#  _De novo_ PROTAC design using graph-based deep generative models

Divya Nori1, Connor W. Coley1,2 & Rocío Mercado2
1Department of Electrical Engineering and Computer Science
2Department of Chemical Engineering
Massachusetts Institute of Technology
Cambridge, MA 02139, USA
{divnor80, ccoley<EMAIL_ADDRESS>

###### Abstract

PROteolysis TArgeting Chimeras (PROTACs) are an emerging therapeutic modality
for degrading a protein of interest (POI) by marking it for degradation by the
proteasome. Recent developments in artificial intelligence (AI) suggest that
deep generative models can assist with the de novo design of molecules with
desired properties, and their application to PROTAC design remains largely
unexplored. We show that a graph-based generative model can be used to propose
novel PROTAC-like structures from empty graphs. Our model can be guided
towards the generation of large molecules (30–140 heavy atoms) predicted to
degrade a POI through policy-gradient reinforcement learning (RL). Rewards
during RL are applied using a boosted tree surrogate model that predicts a
molecule’s degradation potential for each POI. Using this approach, we steer
the generative model towards compounds with higher likelihoods of predicted
degradation activity. Despite being trained on sparse public data, the
generative model proposes molecules with substructures found in known
degraders. After fine-tuning, predicted activity against a challenging POI
increases from 50% to >80% with near-perfect chemical validity for sampled
compounds, suggesting this is a promising approach for the optimization of
large, PROTAC-like molecules for targeted protein degradation.

##  1 Introduction

Of the 1,200 new molecular entities approved by the FDA between 1985-2021,
small molecule drugs approved under a “New Drug Application (NDA)” comprise
$\sim$80% of them, with the other 20% being new biological products [CDER
approvals, 2022]. Generally speaking, small molecules are designed to impede
the function of biologically-relevant target proteins. Small molecule
inhibitors interfere with their targets by accessing specific parts of the
protein and binding strongly enough to affect their behavior. However, it is
estimated that $\sim$75% of the human proteome lacks deep binding sites and is
thus “undruggable” by traditional small molecule inhibitors [Toure and Crews,
2016]. These so-called undruggable targets are nonetheless implicated in a
wide range of diseases, including cancer, autoimmune diseases, and cardio-
metabolomic diseases, motivating the development of therapeutic modalities
beyond small molecule inhibitors.

An example of such an “undrugabble” target is the BCL-2 protein, which
regulates apoptosis, making it a prime target for cancer drug discovery
[Frenzel et al., 2009]. However, in 2021, Lv et al. reported a potent BCL-xL
and BCL-2 dual degrader with significantly improved antitumor activity against
BCL-xL/2-dependent leukemia cells. This degrader belongs to a class of
emerging therapeutic modalities called PRoteolysis TArgeting Chimeras, or
PROTACs. As of the end of 2021, there were 15 heterobifunctional PROTACs in
clinical development [Mullard, 2021]. Generally speaking, though many
exceptions exist, the function of synthetic PROTACs is enabled by a three-
component structure consisting of two binding domains and an organic linker
(Figure 1). The two binding domains include a warhead designed to bind a
protein of interest (POI) and an E3 ligand designed to bind an E3 ligase. In
the ideal scenario, the linker anchors the two proteins together briefly in a
ternary complex, leading to ubiquitination of the POI, which marks it for
degradation by the proteasome.

Figure 1: Example PROTAC structure from protac-db (PubChem CID: 155168919),
highlighting the three general segments found in PROTACs: the warhead, linker,
and E3 ligand.

The functionalities of each component are highly interdependent, such that
rational design of PROTACs remains challenging. However, recent developments
in artificial intelligence (AI) suggest that deep generative models (DGMs) can
assist with the de novo design of molecules with desired pharmacological
profiles [Elton et al., 2019]. While DGMs have been widely applied to the
design of small molecule drugs, DGMs for PROTAC design are typically limited
to optimization of the linker. Here, we introduce a graph-based DGM capable of
designing PROTAC-like molecules atom-by-atom, starting from empty graphs. We
show that the DGM learns to generate PROTAC-like structures containing many
substructures found in known degraders, and we show quantitative improvement
in a scalar model estimate of degradation activity against a POI. As the model
was trained on sparse public data, we did not pursue experimental validation,
but instead publish our workflow for PROTAC design open-source. We make the
following contributions:

  * •

a non-linear, boosted-tree-based model trained on public data for the
prediction of protein degradation activity (DC50) in PROTAC systems,

  * •

application of an existing DGM to distribution-based learning tasks for PROTAC
design (30–140 heavy atoms),

  * •

application of policy-gradient reinforcement learning (RL) using a multi-
objective scoring function to promote the design of structures with predicted
protein degradation activity,

  * •

a case-study where we apply the above three points to the in silico design of
novel PROTAC-like structures for IRAK3 degradation.

##  2 Related work

Recent developments in deep learning have led to the emergence of DGMs for de
novo molecular design [Chen et al., 2018, Jiménez-Luna et al., 2021, Meyers et
al., 2021]. Some of the most successful are variations upon RL-based DGMs for
the design of drug-like small molecules [Segler et al., 2017, Blaschke et al.,
2020, Gao et al., 2022]. Policy-gradient RL has been shown to be successful in
goal-directed drug design tasks which warrant the prioritization of certain
properties, and has been successfully applied to fine-tune DGMs towards the
design of molecules with a specific size, octanol-water partition coefficient
(logP), or predicted pharmacological activity in a multi-objective fashion
[Blaschke et al., 2020, Atance et al., 2022].

Previous work on DGMs for PROTAC design has focused on the conditional design
of the linker starting from a desired PROTAC substructure. For example, a
platform called LinkINVENT used RL to generate favorable connecting components
between a pre-specified warhead and E3 ligand [Guo et al., 2022]. A graph-
based DGM has also been trained to propose 3D linker structures conditioned on
partial PROTAC structures [Imrie et al., 2020]. More recently, a method called
PROTAC-RL was developed which combines a transformer architecture and memory-
assisted RL to linker design given an E3 ligand and warhead [Zheng et al.,
2021].

##  3 Methods

We first discuss the design of a surrogate model for degradation performance,
to serve as a PROTAC scoring function. We then describe the graph-based
molecular DGM, followed by the integration of the surrogate model into an RL
framework and its application towards IRAK3 degrader design.

####  3.0.1 Data pre-processing and feature preparation

Data was retrieved from the open-source PROTAC database (protac-db), which has
compiled various experimental measurements from the literature.[Weng et al., ,
Weng et al., 2020] A single data point includes the PROTAC’s SMILES
representation; the cell type, E3 ligase, and POI targeted in the experiment;
and the DC50 value. DC50 value gives the concentration of PROTAC needed to
degrade 50% of a POI in a given cell type with a specific E3 ligase. This is a
measure of protein degradation activity, where a lower DC50 value indicates a
more potent PROTAC. The full dataset contains 3,994 datapoints, with 3,270
unique PROTACs represented. Datapoints containing duplicate PROTAC structures
are from experiments conducted with the same molecule under different
conditions.

To prepare the data, all rows with no explicit DC50 value were dropped,
resulting in 638 data points. The E3 ligase was represented using a one-hot
representation of seven main classes (CRBN, VHL, IAP, MDM2, DCAF, AhR, or
RNF), where the most common E3 ligase was cereblon (CRBN). Cell type was one-
hot encoded into 148 classes. A comprehensive set of 88 unique sequences was
used to define a vocabulary of bi-grams and tri-grams where each token is an
amino acid. The size of the vocabulary was 7,841 words, and each word was used
as a feature. PROTACs were represented using 1024-bit Morgan molecular
fingerprints, where the fingerprint length was selected from hyperparameter
optimization. Embeddings were concatenated into a final embedding with 9,077
features per data point. The continuous response variable was transformed into
a categorical variable via the following cut-offs to achieve a balanced class
split (appendix Figure 7): DC50 $\geq$ 100 nM $\rightarrow$ no to low activity
(0); DC50 $<$ 100 nM $\rightarrow$ high activity (1).

###  3.1 Surrogate model for protein degradation activity

To evaluate the quality of PROTAC structures, we developed a surrogate model
to predict DC50. The model takes as input the aforementioned embedding
(section 3.0.1). The output is a binary label representing the activity level:
0 (low activity/high DC50) or 1 (high activity/low DC50). Data was divided
into train/test splits using a semi-random 70/30 split, accounting for data-
leakage by avoiding having the same PROTAC structure in both splits. Data
points where a PROTAC was in the training set were moved out of the test set,
leading to 689 training points and 144 points in the hold-out test set. We
trained a boosted tree-based model using Light Gradient Boosted Machine
(LightGBM version 3.2.1) [LightGBM (), package]. Hyperparameters were selected
with Optuna version 2.10.0, using an F1-score objective function and five-fold
cross validation [Optuna (), package]. Varied parameters included bagging
fraction, bagging frequency, learning rate, number of leaves, and feature
fraction.

###  3.2 Graph-based generative model

We tackle the challenge of optimizing all three components simultaneously. We
do this using GraphINVENT [Mercado et al., 2021b, Atance et al., 2022], a
graph-based autoregressive DGM which uses RL for molecular optimization, as it
was previously demonstrated to be successful in the generation of large
natural products of similar size to PROTACs [Mercado et al., 2021a]. To build
the DGM, we followed a three-step workflow: preprocessing, training, and
generation. Preprocessing involves creating step-by-step graph reconstruction
processes for each molecule in the training set. This step-wise information is
then used to train the DGM. As protac-db contains <30 molecules with
phosphorous and iodine, these were removed from the dataset for computational
efficiency (less padding). The final training set consisted of 4,120 molecules
with atom types {C, N, O, F, S, Cl, and Br}, formal charges {-1, 0, and 1},
and a maximum heavy atom count of 139. This set was used to pre-train the DGM
for 200 epochs with a batch size of 50.

Figure 2: Reinforcement learning loop used to fine-tune the pre-trained deep
generative model. BASF stands for “Best Agent So Far” and BAR represents the
“Best Agent Reminder” loss.

###  3.3 RL framework for fine-tuning

We adopt the the memory-aware RL loss used in GraphINVENT [Atance et al.,
2022] to steer our generative model towards PROTACs more likely to be active
using a surrogate model for degradation activity. The framework, illustrated
in Figure 2, begins with the pre-trained DGM, which is used to initialize the
Agent as well as the Best Agent So Far (BASF). Both agents generate a set of
molecules, saving the actions. Sampled molecules from each agent are scored by
their predicted degradation activity, modified by a term that prevents
rewarding duplicate, chemically invalid, heavy atom count <30111Fewest heavy
atoms per molecule in protac-db = 30., or improperly terminated molecules. The
BASF, prior, and current agent log-likelihoods are used to compute the loss
and update the model through gradient descent as described by [Atance et al.,
2022]. This framework was used to fine-tune the model from the best pre-
training epoch, $e^{*}$, for 200 additional steps. The pre-trained model was
fine-tuned 10 times to collect statistics. The agent and BASF each use a
generation batch size of six, where sampled molecules are evaluated at each RL
step using the above scoring mechanism. For training the agent, the Adam
optimizer was used (initial learning rate of $10^{-6}$) with the OneCycle
learning rate scheduler, no weight decay, and $\alpha=0.5$.

10K molecules were sampled from the converged agent at 200 fine-tuning steps.
The molecules were evaluated for 1) degradation activity using the surrogate
model (section 3.1), and 2) chemical diversity using Murcko scaffold
decomposition. These molecules were compared against the 2.5K molecules
sampled from the model at $e^{*}$ before RL fine-tuning.

###  3.4 Case study: optimizing for IRAK3 degradation

We selected interleukin-1 receptor-associated kinase 3 (IRAK3) from protac-db
for fine-tuning the DGM. IRAK3 has been implicated in oncological signaling,
and its inhibition induces T-cell proliferation for reduced tumor burden.
IRAK3 contains an “undruggable” ATP binding site which has been the target of
PROTAC development efforts [Degorce et al., 2020]. This is a challenging case
study where the model has to learn to generate new PROTACs for IRAK3
degradation having seen one example of IRAK3 degraders previously.

##  4 Results

###  4.1 Activity scoring model metrics

We show here the results of the tree-based activity scoring model on the held-
out test set. The model returns a score between 0 and 1 for each input
molecule where higher scores suggest greater PROTAC activity. As shown in
Figure 3, the final model’s test AUC is 0.87, and for molecules with scores
$\leq 0.3$ or $\geq 0.7$, the predicted activity is correct $87.6\%$ of the
time. For molecules that score between $0.3$ and $0.7$, the probability of
incorrect classification is $59.0\%$. Therefore, when using this model for DGM
fine-tuning, molecules that score within this range are not rewarded. However,
$90\%$ of molecules in the test set scored outside of this range, indicating
the model is relatively confident in those predictions.

Figure 3: (a) Receiver-operating characteristic for surrogate model protein
degradation activity as a binary classification task, demonstrating an AUROC
of 0.877 on the test set. (b) Analysis of test set prediction accuracy in
terms of binned predicted activity score.

###  4.2 Fine-tuning DGM to generate active PROTACs

The DGM was fine-tuned using RL from the pre-trained model state at the epoch,
$e^{*}$, that maximized the fraction of valid molecules in the range of epochs
150–200, as models in this range provide a good compromise between the
validity of sampled structures and validation loss (appendix Figure 8).
Starting from the pre-trained model at $e^{*}=192$, we observe that the score
of the sampled molecules, interpretable as a binary activity measure, steadily
increases for the first 100 RL steps before converging (Figure 4), suggesting
that the model is learning to generate molecules that score highly for IRAK3
degradation.

Figure 4: Activity score progression across learning steps during RL training.
Error bars are the standard deviation from the results of 10 distinct runs.

To compare the quality of molecules being generated at these two different
states, 2.5K were sampled from the pre-trained model at $e^{*}$, and 10K
molecules were sampled from the fine-tuned model after 200 RL steps.
Visualizations of randomly selected molecules from the two sampled sets are
shown in Figure 5. What we observe is that at before applying RL, the DGM has
already learned to generate barbell-like molecules, characteristic of
structures in protac-db. Many of the sampled molecules have well-developed E3
ligands and warheads, thought only about half ($50.8\%$) are predicted to be
active degraders. However, after RL fine-tuning, we observe that $83.8\%$ of
sampled molecules demonstrate predicted IRAK3 degradation activity, and nearly
100% chemical validity (appendix Figure 8).

###  4.3 Evaluation of PROTACs generated by the best model

We evaluated the scaffold diversity of the 10K molecules generated from the
DGM after RL. The average number of heavy atoms in this sampled set was 56.46,
compared to 55.09 for protac-db. Additionally, both before and after fine-
tuning, 0% of the sampled molecules were regenerated from the training set; in
other words, they were all novel structures, likely due to the large number of
nodes in the PROTAC graphs and the large action space during generation.

Diversity of generated molecules was evaluated using molecular scaffolds, a
concept applied in medicinal chemistry to represent core substructures in
bioactive compounds. Specifically, we identified the Murcko scaffolds present
in the final 10K set of generated molecules and in the $\sim$5K molecules in
protac-db, then computed the intersection of these two sets. Murcko scaffolds
were identified using RDKit [RDKit (), package]. In the 10K final generated
molecules, we identified 537 unique Murcko scaffolds, whereas in protac-db we
identified 2,907 unique Murcko scaffolds. This is not surprising as during
fine-tuning we are narrowing in on a smaller chemical space. See appendix 9.5
for examples of the most common scaffolds.

In Figure 6b, we highlight the most common substructures shared by the top 100
generated and protac-db molecules. We see that the model has learned to reuse
several substructures repeatedly. We see similar trends when analyzing the top
5 most common substructures from the top 100 predicted IRAK3 degraders (out of
the 10K generated set; appendix Figure 9). Interestingly, the most common
substructure found in the top 100 predicted degraders is
phthalimidinoglutarimide (PubChem CID: 91585), a known IRAK degrader and CRBN
binder [Békés et al., 2022]. The second most common corresponds to a known
degrader for the tau protein (PubChem CID: 137408522). Noticably, all top 5
most common substructures contain the phthalimidinoglutarimide motif (a
substructure of thalidomide and lenalidomide), indicating that our model is
satisfactorily learning the structure of CRBN ligands. This is not surprising
as there is less variation amongst E3 ligands than warheads in protac-db.

Figure 5: Generated molecules randomly sampled from the DGM (a) before and (b)
after reinforcement learning (RL). The black molecules are predicted to be
active for IRAK3 degradation by the surrogate model, whereas the red molecules
are predicted to be inactive. None of the generated molecules appear in the
training set.

##  5 Discussion

###  5.1 A look at the potential new degraders

Above, we show that a graph-based DGM can learn the structure of potentially
new degraders via reinforcement learning such that 82% of the final sampled
molecules are predicted to be potent degraders with DC50 < 100 nM when
optimized against an example task from protac-db. Many of the sampled
molecules contain scaffolds present in known degraders. Although the DGM
receives no information during training on which component is the warhead, the
linker, or the E3 ligand, it learns to generate promising new PROTAC-like
structures based on the final reward for the entire output molecule. It also
does this without any initial seed substructure.

While previous work has primarily applied generative models to design small
molecules containing $\leq 30$ heavy atoms, here we show that our DGM can be
used to generate molecules containing up to 139 heavy atoms with nearly 100%
chemical validity (appendix Figure 8). This indicates that the DGM has learned
chemical rules and can apply them to build large, complex molecules.

Figure 6: (a) Top 5 predicted IRAK3 degraders sampled from the DGM after
reinforcement learning. (b) Top 5 most common substructures shared by the top
100 generated molecules and the known actives in protac-db.

###  5.2 Limitations

The primary avenue for improvement in this work is in increasing the
generalizability of the DC50 prediction model. In this work we were limited by
the sparse nature of the public PROTAC data. Several data points in protac-db,
which are mined from the literature, lacked DC50 measurements, making those
entries unusable. In addition, there is considerable class imbalance between
E3 ligases, cell types, and POIs, which affects the ability of the model to
fully utilize the E3 ligase and cell type information in the dataset (see
appendix 9.1 for an ablation study). While some ligases have hundreds of
measured data points, others have just a few. Addressing these data and
representation limitations could enable the application of more complex
architectures for the degradation prediction model, and also improve the DGM
which builds on the accuracy of the surrogate model for PROTAC design. Another
limitation is that synthesizability considerations have not been factored in
to the DGM in this work, which will be relevant when it comes to experimental
validation and are thus important to address, along with the aforementioned
issues, in future work.

###  5.3 Future work

There remains much to improve for the creation of an automated PROTAC design
pipeline; nonetheless, one main area of improvement is the accuracy of the
DC50 surrogate model. Better representations couldbe used for E3 ligase and
cell type information. For instance, E3 ligase sequence information could be
included, and cell type embeddings could be constructed to encode biological
similarity between types. Additionally, besides the DC50 values listed in
protac-db for the response variable, docking studies could be used to estimate
binding affinities between the PROTAC, E3 ligase, and POI.[Zaidman et al.,
2020, Bond and Crews, 2021]

While the molecules generated are predicted to be active by the surrogate
model, they cannot be deemed true actives from computational predictions
alone. Experimental validation in vitro is essential for moving forward in the
drug development process of any compound designed in silico.

##  6 Conclusions

Here, we have demonstrated how a graph-based DGM can be directed towards the
generation of predicted active PROTACs via policy-gradient RL using a memory-
aware loss function. It can be used to design PROTAC-like structures with up
to 140 heavy atoms. The scoring model used in the RL framework is a boosted
tree-based classification model for protein degradation activity; after
hyperparameter tuning, the model displays a test AUC of $0.87$, though the
generalizability of the model is limited due to the sparse nature of existing
database. RL enhances the percentage of predicted active PROTACs generated by
the DGM from $53\%$ to $82\%$ in 200 learning steps. Analysis of molecules
sampled from the final fine-tuned model shows that while the compounds are
100% novel, they contain substructures present in known protein degraders.
Generally, we have shown that our graph-based model can be used to optimize
large therapeutic molecules such as PROTACs. With the availability of better
public data, and the development of better physics-based models for ternary
structure modeling, machine learning tools can be used to make the PROTAC
design process less formidable. We hope this work inspires future research on
de novo design tools for emerging therapeutic modalities.

##  7 Acknowledgements

D.N. thanks the MIT UROP office for a summer fellowship. R.M. was financially
supported by the Machine Learning for Pharmaceutical Discovery and Synthesis
consortium. We thank Samuel Goldman for useful feedback and discussions.

##  8 Code availability

Code for the surrogate model is available on GitHub at
https://github.com/divnori/Protac-Design. Modified GraphINVENT source code and
generated data, including pre-trained models, fine-tuned models, and generated
structures, can be found at https://doi.org/10.5281/zenodo.7278277.

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##  9 Appendix

###  9.1 Feature importance ablation study

Feature importance was measured via an ablation study using input feature
shuffling on the held-out test set. For a given embedding, the respective
column values were shuffled in the input matrix to randomize the values for
those variables. The scoring model was then used to predict the DC50 class
from the modified input. The results are shown in Table 1, where “Importance”
is calculated by subtracting the AUC and F1 score sum from the original
(unshuffled) model’s AUC and F1 score sum. Input shuffling occurs with slight
variation on each pass, so the experiment was conducted three times and used
to compute the standard error of the mean (SEM) for each importance value.

Shuffled Embedding | AUC | F1 Score | Importance | SEM
---|---|---|---|---
None (Original) | 0.860 | 0.893 | NA | NA
PROTAC structure | 0.611 | 0.832 | 0.310 | 0.012
Receptor (POI) | 0.765 | 0.838 | 0.150 | 0.023
E3 Ligase | 0.855 | 0.893 | 0.005 | 0.000
Cell Type | 0.860 | 0.893 | 0.000 | 0.000
Table 1: Feature importance in the surrogate model.

From Table 1, we observe that the PROTAC molecular fingerprints (1024-bits)
are the most important. The receptor n-grams (7,841 bi-gram & tri-gram
features) follow, with the one-hot encoded E3 ligases (7 features) and cell
types (148 features) being the least important. This shows that the model
learns from both the PROTAC structure and receptor to reliably predict PROTAC
degradation activity for the POI. In comparison, E3 ligase has relatively low
feature importance, whereas the cell type is seemingly not contributing at all
to the model’s learning under the current featurization scheme.

Figure 7: DC50 histogram for the 638 protac-db datapoints used in this work.

###  9.2 Response variable preparation

Figure 7 shows the histogram which was used to determine the threshold for
encoding the response variable, DC50, into balanced binary classes. Based on
this distribution, a threshold of 100 nM was used to split DC50 values into
two classes. All DC50 values <100 were put into one class (1: “high
activity”), and the remaining values were put into another class (0: “no to
low activity”).

F1 Score | Bagging Fraction | Bagging Freq | Learning Rate | Number of Leaves | Feature Frac
---|---|---|---|---|---
0.8316 | 0.8876 | 3 | 0.2299 | 19 | 0.5412
0.8288 | 0.8153 | 3 | 0.2936 | 21 | 0.4045
0.8287 | 0.8784 | 3 | 0.2957 | 20 | 0.3990
0.7126 | 0.6383 | 5 | 0.0346 | 17 | 0.4954
0.6981 | 0.4260 | 4 | 0.0123 | 24 | 0.4600
0.6953 | 0.5313 | 6 | 0.1922 | 11 | 0.5114
Table 2: Surrogate model parameters varied during hyperparameter optimization.

###  9.3 Hyperparameter optimization

Table 2 shows the hyperparameters tuned during surrogate model training. The
top three rows show the best three hyperparamater combinations, ranked using
an F1 objective function. The bottom three rows show the worst three
combinations.

Figure 8: Training loss, validation loss, and fraction valid as a function of
pre-training epochs.

###  9.4 Additional training results

In Figure 8, we show the training/validation loss and fraction of valid
molecules sampled from the DGM as a function of training epochs. Initially, as
the number of epochs increases, the average validation loss increases.
Subsequently, the validation loss plateaus, indicating some amount of
overfitting. The fraction of valid molecules reaches 100% by the final epoch.

###  9.5 Most common substructures

In Figure 9 we illustrate the most common substructures present in the sampled
molecules predicted to be most active after RL. The two left-most molecules in
Figure 9 are known protein degraders.

Figure 9: Most common substructures appearing in the top 100 predicted
degraders for IRAK3, in order of most common (left) to less common (right).


the same for all observers. For after all the theory of quantum mechanics was
arrived at by analysing sets of measurement outcomes under the assumption that
these outcomes were unique and the same for all observers; orthodox
interpretations and the Everett interpretation both take for granted that the
empirical confirmation that has been accrued for quantum mechanics under this
assumption can simply be transferred to a completely different context where
the assumption no longer holds, but as we have seen in detail in this article,
empirical confirmation will not always be maintained under a significant
reinterpretation of the theory, and therefore the proponents of these
interpretations should be obliged to provide an account of how empirical
confirmation is supposed to work in the new setting that they propose.

Indeed, we would suggest that showing explicitly how the interpretation allows
the theory to be empirically confirmed should really be compulsory for anyone
who wants to propose an interpretation of any scientific theory - an
interpretation should not be drawn entirely from the mathematics of a theory,
but should also demonstrate a clear link to the empirical data which is our
evidence for that theory. Paying inadequate attention to the problem of
empirical confirmation results in the formulation of interpretations that are
interpretations of the _mathematics_ but which fail to be compelling
interpretations for the _empirical evidence_ which is the reason for the
mathematics in the first place: we would like to see discussions of the
interpretation of quantum mechanics place more emphasis on the empirical
evidence for the theory, and we would even venture to hope that centering the
evidence in this way might provide a way out of the long-standing impasse over
the interpretation of quantum mechanics.

##  6 Acknowledgements

Thanks to Carlo Rovelli for very helpful discussions. This publication was
made possible through the support of the ID 61466 grant from the John
Templeton Foundation, as part of the “The Quantum Information Structure of
Spacetime (QISS)” Project (qiss.fr). The opinions expressed in this
publication are those of the author and do not necessarily reflect the views
of the John Templeton Foundation.

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