Operators#
Operators are at the core of NN-OpInf. Operators take some inputs, \(v\), and potentially an input state, \(x\), and model some function \(f\),
\(f: (v,x) \mapsto f(v,x)\)
What distinguishes NN-OpInf is that we enforce structure on the inferred operators. As an example, the SpdOperator is given as
\(f: (v,x) \mapsto L(v) L(v)^T x\)
which enforces semi-positive-definiteness.
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Protocol for operator class. |
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\(f: v \mapsto f(v)\) |
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\(f: (v,x) \mapsto L(v)L(v)^T x\) |
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\(f: (v,x) \mapsto [S(v) - S(v)^T] x\) |
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\(f: (v,x) \mapsto A(v)x\) |
\(f: x \mapsto \nabla_x \mathcal{L}(x)\) |
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\(f: x \mapsto \nabla_x \mathcal{L}(x)\) where \(\mathcal{L}(x) = x^T A(x) x\) and \(A(x)\) is an SPD operator. |
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\(f: (f_1,\ldots,f_K) \mapsto \sum_{i=1}^K f_k\) |
\(f: (v,x) \mapsto A_{ijk} x_k v_k\) |
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\(f: (v,x) \mapsto [S_{ijk} - S_{jik}] x_k v_k\) |
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\(f: (v,x) \mapsto \sum_{k=1}^{N} L_kD_kL_k^T x v_k\) |
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\(f \in \mathbb{R}^M\) |