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 vasilyu1983/AI-Agents-public --skill foundations-information-theorygit clone --depth 1 https://github.com/vasilyu1983/AI-Agents-publicWrote 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/vasilyu1983/ai-agents-public/foundations-information-theory)<a href="https://agentmods.dev/skills/vasilyu1983/ai-agents-public/foundations-information-theory"><img src="https://agentmods.dev/badge/skills/vasilyu1983/ai-agents-public/foundations-information-theory/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/vasilyu1983/ai-agents-public/foundations-information-theory"><img src="https://agentmods.dev/badge/skills/vasilyu1983/ai-agents-public/foundations-information-theory.svg" alt="Reviewed on agentmods" width="80" height="20"></a>- NVIDIA SkillSpector warn
SkillSpector: 2 findings, up to medium
These are SkillSpector’s own severities. On a checked sample its high-severity flags on skills were ~96% false positives — a documented command, a public API, a “never do X” rule — so we show them as a caution to read, not a verdict. Why →
- medium analysis-evasion · line 1 Suspicious Unicode normalization or mixed-script contentFix: Review the flagged content for security risks. Ensure no credentials, secrets, or sensitive data are exposed.
- medium Excessive Agency · line 116 Skill enables autonomous high-impact decisions without human-in-the-loop verification. Critical operations (destructive commands, financial transactions, data deletion) should require explicit user confirmation.Fix: Add human-in-the-loop confirmation for destructive, irreversible, or high-impact operations. Never auto-execute commands that modify files, send data, or alter system state.
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 | $0.00043 | $0.03723 |
| Opus 5.5 | $0.00017 | $0.01489 |
| Sonnet 5.5 | $0.00009 | $0.00745 |
| Haiku 4.5 | $0.00004 | $0.00372 |
Grade A, and why
foundations-information-theory 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 13d 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 — 137 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Information Theory Foundations
When to Apply
Apply when a decision depends on a defined distribution:
- Distribution shift or model-update comparison (KL direction, JS with a stated log base)
- Feature relevance or leakage screening by mutual information, with an estimator and a null baseline
- Model comparison across tokenizers (bits-per-byte or bits-per-character, not perplexity)
- Hallucination or abstention gating via semantic entropy over meaning clusters
- RL post-training health: policy-entropy collapse in RLVR
- Context, prompt, KV-cache or agent-handoff compression framed as a measured rate/task-loss tradeoff
- Error floors (Fano), coding limits (entropy, capacity, rate-distortion), model selection (MDL)
- LLM-serving questions: speculative-decoding acceptance, quantization or KV-cache compression claims, log loss vs Brier for calibration (references/llm-practice.md)
Skip or hand off when:
- The question is causal, not dependence: foundations-causal-inference
- Linear or monotonic dependence is enough: Pearson or rank correlation
- The task is significance, error bars or calibration methodology: foundations-statistical-inference
- The task is feedback stability: foundations-control-theory
- Team or human communication design: foundations-team-theory or foundations-grounding-communication (channel capacity is not a measurement there)
- No random variable, sampling frame or estimator can be written down: call the score a proxy and evaluate it on task outcomes
Quick Reference
| # | Primitive | Core formula | Use when | Playbook |
|---|---|---|---|---|
| 1 | Shannon entropy | H(X) = −Σ p log p | Uncertainty of a defined PMF; semantic entropy over meaning clusters; RLVR policy entropy | 01 |
| 2 | Mutual information | I(X;Y) = H(X) − H(X|Y) | Non-linear dependence, relevance, leakage | 02 |
| 3 | KL / JS divergence | D_KL(P‖Q) = Σ p log(p/q) | Directional distribution comparison; JS for symmetric | 03 |
| 4 | Cross-entropy | H(P,Q) = H(P) + D_KL(P‖Q) | Loss, perplexity, bits-per-byte | 04 |
| 5 | Channel capacity | C = max_{p(x)} I(X;Y) | Noisy-channel throughput ceilings with a named transition law | 05 |
| 6 | Rate-distortion | R(D) = min I(X;X̂) s.t. E d ≤ D | Lossy compression under a named distortion | 06 |
| 7 | MDL | L(M) + L(D|M) | Model selection with an explicit code | 07 |
| 8 | Information bottleneck | min I(X;T) − β I(T;Y) | Representation compression with a defined target | 08 |
| 9 | Fano's inequality | H(X|Y) ≤ H_b(P_e) + P_e log(|X|−1) | Error floor from residual uncertainty | 09 |
| 10 | Typical sets / AEP | −(1/n) log p(Xⁿ) → H | Source-coding limits, block-length reasoning | 10 |
| 11 | Redundancy & compression | R = log M − H(X); entropy rate | Code-family choice, NCD, redundancy audits | 11 |
What ships with it
23 files 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.
- agents/openai.yaml 378 B
- assets/templates/information-theory/01-shannon-entropy.md 2.4 KB
- assets/templates/information-theory/02-mutual-information.md 2.2 KB
- assets/templates/information-theory/03-kl-divergence.md 2.5 KB
- assets/templates/information-theory/04-cross-entropy.md 1.9 KB
- assets/templates/information-theory/05-channel-capacity.md 1.8 KB
- assets/templates/information-theory/06-rate-distortion.md 2.1 KB
- assets/templates/information-theory/07-mdl-principle.md 1.9 KB
- assets/templates/information-theory/08-information-bottleneck.md 2.5 KB
- assets/templates/information-theory/09-fano-inequality.md 2.0 KB
- assets/templates/information-theory/10-typical-sets-aep.md 1.7 KB
- assets/templates/information-theory/11-redundancy-compression.md 2.3 KB
- assets/templates/information-theory/README.md 1.8 KB
- data/sources.json 29 KB
- learnings.consolidated.md 606 B
- learnings.md 1.6 KB
- references/formal-theory-map.md 3.9 KB
- references/llm-practice.md 7.7 KB
- references/patterns-scenarios-traps.md 4.0 KB
- references/practical-contract.md 3.3 KB
- references/primitives-overview.md 8.9 KB
- scripts/discrete_information.py 2.9 KB runs code
- scripts/test_discrete_information.py 1.7 KB runs code
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.
- 13d ago Changed 2a8a3d1fe035
- 20d ago Changed · -162 lines 71c8297e93b6
- 1mo ago Changed · -14 lines d43aab6e3cbb
- 1mo ago First seen · 313 lines · 43 tokens per session scan A 0ebb0301f1ab
foundations-information-theory is a skill published in the GitHub repository vasilyu1983/AI-Agents-public (101 stars, last pushed 10d ago), licensed MIT. It adds 43 tokens to every session and 3,723 once invoked, about $0.0002 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 2026-09-03.
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