h_t = \mathbf{A}_t h_{t-1} + \mathbf{B}_t x_t \iff y = \text{SemiSeparable1D}(x) \star C

P(t \in \text{Layer}_k) = \text{TopK}(\mathbf{R}(x_t), C), \quad \text{FLOP}_{\text{saved}} \ge 50\%

\text{Score}(A) \propto N_{\text{samples}}^{\alpha} \cdot \exp(-\beta \cdot \text{Cost}(T))

\gamma = \mathbb{E}[\text{Accepted Tokens per Step}] > 2.5 \implies \text{Speedup} \approx \frac{\gamma}{1 + c}

\text{Attention}(Q, K, V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V

L(N, D) = E + \frac{A}{N^{\alpha}} + \frac{B}{D^{\beta}}, \quad N_{\text{opt}} \propto C^{0.5}, \, D_{\text{opt}} \propto C^{0.5}

\mathbf{R}_{\Theta, m}^d = \text{diag}\left( R_{\theta_1, m}, \dots, R_{\theta_{d/2}, m} \right) \implies \langle R_m q, R_n k \rangle = g(q, k, m-n)

\text{KV-Heads} = \frac{H_{\text{query}}}{G} \implies \text{Bellek Tasarrufu } \approx G\times

K(\mathbf{x}_i, \mathbf{x}_j) = \exp(-\gamma \|\mathbf{x}_i - \mathbf{x}_j\|^2) \implies \text{Sonsuz Boyutlu Hilbert Uzayı}

v_t(j) = \max_i \left( v_{t-1}(i) a_{ij} \right) b_j(y_t)

\text{XOR}(x_1, x_2) \text{ lineer ayrılamaz} \iff \nexists \, \mathbf{w} \text{ s.t. } \mathbf{w}^T \mathbf{x} > 0

E = -\frac{1}{2} \sum_{i,j} w_{ij} s_i s_j + \sum_i \theta_i s_i \implies \frac{dE}{dt} \le 0

P(v, h) = \frac{1}{Z} e^{-E(v,h)}, \quad E(v,h) = -\sum a_i v_i - \sum b_j h_j - \sum v_i h_j w_{ij}

\mathcal{H}(\mathbf{x}) = \mathcal{F}(\mathbf{x}, \{W_i\}) + \mathbf{x} \implies \frac{\partial \mathcal{E}}{\partial \mathbf{x}} = \frac{\partial \mathcal{E}}{\partial \mathcal{H}} \left( \frac{\partial \mathcal{F}}{\partial \mathbf{x}} + \mathbf{I} \right)

\mathcal{L}_{\text{BERT}} = -\sum_{i \in \text{Mask}} \log P(w_i | w_{\setminus i})

\text{P}(Y|X) \ll \sum_Z \text{P}(Y|Z, X) \cdot \text{P}(Z|X) \implies \text{Adım Adım Düşünmenin Gücü}

\mathbf{z}_{t-1} = \text{DiTBlock}(\mathbf{z}_t, t, c) \implies \text{U-Net Mimarisine Elveda}

\min_{\mathbb{P}} \text{KL}(\mathbb{P} \,\|\, \mathbb{R}) \quad \text{s.t.} \quad \mathbb{P}_0 = \mu_0, \, \mathbb{P}_1 = \mu_1