AI Pause Model Open it side by side with the explanations
Hover over a symbol to see its description. Red symbols are our estimates.
AIFM
d E d t = C t r a i n ( t ) S ( t ) (1) \frac{dE}{dt} = C_{train}(t)\, S(t) \tag{1} d t d E = C t r ain ( t ) S ( t ) ( 1 ) E ( t ) ≡ E p (2) E(t) \equiv E_p \tag{2} E ( t ) ≡ E p ( 2 ) C ( t ) = m C C A I F M ( t ) L H = m L L H A I F M ( t p ) (3) \begin{aligned}
C(t) &= m_C\, C^{\mathrm{AIFM}}(t) \\
L_H &= m_L\, L_H^{\mathrm{AIFM}}(t_p)
\end{aligned} \tag{3} C ( t ) L H = m C C AIFM ( t ) = m L L H AIFM ( t p ) ( 3 ) C = C t r a i n + C x p m + C a u t + C e x t (4) \begin{gathered}
C = C_{train} + C_{xpm} + C_{aut} + C_{ext}
\end{gathered} \tag{4} C = C t r ain + C x p m + C a u t + C e x t ( 4 ) C t r a i n ( t ) = 0 C a u t ( t ) = s a u t C ( t ) C e x t = s e x t C ( t p ) C x p m ( t ) = C ( t ) − C e x t − C a u t ( t ) (5) \begin{aligned}
C_{train}(t) &= 0 \\
C_{aut}(t) &= s_{aut}\, C(t) \\
C_{ext} &= s_{ext}\, C(t_p) \\
C_{xpm}(t) &= C(t) - C_{ext} - C_{aut}(t)
\end{aligned} \tag{5} C t r ain ( t ) C a u t ( t ) C e x t C x p m ( t ) = 0 = s a u t C ( t ) = s e x t C ( t p ) = C ( t ) − C e x t − C a u t ( t ) ( 5 ) G i = L H , i + η i C a u t , i L C = max ( ∫ 0 1 G i ρ C d i ) 1 / ρ C (6) \begin{gathered}
G_i = L_{H,i} + \eta_i\, C_{aut,i} \\
L_C = \max \left(\int_0^1 G_i^{\rho_C}\, di\right)^{1/\rho_C}
\end{gathered} \tag{6} G i = L H , i + η i C a u t , i L C = max ( ∫ 0 1 G i ρ C d i ) 1/ ρ C ( 6 ) ∫ 0 1 L H , i d i = L H , ∫ 0 1 C a u t , i d i = C a u t (7) \int_0^1 L_{H,i}\, di = L_H, \qquad \int_0^1 C_{aut,i}\, di = C_{aut} \tag{7} ∫ 0 1 L H , i d i = L H , ∫ 0 1 C a u t , i d i = C a u t ( 7 ) A ( E ) = min ( 1 , A ∞ 1 + e − k ( log E − x 0 ) ) (8) A(E) = \min\left(1, \frac{A_\infty}{1 + e^{-k (\log E - x_0)}}\right) \tag{8} A ( E ) = min ( 1 , 1 + e − k ( l o g E − x 0 ) A ∞ ) ( 8 ) A ( E i ) = i , A ( E A C ) = 1 (9) A(E_i) = i, \qquad A(E_{AC}) = 1 \tag{9} A ( E i ) = i , A ( E A C ) = 1 ( 9 ) η i ( E ) = { η i n i t ( E / E i ) η s l o p e , i ≤ A ( E ) 0 , i > A ( E ) (10) \eta_i(E) =
\begin{cases}
\eta_{init} \left(E / E_i\right)^{\eta_{slope}}, & i \le A(E) \\
0, & i > A(E)
\end{cases} \tag{10} η i ( E ) = { η ini t ( E / E i ) η s l o p e , 0 , i ≤ A ( E ) i > A ( E ) ( 10 ) X = [ α X C ~ x p m ρ X + ( 1 − α X ) L ~ C ρ X ] 1 / ρ X C ~ x p m = C x p m ζ , L ~ C = L C λ (11) \begin{gathered}
X = \Big[\alpha_X\, \tilde C_{xpm}^{\,\rho_X} + (1 - \alpha_X)\, \tilde L_C^{\,\rho_X}\Big]^{1/\rho_X} \\
\tilde C_{xpm} = C_{xpm}^{\zeta}, \qquad \tilde L_C = L_C^{\lambda}
\end{gathered} \tag{11} X = [ α X C ~ x p m ρ X + ( 1 − α X ) L ~ C ρ X ] 1/ ρ X C ~ x p m = C x p m ζ , L ~ C = L C λ ( 11 ) T A I S D ( E ) = T A C S D + s T ( log E − log E A C ) T A I ( E ) = T H ( T A I S D ( E ) ) T ( E ) = E Z [ max ( T H ( Z ) , T A I ( E ) ) ] Z ∼ N ( 0 , 1 ) (12) \begin{gathered}
T_{AI}^{SD}(E) = T_{AC}^{SD} + s_T \left(\log E - \log E_{AC}\right) \\
T_{AI}(E) = T_H\big(T_{AI}^{SD}(E)\big) \\
T(E) = \mathbb{E}_Z\Big[\max\big(T_H(Z), T_{AI}(E)\big)\Big] \\
Z \sim \mathcal{N}(0, 1)
\end{gathered} \tag{12} T A I S D ( E ) = T A C S D + s T ( log E − log E A C ) T A I ( E ) = T H ( T A I S D ( E ) ) T ( E ) = E Z [ max ( T H ( Z ) , T A I ( E ) ) ] Z ∼ N ( 0 , 1 ) ( 12 ) R E = T X (13) RE = T X \tag{13} R E = T X ( 13 ) R S ( t ) = ∫ − ∞ t R E d t ′ (14) RS(t) = \int_{-\infty}^{t} RE\, dt' \tag{14} R S ( t ) = ∫ − ∞ t R E d t ′ ( 14 ) AIFM
S = ( R S R S 0 ) 1 / β (15) S = \left(\frac{RS}{RS_0}\right)^{1/\beta} \tag{15} S = ( R S 0 R S ) 1/ β ( 15 ) R S s = X ( C s , L C ( N s , C a u t , s , E 2025 ) ) (16) RS_s = X\big(C_s, L_C(N_s, C_{aut,s}, E_{2025})\big) \tag{16} R S s = X ( C s , L C ( N s , C a u t , s , E 2025 ) ) ( 16 ) cell = R S ( t p + D ) − R S ( t p ) R S s = 1 R S s ∫ t p t p + D R E d t (17) \text{cell} = \frac{RS(t_p + D) - RS(t_p)}{RS_s} = \frac{1}{RS_s} \int_{t_p}^{t_p + D} RE\, dt \tag{17} cell = R S s R S ( t p + D ) − R S ( t p ) = R S s 1 ∫ t p t p + D R E d t ( 17 ) AI safety work produced in a Full Trust pause, in years of the whole 2025 AI safety field's work.
Staff (18) L H = N e + N v L_H = N_e + N_v L H = N e + N v Compute (18) C x p m = C e + C r C_{xpm} = C_e + C_r C x p m = C e + C r Research (19), (20) X e X_e X e with taste
T ( E p , N e ) T(E_p, N_e) T ( E p , N e ) All papers ∑ i = 1 n \sum_{i=1}^{n} ∑ i = 1 n Paper (22) i = 1 , … , n i = 1, \dots, n i = 1 , … , n Research (24) r i = r s l ∞ ( c i / c ˉ s ) ζ p r_i = r_s\, l_\infty (c_i / \bar c_s)^{\zeta_p} r i = r s l ∞ ( c i / c ˉ s ) ζ p Idea quality (30) v i v_i v i Research effort (30) R E i = T v i r i RE_i = T v_i r_i R E i = T v i r i Review time (25) m h τ m_h \tau m h τ Checked papers (31) ∑ i = 1 n χ i \sum_{i=1}^{n} \chi_i ∑ i = 1 n χ i Exploration (22) C e / M C_e / M C e / M Re-runs (34) C r = κ c ψ C e / M C_r = \kappa_c \psi\, C_e / M C r = κ c ψ C e / M
Research effort (30) R E e = T X e RE_e = T X_e R E e = T X e Verified (21) R E v = φ h R E e RE^v = \varphi_h RE_e R E v = φ h R E e Review work (26) W = m h n τ W = m_h n \tau W = m h n τ Verifiers (30) q W ≤ N v q\, W \le N_v q W ≤ N v The labs pick the N e N_e N e R E v RE^v R E v C x p m = C e + C r L H = N e + N v (18) \begin{gathered}
C_{xpm} = C_e + C_r \\
L_H = N_e + N_v
\end{gathered} \tag{18} C x p m = C e + C r L H = N e + N v ( 18 ) X e = X ( C e , L C ( N e , C a u t , E p ) ) (19) X_e = X\big(C_e, L_C(N_e, C_{aut}, E_p)\big) \tag{19} X e = X ( C e , L C ( N e , C a u t , E p ) ) ( 19 ) T ( E , N e ) = T A I ( E ) + ∫ z ^ ∞ max ( T H ( z ) − T A I ( E ) , 0 ) d Φ ( z ) z ^ = Φ − 1 ( 1 − N e L H ) , T ( E , L H ) = T ( E ) (20) \begin{gathered}
T(E, N_e) = T_{AI}(E) + \int_{\hat z}^{\infty} \max\big(T_H(z) - T_{AI}(E), 0\big)\, d\Phi(z) \\
\hat z = \Phi^{-1}\left(1 - \frac{N_e}{L_H}\right), \qquad T(E, L_H) = T(E)
\end{gathered} \tag{20} T ( E , N e ) = T A I ( E ) + ∫ z ^ ∞ max ( T H ( z ) − T A I ( E ) , 0 ) d Φ ( z ) z ^ = Φ − 1 ( 1 − L H N e ) , T ( E , L H ) = T ( E ) ( 20 ) R E e = T ( E p , N e ) X e R E v = φ h R E e (21) \begin{gathered}
RE_e = T(E_p, N_e)\, X_e \\
RE^v = \varphi_h\, RE_e
\end{gathered} \tag{21} R E e = T ( E p , N e ) X e R E v = φ h R E e ( 21 ) X e = ∑ i = 1 n r i , C e = M ∑ i = 1 n c i = M n c ˉ (22) X_e = \sum_{i=1}^{n} r_i, \qquad C_e = M \sum_{i=1}^{n} c_i = M n \bar c \tag{22} X e = i = 1 ∑ n r i , C e = M i = 1 ∑ n c i = M n c ˉ ( 22 ) not in the model
r i = r s [ l ∞ ρ p ( c i c ˉ s ) ζ p ρ p + c ∞ ρ p ( l i l ˉ s ) λ ρ p ] 1 / ρ p l ∞ ρ p + c ∞ ρ p = 1 ρ p < 0 , l i → ∞ : r i → r s [ l ∞ ρ p ( c i c ˉ s ) ζ p ρ p ] 1 / ρ p (23) \begin{gathered}
r_i = r_s \left[l_\infty^{\rho_p} \left(\frac{c_i}{\bar c_s}\right)^{\zeta_p \rho_p} + c_\infty^{\rho_p} \left(\frac{l_i}{\bar l_s}\right)^{\lambda \rho_p}\right]^{1/\rho_p} \\
l_\infty^{\rho_p} + c_\infty^{\rho_p} = 1 \\
\rho_p < 0, \quad l_i \to \infty: \qquad r_i \to r_s \left[l_\infty^{\rho_p} \left(\frac{c_i}{\bar c_s}\right)^{\zeta_p \rho_p}\right]^{1/\rho_p}
\end{gathered} \tag{23} r i = r s [ l ∞ ρ p ( c ˉ s c i ) ζ p ρ p + c ∞ ρ p ( l ˉ s l i ) λ ρ p ] 1/ ρ p l ∞ ρ p + c ∞ ρ p = 1 ρ p < 0 , l i → ∞ : r i → r s [ l ∞ ρ p ( c ˉ s c i ) ζ p ρ p ] 1/ ρ p ( 23 ) r i = r s l ∞ ( c i c ˉ s ) ζ p ln c i ∼ N ( ln c ˉ − σ c 2 2 , σ c 2 ) (24) \begin{gathered}
r_i = r_s\, l_\infty \left(\frac{c_i}{\bar c_s}\right)^{\zeta_p} \\
\ln c_i \sim \mathcal{N}\left(\ln \bar c - \frac{\sigma_c^2}{2}, \sigma_c^2\right)
\end{gathered} \tag{24} r i = r s l ∞ ( c ˉ s c i ) ζ p ln c i ∼ N ( ln c ˉ − 2 σ c 2 , σ c 2 ) ( 24 ) t s = N s n s τ = κ h t s + p h log 10 n n s (25) \begin{gathered}
t_s = \frac{N_s}{n_s} \\
\tau = \kappa_h t_s + p_h \log_{10} \frac{n}{n_s}
\end{gathered} \tag{25} t s = n s N s τ = κ h t s + p h log 10 n s n ( 25 ) W = m h n τ = m h N s n n s ( κ h + p h t s log 10 n n s ) (26) W = m_h\, n\, \tau = m_h N_s\, \frac{n}{n_s} \left(\kappa_h + \frac{p_h}{t_s} \log_{10} \frac{n}{n_s}\right) \tag{26} W = m h n τ = m h N s n s n ( κ h + t s p h log 10 n s n ) ( 26 ) k X = X e X s = n n s ⏟ paper count vs 2025 ⋅ l ∞ ( c ˉ c ˉ s ) ζ p ⏟ research per paper vs 2025 (27) k_X = \frac{X_e}{X_s} = \underbrace{\frac{n}{n_s}}_{\substack{\text{paper count} \\ \text{vs 2025}}} \cdot \underbrace{l_\infty \left(\frac{\bar c}{\bar c_s}\right)^{\zeta_p}}_{\substack{\text{research per paper} \\ \text{vs 2025}}} \tag{27} k X = X s X e = paper count vs 2025 n s n ⋅ research per paper vs 2025 l ∞ ( c ˉ s c ˉ ) ζ p ( 27 ) Derivation X e = r s l ∞ ∑ i = 1 n ( c ˉ c ˉ s ⋅ c i c ˉ ) ζ p = n r s l ∞ ( c ˉ c ˉ s ) ζ p E e [ ( c i c ˉ ) ζ p ] X s = r s ∑ i = 1 n s ( c i c ˉ s ) ζ p = n s r s E s [ ( c i c ˉ s ) ζ p ] E e [ ( c i c ˉ ) ζ p ] = E s [ ( c i c ˉ s ) ζ p ] = e − ζ p ( 1 − ζ p ) σ c 2 / 2 \begin{gather*}
X_e = r_s\, l_\infty \sum_{i=1}^{n} \left(\frac{\bar c}{\bar c_s} \cdot \frac{c_i}{\bar c}\right)^{\zeta_p} \\
= n\, r_s\, l_\infty \left(\frac{\bar c}{\bar c_s}\right)^{\zeta_p} \mathbb{E}_e\left[\left(\frac{c_i}{\bar c}\right)^{\zeta_p}\right] \tag{27a} \\
X_s = r_s \sum_{i=1}^{n_s} \left(\frac{c_i}{\bar c_s}\right)^{\zeta_p} = n_s\, r_s\, \mathbb{E}_s\left[\left(\frac{c_i}{\bar c_s}\right)^{\zeta_p}\right] \tag{27b} \\
\mathbb{E}_e\left[\left(\frac{c_i}{\bar c}\right)^{\zeta_p}\right] = \mathbb{E}_s\left[\left(\frac{c_i}{\bar c_s}\right)^{\zeta_p}\right] = e^{-\zeta_p (1 - \zeta_p) \sigma_c^2 / 2} \tag{27c}
\end{gather*} X e = r s l ∞ i = 1 ∑ n ( c ˉ s c ˉ ⋅ c ˉ c i ) ζ p = n r s l ∞ ( c ˉ s c ˉ ) ζ p E e [ ( c ˉ c i ) ζ p ] X s = r s i = 1 ∑ n s ( c ˉ s c i ) ζ p = n s r s E s [ ( c ˉ s c i ) ζ p ] E e [ ( c ˉ c i ) ζ p ] = E s [ ( c ˉ s c i ) ζ p ] = e − ζ p ( 1 − ζ p ) σ c 2 /2 ( 27a ) ( 27b ) ( 27c ) c ˉ c ˉ s = C e / ( M n ) C s / ( M n s ) = k C n / n s , k C = C e C s (28) \frac{\bar c}{\bar c_s} = \frac{C_e / (M n)}{C_s / (M n_s)} = \frac{k_C}{n / n_s}, \qquad k_C = \frac{C_e}{C_s} \tag{28} c ˉ s c ˉ = C s / ( M n s ) C e / ( M n ) = n / n s k C , k C = C s C e ( 28 ) n n s = ( k X l ∞ k C ζ p ) 1 / ( 1 − ζ p ) (29) \frac{n}{n_s} = \left(\frac{k_X}{l_\infty k_C^{\zeta_p}}\right)^{1/(1 - \zeta_p)} \tag{29} n s n = ( l ∞ k C ζ p k X ) 1/ ( 1 − ζ p ) ( 29 ) Derivation k X = n n s l ∞ ( k C n / n s ) ζ p = l ∞ k C ζ p ( n n s ) 1 − ζ p ( n n s ) 1 − ζ p = k X l ∞ k C ζ p \begin{gather*}
k_X = \frac{n}{n_s}\, l_\infty \left(\frac{k_C}{n / n_s}\right)^{\zeta_p} = l_\infty\, k_C^{\zeta_p} \left(\frac{n}{n_s}\right)^{1 - \zeta_p} \tag{29a} \\
\left(\frac{n}{n_s}\right)^{1 - \zeta_p} = \frac{k_X}{l_\infty k_C^{\zeta_p}} \tag{29b}
\end{gather*} k X = n s n l ∞ ( n / n s k C ) ζ p = l ∞ k C ζ p ( n s n ) 1 − ζ p ( n s n ) 1 − ζ p = l ∞ k C ζ p k X ( 29a ) ( 29b )
Number of papers n ( t ) n(t) n ( t ) our dataset .
q = min ( 1 , N v W ) v i ∼ P a r e t o ( v m , α v ) , E [ v i ] = 1 R E i = T v i r i , ∑ i = 1 n R E i = T X e = R E e (30) \begin{gathered}
q = \min\left(1, \frac{N_v}{W}\right) \\
v_i \sim \mathrm{Pareto}(v_m, \alpha_v), \qquad \mathbb{E}[v_i] = 1 \\
RE_i = T v_i r_i, \qquad \sum_{i=1}^{n} RE_i = T X_e = RE_e
\end{gathered} \tag{30} q = min ( 1 , W N v ) v i ∼ Pareto ( v m , α v ) , E [ v i ] = 1 R E i = T v i r i , i = 1 ∑ n R E i = T X e = R E e ( 30 ) research effort
R E i RE_i R E i Each dot is a simulated paper, lying on the surface of research effort over its idea quality and compute. The verifiers check the papers above the bar.
χ i = { 1 , R E i among the top q of the papers 0 , otherwise φ h ( q ) = ∑ i = 1 n χ i R E i ∑ i = 1 n R E i ψ ( q ) = ∑ i = 1 n χ i c i ∑ i = 1 n c i (31) \begin{gathered}
\chi_i =
\begin{cases}
1, & RE_i \text{ among the top } q \text{ of the papers} \\
0, & \text{otherwise}
\end{cases} \\
\varphi_h(q) = \dfrac{\sum_{i=1}^{n} \chi_i\, RE_i}{\sum_{i=1}^{n} RE_i} \\[4pt]
\psi(q) = \dfrac{\sum_{i=1}^{n} \chi_i\, c_i}{\sum_{i=1}^{n} c_i}
\end{gathered} \tag{31} χ i = { 1 , 0 , R E i among the top q of the papers otherwise φ h ( q ) = ∑ i = 1 n R E i ∑ i = 1 n χ i R E i ψ ( q ) = ∑ i = 1 n c i ∑ i = 1 n χ i c i ( 31 ) ln R E i = ln K + ε i α v + σ y ξ i ε i ∼ E x p ( 1 ) , ξ i ∼ N ( 0 , 1 ) , σ y = ζ p σ c K = T r s l ∞ v m ( c ~ c ˉ s ) ζ p , c ~ = c ˉ e − σ c 2 / 2 (32) \begin{gathered}
\ln RE_i = \ln K + \frac{\varepsilon_i}{\alpha_v} + \sigma_y \xi_i \\
\varepsilon_i \sim \mathrm{Exp}(1), \qquad \xi_i \sim \mathcal{N}(0, 1), \qquad \sigma_y = \zeta_p \sigma_c \\
K = T r_s\, l_\infty\, v_m \left(\frac{\tilde c}{\bar c_s}\right)^{\zeta_p}, \qquad \tilde c = \bar c\, e^{-\sigma_c^2 / 2}
\end{gathered} \tag{32} ln R E i = ln K + α v ε i + σ y ξ i ε i ∼ Exp ( 1 ) , ξ i ∼ N ( 0 , 1 ) , σ y = ζ p σ c K = T r s l ∞ v m ( c ˉ s c ~ ) ζ p , c ~ = c ˉ e − σ c 2 /2 ( 32 ) Derivation P ( v i ≥ v ) = ( v m v ) α v = P ( ε i ≥ α v ln v v m ) v i = v m e ε i / α v c i = c ~ e σ c ξ i R E i = T v i r s l ∞ ( c i c ˉ s ) ζ p = K e ε i / α v e ζ p σ c ξ i \begin{gather*}
\mathbb{P}(v_i \ge v) = \left(\frac{v_m}{v}\right)^{\alpha_v} = \mathbb{P}\left(\varepsilon_i \ge \alpha_v \ln \frac{v}{v_m}\right) \\
v_i = v_m e^{\varepsilon_i / \alpha_v} \tag{32a} \\
c_i = \tilde c\, e^{\sigma_c \xi_i} \tag{32b} \\
RE_i = T v_i r_s\, l_\infty \left(\frac{c_i}{\bar c_s}\right)^{\zeta_p} \\
= K e^{\varepsilon_i / \alpha_v} e^{\zeta_p \sigma_c \xi_i} \tag{32c}
\end{gather*} P ( v i ≥ v ) = ( v v m ) α v = P ( ε i ≥ α v ln v m v ) v i = v m e ε i / α v c i = c ~ e σ c ξ i R E i = T v i r s l ∞ ( c ˉ s c i ) ζ p = K e ε i / α v e ζ p σ c ξ i ( 32a ) ( 32b ) ( 32c ) χ i = 1 ⟺ ε i α v + σ y ξ i ≥ u G ( x , a ) = Φ ( − x σ y ) + e − a x + a 2 σ y 2 / 2 Φ ( x σ y − a σ y ) q = G ( u , α v ) ψ = G ( u − σ y σ c , α v ) φ h = G ( u − σ y 2 , α v − 1 ) (33) \begin{aligned}
\chi_i = 1 &\iff \frac{\varepsilon_i}{\alpha_v} + \sigma_y \xi_i \ge u \\
G(x, a) &= \Phi\left(-\frac{x}{\sigma_y}\right) \\
&\quad + e^{-a x + a^2 \sigma_y^2 / 2}\, \Phi\left(\frac{x}{\sigma_y} - a \sigma_y\right) \\
q &= G(u, \alpha_v) \\
\psi &= G(u - \sigma_y \sigma_c, \alpha_v) \\
\varphi_h &= G(u - \sigma_y^2, \alpha_v - 1)
\end{aligned} \tag{33} χ i = 1 G ( x , a ) q ψ φ h ⟺ α v ε i + σ y ξ i ≥ u = Φ ( − σ y x ) + e − a x + a 2 σ y 2 /2 Φ ( σ y x − a σ y ) = G ( u , α v ) = G ( u − σ y σ c , α v ) = G ( u − σ y 2 , α v − 1 ) ( 33 ) Derivation q = E [ χ i ] , ψ = E [ χ i c i ] E [ c i ] φ h = E [ χ i R E i ] E [ R E i ] G ( x , a ) = P ( ε i a + σ y ξ i ≥ x ) = E [ min ( 1 , e − a ( x − σ y ξ i ) ) ] E [ f ( ξ i ) e δ ξ i − δ 2 / 2 ] = E [ f ( ξ i + δ ) ] E [ 1 [ σ y ξ i < x ] e a σ y ξ i ] = e a 2 σ y 2 / 2 Φ ( x σ y − a σ y ) v α v v m α v v α v + 1 = ( α v − 1 ) v m α v − 1 v α v , v m = 1 − 1 α v c i E [ c i ] = e σ c ξ i − σ c 2 / 2 R E i E [ R E i ] = v i e σ y ξ i − σ y 2 / 2 \begin{gather*}
q = \mathbb{E}[\chi_i], \qquad \psi = \frac{\mathbb{E}[\chi_i c_i]}{\mathbb{E}[c_i]} \\
\varphi_h = \frac{\mathbb{E}[\chi_i RE_i]}{\mathbb{E}[RE_i]} \tag{33a} \\
G(x, a) = \mathbb{P}\left(\frac{\varepsilon_i}{a} + \sigma_y \xi_i \ge x\right) \\
= \mathbb{E}\left[\min\left(1, e^{-a (x - \sigma_y \xi_i)}\right)\right] \tag{33b} \\
\mathbb{E}\left[f(\xi_i)\, e^{\delta \xi_i - \delta^2 / 2}\right] = \mathbb{E}\left[f(\xi_i + \delta)\right] \tag{33c} \\
\mathbb{E}\left[\mathbf{1}[\sigma_y \xi_i < x]\, e^{a \sigma_y \xi_i}\right] \\
= e^{a^2 \sigma_y^2 / 2}\, \Phi\left(\frac{x}{\sigma_y} - a \sigma_y\right) \tag{33d} \\
v\, \frac{\alpha_v v_m^{\alpha_v}}{v^{\alpha_v + 1}} = \frac{(\alpha_v - 1)\, v_m^{\alpha_v - 1}}{v^{\alpha_v}}, \qquad v_m = 1 - \frac{1}{\alpha_v} \tag{33e} \\
\frac{c_i}{\mathbb{E}[c_i]} = e^{\sigma_c \xi_i - \sigma_c^2 / 2} \\
\frac{RE_i}{\mathbb{E}[RE_i]} = v_i\, e^{\sigma_y \xi_i - \sigma_y^2 / 2} \tag{33f}
\end{gather*} q = E [ χ i ] , ψ = E [ c i ] E [ χ i c i ] φ h = E [ R E i ] E [ χ i R E i ] G ( x , a ) = P ( a ε i + σ y ξ i ≥ x ) = E [ min ( 1 , e − a ( x − σ y ξ i ) ) ] E [ f ( ξ i ) e δ ξ i − δ 2 /2 ] = E [ f ( ξ i + δ ) ] E [ 1 [ σ y ξ i < x ] e a σ y ξ i ] = e a 2 σ y 2 /2 Φ ( σ y x − a σ y ) v v α v + 1 α v v m α v = v α v ( α v − 1 ) v m α v − 1 , v m = 1 − α v 1 E [ c i ] c i = e σ c ξ i − σ c 2 /2 E [ R E i ] R E i = v i e σ y ξ i − σ y 2 /2 ( 33a ) ( 33b ) ( 33c ) ( 33d ) ( 33e ) ( 33f ) C r = κ c ∑ i = 1 n χ i c i = κ c M ψ C e C e ( 1 + κ c M ψ ) = C x p m (34) \begin{gathered}
C_r = \kappa_c \sum_{i=1}^{n} \chi_i c_i = \frac{\kappa_c}{M} \psi C_e \\
C_e \left(1 + \frac{\kappa_c}{M} \psi\right) = C_{xpm}
\end{gathered} \tag{34} C r = κ c i = 1 ∑ n χ i c i = M κ c ψ C e C e ( 1 + M κ c ψ ) = C x p m ( 34 ) max N e R E v (35) \max_{N_e} RE^v \tag{35} N e max R E v ( 35 ) N h = max ( 0 , N e + W − L H ) N v = min ( W , L H − N e ) (36) \begin{gathered}
N_h = \max\big(0, N_e + W - L_H\big) \\
N_v = \min\big(W, L_H - N_e\big)
\end{gathered} \tag{36} N h = max ( 0 , N e + W − L H ) N v = min ( W , L H − N e ) ( 36 ) φ h = ψ = 1 C e = C x p m 1 + κ c / M , R E v = R E e (37) \begin{gathered}
\varphi_h = \psi = 1 \\
C_e = \frac{C_{xpm}}{1 + \kappa_c / M}, \qquad RE^v = RE_e
\end{gathered} \tag{37} φ h = ψ = 1 C e = 1 + κ c / M C x p m , R E v = R E e ( 37 ) cell = { full trust (17) , E p < E A C 1 R S s ∫ t p t p + D R E v d t , E p ≥ E A C (38) \text{cell} =
\begin{cases}
\text{full trust (17)}, & E_p < E_{AC} \\[4pt]
\dfrac{1}{RS_s} \displaystyle\int_{t_p}^{t_p + D} RE^v\, dt, & E_p \ge E_{AC}
\end{cases} \tag{38} cell = ⎩ ⎨ ⎧ full trust (17) , R S s 1 ∫ t p t p + D R E v d t , E p < E A C E p ≥ E A C ( 38 ) Unlimited hiring
Only research that humans reviewed and reproduced counts. Gray numbers are Full Trust's: before AC there is nothing to verify.
Staff (39) N p + N v ≤ L H N_p + N_v \le L_H N p + N v ≤ L H Compute (39) C x p m = C e + C r C_{xpm} = C_e + C_r C x p m = C e + C r Research (40), (41) X e X_e X e at
E A C E_{AC} E A C with taste
T w T_w T w Planned papers (45) a random
q p q_p q p Paper (22) i = 1 , … , n i = 1, \dots, n i = 1 , … , n Research (24) r i = r s l ∞ ( c i / c ˉ s ) ζ p r_i = r_s\, l_\infty (c_i / \bar c_s)^{\zeta_p} r i = r s l ∞ ( c i / c ˉ s ) ζ p Idea quality (30) v i v_i v i Research effort (43) R E i = T w v i r i RE_i = T_w v_i r_i R E i = T w v i r i Planning time (42) m p τ p m_p \tau_p m p τ p Review time (42) m h τ m_h \tau m h τ Checked papers (45) the top
q / q p q / q_p q / q p Planned (45) F = q p n F = q_p n F = q p n Checked (45) V = q n V = q\, n V = q n Exploration (47) q p C e / M q_p C_e / M q p C e / M Re-runs (47) C r = κ c q p ψ C e / M C_r = \kappa_c q_p \psi\, C_e / M C r = κ c q p ψ C e / M Research (43) q p X e q_p X_e q p X e
Research effort (46) q p T w X e q_p T_w X_e q p T w X e Verified (46) R E v = q p φ h T w X e RE^v = q_p \varphi_h T_w X_e R E v = q p φ h T w X e Planners (42) N p = F m p τ p N_p = F m_p \tau_p N p = F m p τ p
Review work (42) F m h τ F m_h \tau F m h τ Verifiers (42) V m h τ ≤ N v V m_h \tau \le N_v V m h τ ≤ N v Verifiers check the top q / q p q / q_p q / q p φ h \varphi_h φ h ψ \psi ψ q / q p q / q_p q / q p N e → 0 N p + N v ≤ L H C x p m = C e + C r (39) \begin{gathered}
N_e \to 0 \\
N_p + N_v \le L_H \\
C_{xpm} = C_e + C_r
\end{gathered} \tag{39} N e → 0 N p + N v ≤ L H C x p m = C e + C r ( 39 ) X e = X ( C e , L C ( 0 , C a u t , E A C ) ) (40) X_e = X\big(C_e, L_C(0, C_{aut}, E_{AC})\big) \tag{40} X e = X ( C e , L C ( 0 , C a u t , E A C ) ) ( 40 ) T ( E , 0 ) = T A I ( E ) T w = ( 1 − w ) T A I ( E A C ) + w T A I ( E p ) (41) \begin{gathered}
T(E, 0) = T_{AI}(E) \\
T_w = (1 - w)\, T_{AI}(E_{AC}) + w\, T_{AI}(E_p)
\end{gathered} \tag{41} T ( E , 0 ) = T A I ( E ) T w = ( 1 − w ) T A I ( E A C ) + w T A I ( E p ) ( 41 ) F = min ( n , N p m p τ p ) , V = min ( F , N v m h τ ) m p τ p = κ p t s + p p log 10 F n s , τ = κ h t s + p h log 10 F n s (42) \begin{gathered}
F = \min\left(n, \frac{N_p}{m_p \tau_p}\right), \qquad V = \min\left(F, \frac{N_v}{m_h \tau}\right) \\
m_p \tau_p = \kappa_p t_s + p_p \log_{10} \frac{F}{n_s}, \qquad \tau = \kappa_h t_s + p_h \log_{10} \frac{F}{n_s}
\end{gathered} \tag{42} F = min ( n , m p τ p N p ) , V = min ( F , m h τ N v ) m p τ p = κ p t s + p p log 10 n s F , τ = κ h t s + p h log 10 n s F ( 42 ) R E v = φ h ( V F ) F T w r ˉ r ˉ = X e n (43) \begin{gathered}
RE^v = \varphi_h\left(\frac{V}{F}\right) F\, T_w \bar r \\
\bar r = \frac{X_e}{n}
\end{gathered} \tag{43} R E v = φ h ( F V ) F T w r ˉ r ˉ = n X e ( 43 ) W p = n m p τ p ∣ F = n = N s n n s ( κ p + p p t s log 10 n n s ) (44) W_p = n\, m_p \tau_p \big|_{F = n} = N_s\, \frac{n}{n_s} \left(\kappa_p + \frac{p_p}{t_s} \log_{10} \frac{n}{n_s}\right) \tag{44} W p = n m p τ p F = n = N s n s n ( κ p + t s p p log 10 n s n ) ( 44 ) q p = F n , q p = 1 ⟺ N p ≥ W p q = V n = min ( q p , N v n m h τ ) (45) \begin{gathered}
q_p = \frac{F}{n}, \qquad q_p = 1 \iff N_p \ge W_p \\
q = \frac{V}{n} = \min\left(q_p, \frac{N_v}{n\, m_h \tau}\right)
\end{gathered} \tag{45} q p = n F , q p = 1 ⟺ N p ≥ W p q = n V = min ( q p , n m h τ N v ) ( 45 ) R E v = q p φ h ( q q p ) T w X e G ( u , α v ) = q q p φ h = G ( u − σ y 2 , α v − 1 ) , ψ = G ( u − σ y σ c , α v ) (46) \begin{gathered}
RE^v = q_p\, \varphi_h\left(\frac{q}{q_p}\right) T_w X_e \\
G(u, \alpha_v) = \frac{q}{q_p} \\
\varphi_h = G(u - \sigma_y^2, \alpha_v - 1), \qquad \psi = G(u - \sigma_y \sigma_c, \alpha_v)
\end{gathered} \tag{46} R E v = q p φ h ( q p q ) T w X e G ( u , α v ) = q p q φ h = G ( u − σ y 2 , α v − 1 ) , ψ = G ( u − σ y σ c , α v ) ( 46 ) C r = κ c M q p ψ ( q q p ) C e C e ( 1 + κ c M q p ψ ( q q p ) ) = C x p m (47) \begin{gathered}
C_r = \frac{\kappa_c}{M}\, q_p\, \psi\left(\frac{q}{q_p}\right) C_e \\
C_e \left(1 + \frac{\kappa_c}{M}\, q_p\, \psi\left(\frac{q}{q_p}\right)\right) = C_{xpm}
\end{gathered} \tag{47} C r = M κ c q p ψ ( q p q ) C e C e ( 1 + M κ c q p ψ ( q p q ) ) = C x p m ( 47 ) max N p R E v (48) \max_{N_p} RE^v \tag{48} N p max R E v ( 48 ) N h = max ( 0 , W p + W − L H ) (49) N_h = \max\big(0, W_p + W - L_H\big) \tag{49} N h = max ( 0 , W p + W − L H ) ( 49 ) q p = q = 1 C e = C x p m 1 + κ c / M , R E v = T w X e N p + N v = min ( L H , W p + W ) (50) \begin{gathered}
q_p = q = 1 \\
C_e = \frac{C_{xpm}}{1 + \kappa_c / M}, \qquad RE^v = T_w X_e \\
N_p + N_v = \min\big(L_H, W_p + W\big)
\end{gathered} \tag{50} q p = q = 1 C e = 1 + κ c / M C x p m , R E v = T w X e N p + N v = min ( L H , W p + W ) ( 50 ) cell = { results verification (38) , E p < E S A R 1 R S s ∫ t p t p + D R E v d t , E p ≥ E S A R (51) \text{cell} =
\begin{cases}
\text{results verification (38)}, & E_p < E_{SAR} \\[4pt]
\dfrac{1}{RS_s} \displaystyle\int_{t_p}^{t_p + D} RE^v\, dt, & E_p \ge E_{SAR}
\end{cases} \tag{51} cell = ⎩ ⎨ ⎧ results verification (38) , R S s 1 ∫ t p t p + D R E v d t , E p < E S A R E p ≥ E S A R ( 51 ) Unlimited hiring
Only research that humans planned, reviewed and reproduced counts. Gray numbers are Results Verification's: before SAR there is nothing to compartmentalize. The main page shows this table.
Engineer's coding labor (40) L C ( 0 , C a u t , E A C ) L_C(0, C_{aut}, E_{AC}) L C ( 0 , C a u t , E A C ) Auditors (52) N a N_a N a of the
W a W_a W a needed
Approved coding labor (52) L C a L_C^a L C a Research (53) X e = X ( C e , L C a ) X_e = X(C_e, L_C^a) X e = X ( C e , L C a ) Verified (46) R E v = q p φ h ( q / q p ) T w X e RE^v = q_p\, \varphi_h(q / q_p)\, T_w X_e R E v = q p φ h ( q / q p ) T w X e From the research on, everything is as in Compartmentalization (41)–(50). W a = κ a L C ( 0 , C a u t , E A C ) L C a = min ( L C ( 0 , C a u t , E A C ) , N a κ a ) (52) \begin{gathered}
W_a = \kappa_a\, L_C(0, C_{aut}, E_{AC}) \\
L_C^a = \min\left(L_C(0, C_{aut}, E_{AC}), \frac{N_a}{\kappa_a}\right)
\end{gathered} \tag{52} W a = κ a L C ( 0 , C a u t , E A C ) L C a = min ( L C ( 0 , C a u t , E A C ) , κ a N a ) ( 52 ) X e = X ( C e , L C a ) (53) X_e = X\big(C_e, L_C^a\big) \tag{53} X e = X ( C e , L C a ) ( 53 ) cell = { compartmentalization (51) , E p < E S A R 1 R S s ∫ t p t p + D R E v d t , E p ≥ E S A R (54) \text{cell} =
\begin{cases}
\text{compartmentalization (51)}, & E_p < E_{SAR} \\[4pt]
\dfrac{1}{RS_s} \displaystyle\int_{t_p}^{t_p + D} RE^v\, dt, & E_p \ge E_{SAR}
\end{cases} \tag{54} cell = ⎩ ⎨ ⎧ compartmentalization (51) , R S s 1 ∫ t p t p + D R E v d t , E p < E S A R E p ≥ E S A R ( 54 ) Unlimited hiring
Only research that humans planned, approved, reviewed and reproduced counts. Gray numbers are Results Verification's: before SAR there is nothing to compartmentalize.
Pause 3 years AI safety years
AI safety years with N a N_a N a