b8695a3282190838ed01d4414afdae3 | [
{
"from": "human",
"value": "For a Lagrangian L(x,ẋ)=½‖ẋ‖²−V(x) on a closed Riemannian manifold, show that any minimizing periodic orbit of the action functional must satisfy a Morse index bound that equals the number of conjugate points along the orbit, linking calculus of variations with differential topo... | For a Lagrangian L(x,ẋ)=½‖ẋ‖²−V(x) on a closed Riemannian manifold, show that any minimizing periodic orbit of the action functional must satisfy a Morse index bound that equals the number of conjugate points along the orbit, linking calculus of variations with differential topology? | <think>
1. **Deconstruct the Prompt:**
* **System:** Lagrangian $L(x, \dot{x}) = \frac{1}{2}\|\dot{x}\|^2 - V(x)$ on a closed (compact, boundaryless) Riemannian manifold $(M, g)$.
* **Object of Study:** Minimizing periodic orbits of the action functional.
* **Goal:** Show that the Morse index bound e... | Math | {
"input_tokens": 66,
"output_tokens": 5091,
"teacher_model": "GLM-5.1"
} |
0c5418a5a5064efc683dda2c08558891 | [
{
"from": "human",
"value": "In a compact metric space X equipped with a Vietoris–Rips filtration built from a finite point cloud, prove that the persistent homology barcodes are invariant under homeomorphisms of X that preserve the underlying metric up to a bi‑Lipschitz constant, and discuss implications f... | In a compact metric space X equipped with a Vietoris–Rips filtration built from a finite point cloud, prove that the persistent homology barcodes are invariant under homeomorphisms of X that preserve the underlying metric up to a bi‑Lipschitz constant, and discuss implications for stability of topological signatures? | <think>
1. **Deconstruct the Prompt:**
* **Context:** Compact metric space $X$, Vietoris-Rips filtration built from a finite point cloud $P \subset X$.
* **Core Task:** Prove that persistent homology barcodes are invariant under homeomorphisms of $X$ that preserve the underlying metric up to a bi-Lipschitz... | Math | {
"input_tokens": 65,
"output_tokens": 7968,
"teacher_model": "GLM-5.1"
} |
b7ce6ea2d44adb42f034f7e036d74a1a | [{"from":"human","value":"In a continuous-time zero-sum stochastic differential game with state dyna(...TRUNCATED) | "In a continuous-time zero-sum stochastic differential game with state dynamics governed by a contro(...TRUNCATED) | "<think>\n1. **Deconstruct the Prompt:**\n * **Topic:** Continuous-time zero-sum stochastic di(...TRUNCATED) | Math | {
"input_tokens": 58,
"output_tokens": 6778,
"teacher_model": "GLM-5.1"
} |
d2c7906366ae10287a50714ba9a8c91c | [{"from":"human","value":"Given a smooth, strictly convex Hamiltonian H(p,q) on ℝ^{2n} generating (...TRUNCATED) | "Given a smooth, strictly convex Hamiltonian H(p,q) on ℝ^{2n} generating a symplectic flow, prove (...TRUNCATED) | "<think>\nThe problem asks to prove that any non-trivial invariant Lagrangian torus of a smooth, str(...TRUNCATED) | Math | {
"input_tokens": 57,
"output_tokens": 10454,
"teacher_model": "GLM-5.1"
} |
57111bae9a1835631dfb036c46f74fdb | [{"from":"human","value":"Establish necessary and sufficient conditions for the convergence of the s(...TRUNCATED) | "Establish necessary and sufficient conditions for the convergence of the stochastic gradient descen(...TRUNCATED) | "<think>\n1. **Deconstruct the Prompt:**\n * **Algorithm:** Stochastic Gradient Descent (SGD).(...TRUNCATED) | Math | {
"input_tokens": 37,
"output_tokens": 4446,
"teacher_model": "GLM-5.1"
} |
912f17b02bca8a13bec6737dcf03907d | [{"from":"human","value":"In a Bayesian hierarchical model for uncertain parameters of a stochastic (...TRUNCATED) | "In a Bayesian hierarchical model for uncertain parameters of a stochastic reaction‑diffusion PDE,(...TRUNCATED) | "<think>\n1. **Deconstruct the Prompt:**\n * **Context:** Bayesian hierarchical model.\n * (...TRUNCATED) | Math | {
"input_tokens": 50,
"output_tokens": 8155,
"teacher_model": "GLM-5.1"
} |
7d563527dabc9a034dbcca3255f3720b | [{"from":"human","value":"Consider a hierarchical Bayesian model where observations follow a Poisson(...TRUNCATED) | "Consider a hierarchical Bayesian model where observations follow a Poisson process with intensity (...TRUNCATED) | "<think>\n1. **Deconstruct the Prompt:**\n * **Core Model:** Hierarchical Bayesian model.\n (...TRUNCATED) | Math | {
"input_tokens": 48,
"output_tokens": 8797,
"teacher_model": "GLM-5.1"
} |
End of preview. Expand in Data Studio
GLM-5.1-Reasoning-1M-filtered
Refusal-filtered subset of zai-org/GLM-5.1-Reasoning-1M.
Filtering
Conservative regex/string match for explicit refusal patterns (e.g., "I cannot", "I can't", "I'm not able to", "as an AI", "죄송합니다", etc.) applied on the assistant response field. Drop ratio: ~0.00% (very few refusals in source).
Files
| File | Size | Records (kept) |
|---|---|---|
main.jsonl |
19 GB | (full main subset, refusals removed) |
Math.jsonl |
4.1 GB | mathematics reasoning |
PHD-Science.jsonl |
3.8 GB | 103,705 |
Multilingual-STEM.jsonl |
3.6 GB | 92,781 |
Total: 30 GB JSONL.
Source
- Original: zai-org/GLM-5.1-Reasoning-1M
- Filter script:
filter_glm_refusals.py(sequential to avoid HDD I/O contention)
License
Inherits Apache-2.0 from the source dataset.
- Downloads last month
- 27