Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx agentmods add skills/tensormux/kernel-skills/write-numerically-stable-kernelnpx skills add tensormux/kernel-skills --skill write-numerically-stable-kernelgit clone --depth 1 https://github.com/tensormux/kernel-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/tensormux/kernel-skills/write-numerically-stable-kernel)<a href="https://agentmods.dev/skills/tensormux/kernel-skills/write-numerically-stable-kernel"><img src="https://agentmods.dev/badge/skills/tensormux/kernel-skills/write-numerically-stable-kernel.svg" alt="Measured on agentmods" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5 | $0.00000 | $0.02859 |
| Opus 5 | $0.00000 | $0.01430 |
| Sonnet 5 | $0.00000 | $0.00572 |
| Haiku 4.5 | $0.00000 | $0.00286 |
Grade A, and why
write-numerically-stable-kernel scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 4d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 108 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Skill: Write a Numerically Stable Kernel
Purpose
Guide the agent through identifying numerical instability risks in a kernel's computation path and applying the correct stabilization strategy for each risk class.
Use this when
- Writing or reviewing a kernel that contains reductions, accumulations, exponentials, logarithms, or divisions over floating-point inputs.
- A kernel produces correct results in fp32 but diverges when run in fp16 or bf16.
- A kernel computes variance, softmax, log-softmax, cross-entropy, or layer normalization — all of which have standard stable formulations that differ from the naive algebraic form.
- A kernel accumulates a large number of values (e.g., dot products over long sequences, large reduction trees).
- Results show inf, NaN, or unexpectedly large relative error relative to a double-precision reference.
Do not use this when
- The computation is already fp32 or fp64 throughout, operates on bounded inputs, and correctness has been validated against a reference. Do not add unnecessary stabilization steps that cost performance without improving correctness.
- The instability is caused by a bug (wrong indexing, wrong reduction tree, missing synchronization) rather than a precision limitation. Fix the bug first.
- The application explicitly accepts approximate computation (e.g., stochastic rounding for training with intentional noise). Understand the tolerance before adding stabilization overhead.
Inputs the agent should gather first
- The mathematical definition of the computation, written out explicitly — not just "softmax" but the exact formula being implemented.
- Input dtype (fp16, bf16, fp32, fp64) and whether that dtype is fixed or configurable.
- Expected input value range: are inputs bounded, potentially large, or potentially near zero?
- Accumulation length: how many values are summed or dot-producted? Longer accumulations accumulate more rounding error.
- Whether the output is consumed by a loss function, an activation, or another reduction — downstream consumers may have their own precision requirements.
- Hardware: which compute capability? On Hopper (sm_90), fp8 and bf16 tensor core paths have different precision characteristics than on Ampere.
- Whether correctness is validated against a double-precision reference or only against another fp16 run.
What ships with it
1 file beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 4d ago First seen · 108 lines · 0 tokens per session scan A 402ec2a63a6a
write-numerically-stable-kernel is a skill published in the GitHub repository tensormux/kernel-skills (73 stars, last pushed 2mo ago), licensed MIT. It costs nothing until one of its globs matches a file; then it loads 2,859 tokens. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.
Other skills, from other repositories
quantum-qiskit
Reference qiskit 2.x patterns for variational quantum machine learning. Covers data-encoding feature maps, variational quantum classifier (VQC) training, variational quantum eigensolver (VQE) for chemistry, matrix-product-state circuits, and noise model integration. Use when writing Python code that imports qiskit…
fba-simulator
Run Flux Balance Analysis (FBA) and related constraint-based simulations using COBRApy. Covers standard FBA, parsimonious FBA (pFBA), Flux Variability Analysis (FVA), loopless FBA, gene/reaction knockouts, and carbon source swapping. Outputs flux distributions and CSV files.
flux-analyzer
Analyse FBA flux distributions to extract biological insights. Covers gene essentiality, phenotypic phase planes, flux sampling, pathway-level aggregation, secretion product prediction, and production of publication- quality figures.
gsmm-validator
Validate a COBRApy genome-scale metabolic model for mass/charge balance, stoichiometric consistency, biomass producibility, dead-end metabolites, thermodynamic loops, and GPR rule formatting. Outputs a structured validation report with errors and warnings.
metabolic-study-planner
Plan publishable constraint-based metabolic modelling studies when the user has a broad biological or metabolic-engineering topic but no concrete dataset, organism, model, or hypothesis. Selects feasible BiGG/COBRA models, objectives, perturbations, analyses, metrics, figures, and risk controls before FBA code is…
gsmm-builder
Build or load a genome-scale metabolic model (GSMM) using COBRApy. Covers loading from BIGG, constructing minimal models from scratch, setting medium constraints, and exporting validated .json model files.