PreTS-1T 第五代生成式AI
基于RLLM多模态可预测性思维增强收缩参数群的新一代人工智能系统，在数学基础和架构设计上实现革命性突破。
$$\mathit{Ker}^{-1} \left\langle Q, K, V \right\rangle
\rightsquigarrow
\frac{
\left\langle
\cos\left( T^{-1} \left|
\begin{matrix}
1 & 0 \\
0 & 1
\end{matrix}
\right|
\sum_{s=3}^{m} K^{s} \frac{K_{Q_{(t)}}^{s-1}}{2}
\right),
\;
\sin\left( T^{-1} \left|
\begin{matrix}
0 & 1 \\
1 & 0
\end{matrix}
\right|
\sum_{s=3}^{m} Q^{s} \frac{Q_{K_{(t)}}^{s-1}}{2}
\right)
\right\rangle
}{
\tanh(V)^2
}$$
$$\mathrm{softmax}\left( \frac{(QK^{T}) \odot M}{\sqrt{d_k}} \right) \cdot V
\rightsquigarrow
\mathrm{softmax}\left(
\frac{ \langle \cos(A), \sin(B) \rangle }{ \tanh(V)^2 }
\right)
and {.}
A = T^{-1} \begin{vmatrix} 1 & 0 \\ 0 & 1 \end{vmatrix} \sum_{s=3}^{m} K^{s} \frac{K_{Q(t)}^{s-1}}{2}, \quad
B = T^{-1} \begin{vmatrix} 0 & 1 \\ 1 & 0 \end{vmatrix} \sum_{s=3}^{m} Q^{s} \frac{Q_{K(t)}^{s-1}}{2}$$
$$
\left\lbrack \tanh\left( \sum_{s = 2}^{m} \left( t_{1}^{s} \cdot W_{Q} \land {t_{11}^{s} \cdot W_{K}}^{T} \right) \right) \right\rbrack_{\text{token}_{j}\_ \text{head}_{i}}^{\langle \omega, i \cdot \omega \rangle}
\times
\left( W_{Q} \land {W_{K}}^{T} \right)
\rightsquigarrow
\left( \frac{1}{4} \right)^{\langle \omega_{*}, i \cdot \omega_{*} \rangle} p \cdot \sqrt{2}
\left\lbrack \sin\left( \frac{b_{2}}{2} + \frac{\pi}{4} + n \cdot \frac{\pi}{4} \right) \cos\left( \sum_{i = 2}^{m} W_{i}^{Q} + \sum_{i = 1}^{m} i \cdot \frac{W_{i}^{K}}{2} \right) \right\rbrack^{\langle \omega, i \cdot \omega \rangle}
$$
$$
L_{Lie}^{\tan} = \tan\left\| W_{1}^{L} * W_{2}^{R} - \mathrm{Skew}\left( W_{\exp}^{\wedge} \right) \right\|^{2}
$$
$$
\begin{aligned}
L_{Lie}^{\tan} = \tan\Bigg[
& {}_{L}\left[ \tanh\left( \sum_{s=2}^{m} \left( t_{1}^{s} \cdot W_{Q} \wedge (t_{11}^{s} \cdot W_{K})^{T} \right) \right) \right]_{\text{token}_{j}\text{head}_{i}}^{\langle \omega, i \cdot \omega \rangle}
{}_{R}\left[ \tanh\left( \sum_{s=2}^{m} \left( t_{2}^{s} \cdot W_{K}^{T} \wedge t_{21}^{s} \cdot W_{Q} \right) \right) \right]_{\text{token}_{j}\text{head}_{i}}^{\langle \omega, i \cdot \omega \rangle} \\
& + \text{Skew}^{2}\left( W_{\exp}^{\wedge} \right) \\
& - 2{}_{L}\left[ \tanh\left( \sum_{s=2}^{m} \left( t_{1}^{s} \cdot W_{Q} \wedge (t_{11}^{s} \cdot W_{K})^{T} \right) \right) \right]_{\text{token}_{j}\text{head}_{i}}^{\langle \omega, i \cdot \omega \rangle}
{}_{R}\left[ \tanh\left( \sum_{s=2}^{m} \left( t_{2}^{s} \cdot W_{K}^{T} \wedge t_{21}^{s} \cdot W_{Q} \right) \right) \right]_{\text{token}_{j}\text{head}_{i}}^{\langle \omega, i \cdot \omega \rangle}
\text{Skew}\left( W_{\exp}^{\wedge} \right)
\Bigg]
\end{aligned}
$$
$$
\text{LayerNorm}(x_1, x_2, x_3) = \tanh(x_1, x_2, x_3)^2 \times \frac{x - \mu}{\sigma^2 + \varepsilon}, \quad \text{and} \quad \tanh(x_1, x_2, x_3)^2 \rightsquigarrow I
, \quad \text{and} \quad \
\mu = \text{np.mean}\left[ \tan\left( \left\| W_{1,2}^{L \times R} - \text{Skew}(W_{\exp}^{\wedge}) \right\|^2 + N_{1,2} - \frac{\pi}{4} \right) \right]
, \quad \text{and} \quad \
\sigma^2 = \text{np.var}\left( \tan\left[ \left\| W_{1,2}^{L \times R} - \text{Skew}(W_{\exp}^{\wedge}) \right\|^2 + N_{1,2} - \frac{\pi}{4} \right], \ \text{ddof} = 1 \right)
$$
🧠 思维增强架构
RLLM多模态可预测性思维增强收缩参数群，实现动态调整计算策略，具备AGI雏形特征。
⚡ 弹性稀疏注意力
ENL-MLA机制动态调整稀疏模式，避免传统Top-k的维度坍缩问题，计算复杂度降至O(NlogN)。
🌐 多模态融合
通过超球纤维丛进行模态融合，实现隐式统一表征，支持跨模态高维超切片滑动核痕特征优化。