\begin{algorithm}[htbp]
\caption{Noisy Nodes algorithm}\label{alg:nn}
\begin{algorithmic}[1]
\Require
\Statex$\tau$: Scale of coordinate noise
\Statex$GNN_{\theta}$: Graph Neural Network with parameter $\theta$
\Statex ${\rm NoiseHead}_{\theta_{n}}$: Network module with parameter $\theta_{n}$ for prediction of node-level noise of each atom
\Statex ${\rm LabelHead}_{\theta_{l}}$: Network module with parameter $\theta_{l}$ for prediction of graph-level label of $x_{i}$
\Statex$X$: Training dataset
\Statex$x_i$: Input conformation
\Statex$y_i$: Label of $x_i$
\Statex$T$: Training steps
\Statex$\mathcal N$: Gaussian distribution
\Statex$\lambda_{p}$: Loss weight of property prediction loss
\Statex$\lambda_{n}$: Loss weight of Noisy Nodes loss
\While{$T \neq 0$}
    \State $x_i, y_i$ = dataloader($X$)  \Comment{random sample $x_i$ and corresponding label $y_i$ from $X$}
    \State  $\tilde{x} = x_{i} + \Delta{x_i}$ , where $\Delta{x_i} \sim \mathcal{N}(0, {\tau}^2I_{3N})$, $N$ is atom number of $x_i$
    \State $y_{i}^{pred}={\rm LabelHead}_{\theta_{l}}(GNN_{\theta}(\tilde{x}))$
    \State $\Delta{x_i}^{pred}={\rm NoiseHead}_{\theta_{n}}(GNN_{\theta}(\tilde{x}))$
    \State Loss = $\lambda_{p}$PropertyPredictionLoss$(y_{i}^{pred}, y_i)$+$\lambda_{n}||\Delta{x_i}^{pred} - \Delta{x_i}||_{2}^{2}$
    \State Optimise(Loss)
    \State $T = T - 1$
\EndWhile
\end{algorithmic}
\end{algorithm}

\begin{algorithm}
[htbp]
\caption{Noisy Nodes algorithm}\begin{algorithmic}
[1]
\Require
\Statex$\tau$: Scale of coordinate noise
\Statex$GNN_{\theta}$: Graph Neural Network with parameter $\theta$
\Statex ${\rm NoiseHead}_{\theta_{n}}$: Network module with parameter $\theta_{n}$ for prediction of node-level noise of each atom
\Statex ${\rm LabelHead}_{\theta_{l}}$: Network module with parameter $\theta_{l}$ for prediction of graph-level label of $x_{i}$
\Statex$X$: Training dataset
\Statex$x_i$: Input conformation
\Statex$y_i$: Label of $x_i$
\Statex$T$: Training steps
\Statex$\mathcal N$: Gaussian distribution
\Statex$\lambda_{p}$: Loss weight of property prediction loss
\Statex$\lambda_{n}$: Loss weight of Noisy Nodes loss
\While{$T \neq 0$}
\State $x_i, y_i$ = dataloader($X$) \Comment{random sample $x_i$ and corresponding label $y_i$ from $X$}
\State $\tilde{x} = x_{i} + \Delta{x_i}$ , where $\Delta{x_i} \sim \mathcal{N}(0, {\tau}^2I_{3N})$, $N$ is atom number of $x_i$
\State $y_{i}^{pred}={\rm LabelHead}_{\theta_{l}}(GNN_{\theta}(\tilde{x}))$
\State $\Delta{x_i}^{pred}={\rm NoiseHead}_{\theta_{n}}(GNN_{\theta}(\tilde{x}))$
\State Loss = $\lambda_{p}$PropertyPredictionLoss$(y_{i}^{pred}, y_i)$+$\lambda_{n}||\Delta{x_i}^{pred} - \Delta{x_i}||_{2}^{2}$
\State Optimise(Loss)
\State $T = T - 1$
\EndWhile
\end{algorithmic}
\end{algorithm}
{
    "title": "fractional denoising for 3d molecular pre-training",
    "id": "2307.10683",
    "abstract": "coordinate denoising is a promising 3d molecular pre-training method, which has achieved remarkable performance in various downstream drug discovery tasks. theoretically, the objective is equivalent to learning the force field, which is revealed helpful for downstream tasks. nevertheless, there are two challenges for coordinate denoising to learn an effective force field, i.e. low coverage samples and isotropic force field. the underlying reason is that molecular distributions assumed by existing denoising methods fail to capture the anisotropic characteristic of molecules. to tackle these challenges, we propose a novel hybrid noise strategy, including noises on both dihedral angel and coordinate. however, denoising such hybrid noise in a traditional way is no more equivalent to learning the force field. through theoretical deductions, we find that the problem is caused by the dependency of the input conformation for covariance. to this end, we propose to decouple the two types of noise and design a novel fractional denoising method (frad), which only denoises the latter coordinate part. in this way, frad enjoys both the merits of sampling more low-energy structures and the force field equivalence. extensive experiments show the effectiveness of frad in molecular representation, with a new state-of-the-art on 9 out of 12 tasks of qm9 and on 7 out of 8 targets of md17.",
    "categories": "q-bio.qm cs.lg physics.chem-ph",
    "doi": "",
    "created": "2023-07-20",
    "updated": "2024-02-26",
    "authors": [
        "shikun feng",
        "yuyan ni",
        "yanyan lan",
        "zhi-ming ma",
        "wei-ying ma"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2307.10683"
}
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