数学基础与公式
逆核概率分布的弹性与伸缩非线性
\[
\left\langle \nabla_{s}^{l_{\tau}},\nabla_{s}^{l_{\eta}} \right\rangle_{{token}_{j}\_{head}_{i}}^{\left\langle \omega,i\omega \right\rangle} \rightsquigarrow {\pm \left\lbrack {Tanh}_{}^{\left\langle \omega,i\omega \right\rangle}\left( \sum_{s = 2}^{m}{l_{\left\langle \theta,\beta \right\rangle}^{s}\left( \theta_{l}^{s} \vee \beta_{l}^{s} \right)\ } \right) \right\rbrack}_{{token}_{j}\_{head}_{i}}^{i^{+},j^{-}}
\]
高维超切片滑动核迹特征
\[
\left\langle \nabla_{s}^{l_{\tau}},\nabla_{s}^{l_{\eta}} \right\rangle_{{token}_{j}\_{head}_{i}}^{\left\langle \omega,i\omega \right\rangle} \rightsquigarrow {\pm \left\lbrack {Tanh}_{}^{\left\langle \omega,i\omega \right\rangle}\left( \sum_{s = 2}^{m}{l_{\left\langle \theta,\beta \right\rangle}^{s}\left( \theta_{l}^{s} \land \beta_{l}^{s} \right)\ } \right) \right\rbrack}_{{token}_{j}\_{head}_{i}}^{i^{+},j^{-}}
\]
芽核振动有效核痕函数方程
\[
\lambda_{kernel\ range}^{+ + , - -} = ArcCos\left\lbrack \left( \frac{1}{4} \right)^{4}\left\lbrack \left( Sin\left( \frac{1}{2} + \sum_{i = 2}^{m}\frac{a - 3C}{2 \bullet Matrix\left\lbrack Det(n \times n) \right\rbrack_{A_{m}}} \right) + \frac{\pi}{4} \right) + \left( Sin\left( \frac{1}{2} - \sum_{i = 2}^{m}\frac{a - 3C}{2 \bullet Matrix\left\lbrack Det(n \times n) \right\rbrack_{A_{m}}} \right) + \frac{\pi}{4} \right) \right\rbrack_{}^{4 - 1} \right\rbrack_{kernel\ range}^{i^{+},j^{-}}
\]
稀疏注意力得分
\[
Attention(Q,K,V) = softmax\left( \frac{\left( QK^{T} \right)\bigodot M}{\sqrt{d_{k}^{}}} \right) \bullet V
\]
非线性弹性稀疏注意力得分
$$softmax\left( \frac{\left( QK^{T} \right) \bigodot M}{\sqrt{d_k}} \right) \bullet V
\rightsquigarrow
softmax\left(
\frac{
\left\langle
\cos\left(
T^{-1}
\left| \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right|
\sum_{s = 3}^{m} K^{s} \frac{K_{Q_{(t)}}^{s - 1}}{2}
\right),
\sin\left(
T^{-1}
\left| \begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix} \right|
\sum_{s = 3}^{m} Q^{s} \frac{Q_{K_{(t)}}^{s - 1}}{2}
\right)
\right\rangle
}
{\tanh(V)^2}
\right)$$
$$
softmax\left( K^{-1} \left\langle Q, K, V \right\rangle \right)
\rightsquigarrow
softmax\left( \frac{\left( QK^{T} \right) \bigodot M}{\sqrt{d_k}} \right) \bullet V,\ and
$$
$$softmax\left( \frac{\left( QK^{T} \right) \bigodot M}{\sqrt{d_k}} \right) \bullet V
\rightsquigarrow
softmax\left(
\frac{
\left\langle
\cos\left(
T^{-1}
\left| \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right|
\sum_{s = 3}^{m} K^{s} \frac{K_{Q_{(t)}}^{s - 1}}{2}
\right),
\sin\left(
T^{-1}
\left| \begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix} \right|
\sum_{s = 3}^{m} Q^{s} \frac{Q_{K_{(t)}}^{s - 1}}{2}
\right)
\right\rangle
}
{\tanh(V)^2}
\right)$$
多模态融合对齐损失
\[
L_{\left\langle align,Z_{tank} \right\rangle}^{} = \left\langle \lambda\left\| \theta - \ z(\theta,\rho) \right\|_{2}\ ,\ - \log\frac{e_{}^{Sin(t,i)/\tau}}{\sum_{j = 1}^{N}e_{}^{Sin(t,j)/\tau}} \right\rangle
\]