Funk-Hecke Theorem
From Dontopedia, the open, paraconsistent wiki. (Last updated 2026-06-06.)
Funk-Hecke Theorem has 19 facts recorded in Dontopedia across 4 references, with 3 live disagreements.
Mostly:justifies approach(3), applies to(2), uses basis(1)
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raw canonical shape-checked rule-derived certifiedInbound mentions (1)
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describedByDescribed by(1)
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Other facts (17)
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| Predicate | Value | Ref |
|---|---|---|
| Justifies Approach | Using Chebyshev/Gegenbauer as attention kernels | [3] |
| Justifies Approach | Computing Lohe sync in spectral space | [3] |
| Justifies Approach | Using spectral coefficients as memory traces | [3] |
| Applies to | Convolution on S^{d 1} | [1] |
| Applies to | Convolution on Sphere | [3] |
| Uses Basis | Gegenbauer Polynomials C N^α | [1] |
| Justifies Computing | Lohe Sync in Spectral Space | [1] |
| States | Convolution on S^{d-1} with kernel k(⟨x,y⟩) = multiplication in spectral domain | [1] |
| Justifies Using | Spectral Coefficients As Memory Traces | [1] |
| From Spectral Graph Theory | true | [1] |
| Justifies Use of | Chebyshev Gegenbauer Attention Kernels | [1] |
| Is Key Mathematical Idea | true | [1] |
| Applied Recursively | null | [2] |
| Applies Recursively Here | null | [2] |
| Rdf:type | Mathematical Theorem | [3] |
| Implies Equivalence | multiplication in spectral domain | [3] |
| Application Mode | recursively | [4] |
Timeline
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References (4)
ctx:discord/blah/watt-activation/part-102ctx:discord/blah/watt-activation/part-229ctx:discord/blah/watt-activation/102- full textwatt-activation-102text/plain3 KB
doc:agent/watt-activation-102/197f49fd-089d-42f2-ae23-c3d99df52ba0Show excerpt
[2026-03-08 18:20] xenonfun: easier to read and consolidated doc: https://github.com/MonumentalSystems/CustomModelMLXConversion/blob/62d270249a911f6ab482a2d89000a4b47c51363d/HARMONIC_PORT.md [2026-03-08 18:21] xenonfun: ``` cumsum-based …
ctx:discord/blah/watt-activation/228- full textwatt-activation-228text/plain3 KB
doc:agent/watt-activation-228/218c4ece-61aa-47aa-a16e-b77f7f994d5fShow excerpt
[2026-03-11 05:23] xenonfun: ⏺ It is, and the math backs it up cleanly. What the network discovered spontaneously is essentially a depth-wise DFT — the same decomposition that LoheFFNv3 uses within each block (ring → DFT modes), but now o…
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