Ready to supercharge your AI agents?

Install any skill in seconds. Free to start, no credit card required.

Get Started Free →

Gradient Methods · vibeeval | DecimalAI

scienceby vibeeval

Gradient Methods

vibeeval/gradient-methods

Source vibeeval/vibecosystem ↗License MIT

Problem-solving strategies for gradient methods in optimization

SkillScore100Maintained

Automatic

Research pack

Last verified 8/3/2026

What it changes

Passed 22 of 22 test cases with the skill, and 21 of 22 without it.

Without skill95%

With skill100%

Checks it passed that the model alone missed

Executes sympy_compute.py diff with --var option specifying variables

1 fixed21 passed either way0 still failing0 broke

Pass-rate lift: +5 pp
Tokens: +19%
Agent turns: 0%
Response time: -29%

Model gemini-3.6-flashMeasured 8/3/2026v122 of 22 cases passed with skill

Tokens, turns and time describe resource use, not a dollar price.

Use this skill

Save it into your project's skills folder. Claude Code picks it up in its next session.

curl -fsSL --create-dirs -o .claude/skills/vibeeval-gradient-methods/SKILL.md https://app.decimal.ai/s/vibeeval-gradient-methods/SKILL.md

Want it pinned and updatable? pip install "decimalai>=0.15", then decimalai skills add vibeeval-gradient-methods, and start Claude Code with claude --plugin-dir "$(git rev-parse --show-toplevel)/.agents"

1 · One-time — install the CLI (docs ↗)

pip install "decimalai>=0.15"

2 · Get the skill — writes .agents/skills/vibeeval-gradient-methods/ and pins it in .decimal/skills.lock

decimalai skills add vibeeval-gradient-methods

No CLI? Get the same file — curl · raw file

curl -fsSL --create-dirs -o .claude/skills/vibeeval-gradient-methods/SKILL.md https://app.decimal.ai/s/vibeeval-gradient-methods/SKILL.md

Raw file: /s/vibeeval-gradient-methods/SKILL.md ↗ · machine-readable summary at /s/vibeeval-gradient-methods.json ↗

Safety checks: 3 of 3 passed

Code scan CleanIntent PassedContent Clean

See it in action

A test case the skill fixed. Same model, same prompt, with and without the skill.

Prompt

How can I compute the symbolic gradient of x^2 + y^2 with respect to variables x and y using command-line tools?

What was checked, without and with the skill
Checked	Without skill	With skill
Executes sympy_compute.py diff with --var option specifying variables	Missed	Passed

case-10 · gemini-3.6-flash · 8/3/2026 · answers are capped and redacted

What's inside

The instructions your model reads when the skill loads.

SKILL.md71 linessingle file

Gradient Methods

When to Use

Use this skill when working on gradient-methods problems in optimization.

Decision Tree

Basic Gradient Descent
- Update: x_{k+1} = x_k - alpha * grad f(x_k)
- Step size alpha: fixed, diminishing, or line search
- Convergence: O(1/k) for convex, linear for strongly convex

Step Size Selection

Method	Approach
Fixed	alpha constant (requires tuning)
Backtracking	Armijo condition: f(x - alphagrad) <= f(x) - calpha*
Exact line search	minimize f(x - alpha*grad) over alpha
Adaptive	Adam, RMSprop (ML applications)

Accelerated Methods
- Momentum: add velocity term
- Nesterov: look-ahead gradient
- Conjugate gradient: for quadratic functions
- scipy.optimize.minimize(f, x0, method='CG') - conjugate gradient
Newton's Method
- Update: x_{k+1} = x_k - H^{-1} * grad f
- Requires Hessian (expensive but quadratic convergence)
- Quasi-Newton (BFGS): approximate Hessian
- scipy.optimize.minimize(f, x0, method='BFGS')
Convergence Diagnostics
- Monitor ||grad f|| < tolerance
- Check function value decrease
- Watch for oscillation (step size too large)
- sympy_compute.py diff "f" --var x for gradient

Track record

Benchmark

22 / 22

test cases passed, vs 21 / 22 without

Adoption

Users: 0
Times used: 0

Safety and source details

SkillSafety

✓ 3 of 3 passed

Code scan15 of 15 checks clean

0 critical · 0 warning · 0 info — scanner v4 — 8/1/2026

View 15 scanner checks

live_secretremote_code_executionreverse_shelldata_exfiltrationssrf_metadataagent_snoopinganti_refusaldestructive_commandsobfuscated_unicodeunicode_homoglyphopaque_blobsuspicious_urltool_overreachtrigger_abuseprompt_injection_phrasing

IntentSafe

LLM judge · does the skill do what it claims

ContentClean

LLM judge · policy & harmful-content review

Source

Imported

vibeeval / vibecosystem

skills/math/optimization/gradient-methods/SKILL.md

View on GitHub ↗

License MITImported 8/1/2026Version v1

More skills from the same source and nearby in the registry, with their headline benchmark lift.

Ready to supercharge your AI agents?

See it in action

What's inside

Gradient Methods

When to Use

Decision Tree

Track record

Benchmark

Adoption

SkillSafety

Source

Related skills