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md/train/O-XJwyoIF-k/O-XJwyoIF-k.md

@@ -455,7 +455,7 @@ $$
 f : = \mathsf { d e c o d e } _ { M } ^ { \ddag } \circ \mathsf { m e m o r i z e } _ { K , M } ^ { \ddag } \circ \mathsf { e n c o d e } _ { K } ^ { \ddag } .
 $$
 
-small ε1, ε2, ε3 so that ωf0 (2−K ) + 2−M ≤ η2 and ωdecode‡M  Here, for any $\eta > 0$ , by choosing sufficiently large $\begin{array} { r } { \omega _ { \mathsf { d e c o d e } _ { M } ^ { \ddag } } \left( \omega _ { \mathsf { m e m o r i z e } _ { K , M } ^ { \ddag } } ( \varepsilon _ { 1 } ) + \varepsilon _ { 2 } \right) + \varepsilon _ { 3 } \le \frac { \eta } { 2 } } \end{array}$ $K , M$ , sufficiently large $\mathcal { T } _ { 2 } , \mathcal { T } _ { 3 }$ , and sufficiently , we have
+small ε1, ε2, ε3 so that ωf0 (2−K ) + 2−M ≤ η2 and ωdecode‡M  Here, for any $\eta > 0$ , by choosing sufficiently large $\begin{array} { r } { \omega _ { \mathsf { d e c o d e } _ { M } ^ { \ddag } } \left( \omega _ { \mathsf { m e m o r i z e } _ { K , M } ^ { \ddag } } ( \varepsilon _ { 1 } ) + \varepsilon _ { 2 } \right) + \varepsilon _ { 3 } \le \frac { \eta } { 2 } } \end{array}$ $K , M$ , sufficiently large $\mathcal { T } _ { 2 } , \mathcal { T } _ { 3 }$ , and sufficiently , we have
 
 $$
 \operatorname* { s u p } _ { x \in [ 0 , 1 ] ^ { d _ { x } } \setminus \mathcal { D } _ { \gamma } } \| f ^ { \prime } ( x ) - f ( x ) \| _ { \infty } \leq \eta \quad \mathrm { a n d } \quad f ( [ 0 , 1 ] ^ { d _ { x } } ) \subset [ - \frac { \eta } { 2 } , 1 + \frac { \eta } { 2 } ] ^ { d _ { x } }