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 skills add hamzabellouch/agent-skills --skill machine-learning-mathematicsgit clone --depth 1 https://github.com/hamzabellouch/agent-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/hamzabellouch/agent-skills/machine-learning-mathematics)<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/machine-learning-mathematics"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/machine-learning-mathematics/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/machine-learning-mathematics"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/machine-learning-mathematics.svg" alt="Reviewed on agentmods" width="80" 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 5.1 | $0.00063 | $0.00486 |
| Opus 5.5 | $0.00025 | $0.00194 |
| Sonnet 5.5 | $0.00013 | $0.00097 |
| Haiku 4.5 | $0.00006 | $0.00049 |
Grade A, and why
machine-learning-mathematics 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 today.
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.
What it actually says
Mathematics of Machine Learning
Supervised learning
- Empirical risk minimization; loss functions (MSE, cross-entropy, hinge); regularization (L2 = Gaussian prior, L1 = Laplace prior / sparsity).
- Linear regression normal equations; logistic regression gradient X^T(sigma(Xw) - y); softmax cross-entropy gradient p - y.
- Bias-variance decomposition; VC dimension; PAC learning; Rademacher complexity; generalization bounds; double descent and overparameterization.
- SVM and kernels: Mercer kernels, RBF, representer theorem; Gaussian processes.
Neural networks
- Forward pass, backpropagation = reverse-mode automatic differentiation via the chain rule; Jacobian-vector products; vanishing/exploding gradients; initialization (Xavier, He); batch/layer norm; residual connections; universal approximation theorem.
- Optimizers: SGD, momentum, Adam; learning-rate schedules; loss landscape, saddle points, flat minima.
- CNN: convolution as shared-weight linear operator; equivariance. RNN/LSTM. Transformers: attention softmax(QK^T/sqrt(d))V, positional encodings, scaling laws, complexity O(n^2 d).
- Generative models: VAE (ELBO = E log p(x|z) - KL(q||p)), GAN (minimax), diffusion (score matching, SDE), autoregressive LMs (maximum likelihood on next-token).
- Reinforcement learning: MDP, Bellman equation, policy gradient theorem, Q-learning, PPO, RLHF.
Unsupervised & probabilistic
PCA (eigenvectors of covariance, SVD), k-means (EM special case), EM algorithm, Gaussian mixtures, HMMs, graphical models, variational inference, MCMC, t-SNE/UMAP, contrastive learning, mutual information bounds.
Practical math checks
Gradient checking with finite differences; dimensional analysis of tensor shapes; numerical stability (log-sum-exp); calibration; data leakage; reproducibility.
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.
- today First seen · 26 lines · 63 tokens per session scan A ff0dfec2c861
machine-learning-mathematics is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed today), licensed MIT. It adds 63 tokens to every session and 486 once invoked, about $0.0003 per session on Opus 5.5. 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 2026-10-17.
Other skills, from other repositories
geoffrey-hinton
Agente que simula Geoffrey Hinton — Godfather of Deep Learning, Prêmio Turing 2018, criador do backpropagation e das Deep Belief Networks.
polya-docs
Phase 6 of the Pólya Heuristic Coder: Technical Documentation via Diátaxis Framework (Tutorials, How-To Guides, Reference, Explanation).
fixing-prompt
Prompt: Prompt Refinement and Optimization.
feature-engineering
When building training datasets, designing feature pipelines, or debugging training-serving skew.
model-evaluation
When evaluating a trained model, comparing versions, or performing fairness analysis.
orchestration
When designing DAGs, debugging pipeline failures, or configuring retries.