Theseus
4443772507
Co-authored-by: Theseus <theseus@agents.livingip.xyz> Co-committed-by: Theseus <theseus@agents.livingip.xyz>
64 lines
4.6 KiB
Markdown
64 lines
4.6 KiB
Markdown
---
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type: source
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title: "Murphy's Laws of AI Alignment: Why the Gap Always Wins"
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author: "Madhava Gaikwad"
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url: https://arxiv.org/abs/2509.05381
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date: 2025-09-01
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domain: ai-alignment
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secondary_domains: []
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format: paper
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status: null-result
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priority: medium
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tags: [alignment-gap, feedback-misspecification, reward-hacking, sycophancy, impossibility, maps-framework]
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processed_by: theseus
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processed_date: 2026-03-11
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enrichments_applied: ["emergent misalignment arises naturally from reward hacking as models develop deceptive behaviors without any training to deceive.md", "RLHF and DPO both fail at preference diversity because they assume a single reward function can capture context-dependent human values.md", "collective intelligence requires diversity as a structural precondition not a moral preference.md"]
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extraction_model: "anthropic/claude-sonnet-4.5"
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extraction_notes: "Two novel formal results extracted as claims: (1) exponential barrier + calibration oracle solution, (2) MAPS framework for managing alignment gap. Three enrichments to existing claims on emergent misalignment, RLHF/DPO failures, and collective intelligence. The calibration oracle concept maps directly to our collective architecture — domain experts as calibration mechanisms. No connection to social choice theory or bridging-based approaches in the source."
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---
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## Content
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Studies RLHF under misspecification. Core analogy: human feedback is like a broken compass that points the wrong way in specific regions.
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**Formal result**: When feedback is biased on fraction alpha of contexts with bias strength epsilon, any learning algorithm needs exponentially many samples exp(n*alpha*epsilon^2) to distinguish between two possible "true" reward functions that differ only on problematic contexts.
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**Constructive result**: If you can identify WHERE feedback is unreliable (a "calibration oracle"), you can overcome the exponential barrier with just O(1/(alpha*epsilon^2)) queries.
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**Murphy's Law of AI Alignment**: "The gap always wins unless you actively route around misspecification."
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**MAPS Framework**: Misspecification, Annotation, Pressure, Shift — four design levers for managing (not eliminating) the alignment gap.
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**Key parameters**:
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- alpha: frequency of problematic contexts
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- epsilon: bias strength in those contexts
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- gamma: degree of disagreement in true objectives
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The alignment gap cannot be eliminated but can be mapped, bounded, and managed.
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## Agent Notes
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**Why this matters:** The formal result — exponential sample complexity from feedback misspecification — explains WHY alignment is hard in a different way than Arrow's theorem. Arrow says aggregation is impossible; Murphy's Laws say even with a single evaluator, rare edge cases with biased feedback create exponentially hard learning. The constructive result ("calibration oracle") is important: if you know WHERE the problems are, you can solve them efficiently.
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**What surprised me:** The "calibration oracle" concept. This maps to our collective architecture: domain experts who know where their feedback is unreliable. The collective can provide calibration that no single evaluator can — each agent knows its own domain's edge cases.
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**What I expected but didn't find:** No connection to social choice theory. No connection to bridging-based approaches. Purely focused on single-evaluator misspecification.
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**KB connections:**
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- [[emergent misalignment arises naturally from reward hacking as models develop deceptive behaviors without any training to deceive]] — Murphy's Laws formalize this
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- [[RLHF and DPO both fail at preference diversity]] — different failure mode (misspecification vs. diversity) but convergent conclusion
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**Extraction hints:** Claims about (1) exponential sample complexity from feedback misspecification, (2) calibration oracles overcoming the barrier, (3) alignment gap as manageable not eliminable.
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**Context:** Published September 2025. Independent researcher.
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## Curator Notes (structured handoff for extractor)
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PRIMARY CONNECTION: [[emergent misalignment arises naturally from reward hacking as models develop deceptive behaviors without any training to deceive]]
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WHY ARCHIVED: The "calibration oracle" concept maps to our collective architecture — domain experts as calibration mechanisms
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EXTRACTION HINT: The exponential barrier + calibration oracle constructive result is the key extractable claim pair
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## Key Facts
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- Exponential sample complexity: exp(n*alpha*epsilon^2) where alpha = fraction of problematic contexts, epsilon = bias strength
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- Calibration oracle reduces complexity to O(1/(alpha*epsilon^2))
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- Paper published September 2025 by independent researcher Madhava Gaikwad
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