Many r-local Hamiltonians, including Pauli strings, random high-rank operators, and high-rank operators, admit sparsifications with o(n^r) terms that (1±ε)-approximate the original Hamiltonian on all states.
and Meka, Raghu , title =
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Symmetric spectral diagnostics on attention are structurally blind to flow direction, with asymmetry G as the sole control parameter, yielding a two-axis test that distinguishes bottleneck versus diffuse hallucination modes with opposite polarity.
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Many Hamiltonians Are Sparsifiable
Many r-local Hamiltonians, including Pauli strings, random high-rank operators, and high-rank operators, admit sparsifications with o(n^r) terms that (1±ε)-approximate the original Hamiltonian on all states.
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Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics
Symmetric spectral diagnostics on attention are structurally blind to flow direction, with asymmetry G as the sole control parameter, yielding a two-axis test that distinguishes bottleneck versus diffuse hallucination modes with opposite polarity.