Author Correction: An open-source family of large encoder-decoder foundation models for chemistry

Correction to: Communications Chemistry 10.1038/s42004-025-01585-0, published online 01 July 2025

In the version of this Article initially published, there were typographical errors in Equations (2) and (3), where transpose operations were inadvertently omitted, leading to apparent dimensional inconsistencies. Equations (2) and (3) have been corrected as follows:

$$\mathbf{z}=\left(\mathrm{LayerNorm}\left(\mathrm{GELU}\left({\mathbf{W}}_1^{\top }\mathbf{x}+{\mathbf{b}}_1\right)\right)\right){\mathbf{W}}_2$$ 2

where $\mathbf{x}\in {\mathbb{R}}^{D\times L}$, ${\mathbf{W}}_1\in {\mathbb{R}}^{D\times L}$, ${\mathbf{b}}_1\in {\mathbb{R}}^L$, and ${\mathbf{W}}_2\in {\mathbb{R}}^{L\times L}$, yielding $\mathbf{z}\in {\mathbb{R}}^L$;

$${\widehat{\mathbf{x}}}^{\top }=\left(\mathrm{LayerNorm}\left(\mathrm{GELU}\left(\mathbf{z}{\mathbf{W}}_3+{\mathbf{b}}_3\right)\right)\right){\mathbf{W}}_4$$ 3

where ${\mathbf{W}}_3\in {\mathbb{R}}^{L\times L}$, ${\mathbf{b}}_3\in {\mathbb{R}}^L$, and ${\mathbf{W}}_4\in {\mathbb{R}}^{L\times D}$, producing $\widehat{\mathbf{x}}\in {\mathbb{R}}^{D\times L}$.

For comparison, the original equations were written as

$$\mathbf{z}=\left(\mathrm{LayerNorm}\left(\mathrm{GELU}\left(\mathbf{x}{\mathbf{W}}_1+{\mathbf{b}}_1\right)\right)\right){\mathbf{W}}_2$$ 2

where $\mathbf{z}\in {\mathbb{R}}^L$, ${\mathbf{W}}_1\in {\mathbb{R}}^{D\times L}$, ${\mathbf{b}}_1\in {\mathbb{R}}^L$, and ${\mathbf{W}}_2\in {\mathbb{R}}^{L\times L}$;

$$\widehat{\mathbf{x}}=\left(\mathrm{LayerNorm}\left(\mathrm{GELU}\left(\mathbf{z}{\mathbf{W}}_3+{\mathbf{b}}_3\right)\right)\right){\mathbf{W}}_4$$ 3

where $\widehat{\mathbf{x}}\in {\mathbb{R}}^{D\times L}$, ${\mathbf{W}}_3\in {\mathbb{R}}^{L\times L}$, ${\mathbf{b}}_3\in {\mathbb{R}}^L$, ${\mathbf{W}}_4\in {\mathbb{R}}^{L\times D}$.

The equations are now amended in the HTML and PDF versions of the Article.