Machine Learning for Molecules: Lessons and Challenges of Data-Centric Chemistry

Machine Learning for Molecules
Lessons and Challenges of Data-Centric Chemistry
Ichigaku Takigawa
https://itakigawa.github.io/
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Feb 5th, 2022

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୍઒Ұֶ
TAKIGAWA Ichigaku
https://itakigawa.github.io
• 1995-2004 Hokkaido Univ (Grad School. Engineering)
2004 PhD Computer Science
• 2005-2011 Kyoto Univ (Inst. Chemical Research)
Bioinformatics Center, Assist. Prof.
Grad School Pharmaceutical Sciences, Assit. Prof.
• 2012-2018 Hokkaido Univ (Grad School. Info Sci & Tech)
Large-Scale Knowledge Processing Lab, Assoc. Prof.
2015-2018 JST PRESTO for Materials Informatics
• 2019- RIKEN Center for AI Project @ ATR Kyoto
2019- Hokkaido Univ
(Inst. Chemical Reaction Design & Discovery)
Hi, I am a machine-learning researcher
RIKEN AIP Kyoto, Kyoto Univ CiRA, Nikon
jointly working on stem cell biology.

View Slide

୍઒Ұֶ
TAKIGAWA Ichigaku
https://itakigawa.github.io
• 1995-2004 Hokkaido Univ (Grad School. Engineering)
2004 PhD Computer Science
• 2005-2011 Kyoto Univ (Inst. Chemical Research)
Bioinformatics Center, Assist. Prof.
Grad School Pharmaceutical Sciences, Assit. Prof.
• 2012-2018 Hokkaido Univ (Grad School. Info Sci & Tech)
Large-Scale Knowledge Processing Lab, Assoc. Prof.
2015-2018 JST PRESTO for Materials Informatics
• 2019- RIKEN Center for AI Project @ ATR Kyoto
2019- Hokkaido Univ
(Inst. Chemical Reaction Design & Discovery)
But also, I am a machine-learning user
RIKEN AIP Kyoto, Kyoto Univ CiRA, Nikon
jointly working on stem cell biology.

View Slide

Inst. Chemical Reaction Design and Discovery
https://www.icredd.hokudai.ac.jp
We're working on real-world
chemistry with great chemists!
Prof. Ben List got 2021 Nobel Prize in Chemistry

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My interest: Machine learning with discrete structures
Discrete structures, i.e., combinatorial or algebraic structures
such as sets, groups, permutations, combinations, sequences, trees, and graphs
Target objects Relations between target objects
ML models

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https://cen.acs.org/physical-chemistry/computational-chemistry/Exploring-chemical-space-AI-take/98/i13
Molecules clearly have a combinatorial aspect

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How can ML leverage these combinatorial nature?
• A molecule is a set of atoms and bonds
• A chemical reaction is a recombination pattern of bonds
Compositionality and hiearchy
Similar to natural language?
We combine words to make any
complicated sentences.
The underlying rules are (largely)
governed by many-body
quantum chemistry of electrons
Substituents

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This talk
1. What actually ML is?
2. The dark side: Modern aspects of ML
3. The light side: Deep learning for molecules
A quick review on the dark side and light side of ML
from both viewpoints as an ML algorithm researcher and an ML practitioner/user
May the ML Force be with you…
Science is built up of facts, as a house is built of stones;
but an accumulation of facts is no more a science than
a heap of stones is a house. Henri Poincaré "Science and hypothesis"
This slide is available at
https://itakigawa.github.io/news.html

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ML converts data into "prediction"
get weight, height

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get weight, height
5 6.25 7.5 8.75 10
90 112.5 135 157.5 180
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Weight (g)
Height (cm)
ӪOrange
ӪApple

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get weight, height
5 6.25 7.5 8.75 10
90 112.5 135 157.5 180
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Weight (g)
Height (cm)
ӪOrange
ӪApple

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get weight, height
5 6.25 7.5 8.75 10
90 112.5 135 157.5 180
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Weight (g)
Height (cm)
ӪOrange
ӪApple
Height (cm)
Weight (g)
ӪApple
ӪOrange
A program for "prediction"

View Slide

ӪApple
ӪOrange
5 6.25 7.5 8.75 10
90 112.5 135 157.5 180
●
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●
●
●
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Weight (g)
Height (cm)
ӪApple
ӪOrange
Height (cm)
Weight (g)

View Slide

ӪApple
ӪOrange
5 6.25 7.5 8.75 10
90 112.5 135 157.5 180
●
●
●
●
●
●
●
●
●
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Weight (g)
Height (cm)
ӪApple
ӪOrange
Height (cm)
Weight (g)
Now we got a computer program to predict "orange or apple"
for any unseen ones directly from collected data

View Slide

ML is a new (lazy) way of programming
Object recognition
Game play
ˑ֮׶ָהֲ˒
J’aime la
musique I love music
Speech recognition
Machine translation
Super resolution
ML generates a computer program just by giving many input-output examples
even when we don't know the underlying mechanism between inputs and outputs.

View Slide

This simple idea is more powerful than you may think
Remarkably powerful when we have relevant input-output examples (it's useless if we don't)

View Slide

Many ways to mathematically represent the boundary
ر٦ة Decision
Tree
Random
Forest GBDT
Nearest
Neighbor
Logistic
Regression
SVM
Gaussian
Process
Neural
Network
This is why you see too many algorithms when you start to learn ML…

View Slide

But anyway, we're just tweaking parameters for a good fit
p1 p2 p3 p4

Surface model
Internally, we're just ﬁtting a surface to given points by adjusting its parameter values.
Random Forest
Gaussian Process
Logistic Regression

View Slide

Deep Learning (Representation Learning)
q1 q2 q3 q4

Surface model
Input variables
Standard ML
Random
Forest
GBDT
Nearest
Neighbor
SVM
Gaussian
Process
Neural
Network

View Slide

Deep Learning (Representation Learning)
q1 q2 q3 q4

p1 p2 p3 p4

Variable transformation
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z1
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
z2
-BUFOUWBSJBCMFT
Deep Learning
5IJTQBSUDBOCFTJNQMF
JGXFDBOOEBOEMFBSO
BHPPESFQSFTFOUBUJPO
PGUIFJOQVU
Standard ML
Input variables
Surface model

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Pitfall: The lure of wishful wordings
The current ML is stunningly powerful but it's very different from our sci-fi image of "AI".
Be careful about these "wishful" wordings that needlessly distract and mislead us!
Why Is AI So Dumb?
A SPECIAL REPORT
"Artificial intelligence" doesn't mean that we have something artificial also intelligent like us.
"Machine learning" doesn't mean that machines actually learn things like us.

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This talk

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The dark side: Modern aspect of ML
• High dimensionality: Too many input variables
We tend to use many input variables because ML is completely unaware of any information
not in the input variables. Missing relevant factors results in spurious correlation.
100 x 100 RGB image = 30 thousand variables
e.g.)
1000 x 1000 RGB image = 3 million variables

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• Overrepresentation: Too many parameters
ResNet50: 26 million params
ResNet101: 45 million params
EﬃcientNet-B7: 66 million params
VGG19: 144 million params
12-layer, 12-heads BERT: 110 million params
24-layer, 16-heads BERT: 336 million params
GPT-2 XL: 1558 million params
GPT-3: 175 billion params
e.g.)
Remember that we're ﬁtting a surface with hundreds million parameters in a several million
dimensional space!
• High dimensionality: Too many input variables
We tend to use many input variables because ML is completely unaware of any information
not in the input variables. Missing relevant factors results in spurious correlation.
100 x 100 RGB image = 30 thousand variables
e.g.)
1000 x 1000 RGB image = 3 million variables

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• Data hungriness: Big data is big for human, but can be too small for ML models…
As a result, it requires huge good data to make current ML models work.

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• Data hungriness: Big data is big for human, but can be too small for ML models…
As a result, it requires huge good data to make current ML models work.
Think twice about how complex the input-output relationship you are trying to find by ML is.
How many samples will be statistically sufficient to estimate 2-variable functions like these?
What if you're fitting a 100-variable function, or 10-thousand-variable function?

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The curse of dimensionality
Bronstein MM, Bruna J, Cohen T, Veličković P.
Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges.
arXiv [cs.LG]. 2021. http://arxiv.org/abs/2104.13478
A classic result in function approximation: If we must approximate a function of d variables and
we know only that it is Lipschitz, say, then we need order (1/ε)d observations on a grid in order
to obtain an approximation scheme with uniform approximation error ε.
for all
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
f : Rd ! R
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
x, x0 2 Rd
-Lipschitz
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
|f(x) f(x0)| 6 Lkx x0k
AAAChHichVG7SgNBFD1ZNcZ31EawCQbFQsJE4wMLCdpYWJjERCGK7K6TOLjZXXYngRj8AW0VCysFC/ED/AAbf8AinyCWEWwsvNksiAb1LrNz5sw9d87M1WxDuJKxekDp6OwKdod6evv6BwaHwsMjOdcqOzrP6pZhOTua6nJDmDwrhTT4ju1wtaQZfFs7Wmvub1e44wrL3JJVm++V1KIpCkJXJVGpjf1wlMWYF5F2EPdBFH5sWuEH7OIAFnSUUQKHCUnYgAqXvjziYLCJ20ONOIeQ8PY5TtBL2jJlccpQiT2if5FWeZ81ad2s6XpqnU4xaDikjGCSPbM71mBP7J69sI9fa9W8Gk0vVZq1lpbb+0OnY5n3f1UlmiUOv1R/epYoYMnzKsi77THNW+gtfeX4spFZTk/WptgNeyX/16zOHukGZuVNv03x9NUffjTyQi9GDYr/bEc7yM3G4guxRCoRTa76rQphHBOYpn4sIol1bCJL9TnOcI4LJajMKHPKfCtVCfiaUXwLZeUTeMOPzA==
L
Donoho DL,
High-dimensional data analysis: The curses and blessings of dimensionality.
Plenary Lecture, AMS National Meeting on Mathematical Challenges of the 21st Century. 2000.
gives similar outputs for similar inputs

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The interpolation vs extrapolation argument
https://youtu.be/86ib0sfdFtw
• If we deﬁne 'interpolation' as
Interpolation occurs for a sample x whenever this
sample falls inside the given dataset’s convex hull.
• Then, the paper empirically and theoretically
demonstrates that "on any high-dimensional (>100)
dataset, interpolation almost surely never happens."
• "Those results challenge the validity of our current
interpolation/extrapolation deﬁnition as an indicator of
generalization performances. "
• In high dimension, even just determining interpolation
or extrapolation is already counter-intuitive…
Balestriero R, Pesenti J, LeCun Y.
Learning in High Dimension Always Amounts to Extrapolation.
Over 3 hours interview with authors
@ MLStreetTalk
sample x
dataset’s
convex hull

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Assessing ML predictions is intrinsically very hard!
It is quite obvious that ML correctly makes prediction for the given training data.
ML predictions must be evaluated by using some data except the given training data,
but they can mean any data we haven't seen yet.
✓ We have no other choice but to use some ﬁnite data for assessing any ML predictions.
✓ They are already in hand, and unintended cheating (data leakage) is very likely to happen
ԮTraining ԯValidation ԰Test
Example/Practice Questions + Answers Practice Tests + Answers Real Test (+ Answers)

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Big challenge: Rashomon effect and underspecification
Rashomon Effect: The multiplicity of good ML models
In general, we can have many equally good but very different ML models that give equally
accurate predictions for the given data.

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• Many explanations can exist for a single set of ﬁnite observations in general .
(whether they are given by ML or by human experts.)

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• Many explanations can exist for a single set of finite observations in general .
(whether they are given by ML or by human experts.)
• They can largely disagree in a underspecified situation where data is statistically insufficient.
Any ML model will work Different models can give very different predictions for out-of-sample cases
Neural Network (Tanh) Kernel Ridge (RBF) Neural Network (ReLU)

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https://arxiv.org/abs/2011.03395
https://ai.googleblog.com/2021/10/
how-underspecification-presents.html
• We often see ML failures in real-world domains even when we trained them on well-curated
data that structurally matched with the application domain.
• "While ML models are validated on held-out data, this validation is often insufficient to
guarantee that the models will have well-defined behavior when they are used in a new
setting. "
Underspecification appears in many practical ML systems?

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Berner J, Grohs P, Kutyniok G, Petersen P.
The Modern Mathematics of Deep Learning. arXiv [cs.LG]. 2021. http://arxiv.org/abs/2105.04026
Zhang C, Bengio S, Hardt M, Recht B, Vinyals O.
Understanding deep learning (still) requires rethinking generalization. Commun ACM. 2021;64: 107–115.
Many points in ML are still open problems!
Definitely we still need to rethink our traditional understanding on concepts like generalization,
overfitting, bias-variance tradeoff, interpolation/extrapolation, the curse of dimensionality, etc.
• Too high expressive power
Zero training error on random labels. (DL can represent any function / memorize entire data)
• Benign overfitting (when interpolating noisy training data)
Low test error even when we have zero training error on noisy training data.
• Implicit regularization
Stochastic optimization like SGD prefers low-complexity solutions.

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A toy case: 'Benign' zero training error on noisy data
PolyReg(1)
RMSE 0.299
PolyReg(3)
RMSE 0.28
PolyReg(5)
RMSE 0.225
PolyReg(7)
RMSE 0.113
PolyReg(10)
RMSE 0.0189
PolyReg(15)
RMSE 0.00737
PolyReg(20)
RMSE 0.000
PolyReg(30)
RMSE 0.000
ExtraTrees (no bootstrap)
RMSE 0.000
ExtraTrees (bootstrap)
RMSE 0.0121
Random Forest
RMSE 0.012
LGBM
RMSE 0.0508
95%-CI 95%-CI 95%-CI 95%-CI
Problematic overﬁtting by polynomial regression of order k
clearly overﬁtted but harmless (still informative)
also we can assess
the uncertainty

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This talk

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1. Regularization (inc. implicit regularization by SGD)
ML's interests: How to tame the high dimensionality?
2. Good initial value (warm start) of general use
Control, restrict, or stabilize the solution space or optimization
Trying to ﬁnd the global minimum of
very bumpy loss landscape…
Large-scale pretraining and its transfer

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1. Regularization (inc. implicit regularization by SGD)
ML's interests: How to tame the high dimensionality?
2. Good initial value (warm start) of general use
Control, restrict, or stabilize the solution space or optimization
Trying to ﬁnd the global minimum of
very bumpy loss landscape…
Large-scale pretraining and its transfer
3. Relevant "inductive bias"
ML models that can represent any function make worse the risk of
Rashomon effect, underspeciﬁcation, and spurious correlation.
Design inductive biases (features, architectures, models, etc)
by chemical knowledge, expert intuition, and theory
so that ML models don't unintentionally represent a function
that lacks any chemical validity.

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Graph Neural Networks (GNNs) in general
GNN
Layer
1
3
2 4
1
2 3
4
5
6
1 2 3 4
1 2 3 4 5 6
Node
features
Edge
features
1
3
2 4
1
2 3
4
5
6
1 2 3 4
1 2 3 4 5 6
Global
Pooling
(Readout)
Graph-level
Prediction
Node-level
Prediction
Edge-level
Prediction
Update
Update
Head
Head
Head
× Layers
Derrow-Pinion A, She J, Wong D,
Lange O, Hester T, Perez L, et al.
ETA Prediction with Graph Neural
Networks in Google Maps.
CIKM 2021
Fang X, Huang J, Wang F, Zeng L,
Liang H, Wang H. ConSTGAT:
Contextual Spatial-Temporal Graph
Attention Network for Travel Time
Estimation at Baidu Maps.
KDD 2020
Dong XL, He X, Kan A, Li X, Liang
Y, Ma J, et al. AutoKnow: Self-
Driving Knowledge Collection for
Products of Thousands of
Types.
KDD 2020
Dighe P, Adya S, Li N,
Vishnubhotla S, Naik D,
Sagar A, et al. Lattice-Based
Improvements for Voice
Triggering Using Graph
Neural Networks.
ICASSP 2020
Travel Time Estimation (Google Maps, Baidu Maps) Siri Triggering (Apple) Knowledge Collection (Amazon)

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Graph neural networks for chemical problems
Topology
An input graph
Edge
Features
Node
features
p1 p2 p3

Representation
Learning
q1 q2 q3

Classiﬁcation /
Regression Head
Other Info (Conditions, Environment, …)

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Molecular graphs
1. 2.
1 2 1 0
2 3 12 0
3 4 12 0
4 5 12 0
5 6 12 0
6 7 12 0
7 8 2 0
7 9 12 0
9 10 12 0
10 11 2 0
10 12 12 0
12 13 1 0
9 14 1 0
6 2 12 0
12 5 12 0
1. 2. 3. 4. 5. 6.
1 C 6 4 3 0 12.011 0
2 N 7 3 0 0 14.007 1
3 C 6 3 1 0 12.011 1
4 N 7 2 0 0 14.007 1
5 C 6 3 0 0 12.011 1
6 C 6 3 0 0 12.011 1
7 C 6 3 0 0 12.011 1
8 O 8 1 0 0 15.999 0
9 N 7 3 0 0 14.007 1
10 C 6 3 0 0 12.011 1
11 O 8 1 0 0 15.999 0
12 N 7 3 0 0 14.007 1
13 C 6 4 3 0 12.011 0
14 C 6 4 3 0 12.011 0
8
11
12
2
9
4
6
5
7
10
3
13
1
14
Node features Edge features
1. Atomic number
2. # of directly-bonded neighbors
3. # of hydrogens
4. Formal charge
5. Atomic mass
6. Is in a ring?
1. Bond type
2. Stereochemistry

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Geometric graphs
Non-geometric node features
Non-geometric edge features
+ Can be added

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https://youtu.be/uF53xsT7mjc
https://youtu.be/w6Pw4MOzMuo
ICLR 2021 Keynote (Michael Bronstein) Seminar Talk (Petar Veličković)
Geometric Deep Learning (GDL)
Bronstein MM, Bruna J, Cohen T, Veličković P.
Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges.
https://geometricdeeplearning.com

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Atz K, Grisoni F, Schneider G.
Geometric deep learning on molecular representations.
Nature Machine Intelligence. 2021;3: 1023–1032. https://arxiv.org/abs/2107.12375
GDL for molecular representations
We need to consider equivariance
under E(3) or SE(3) for some
geometric features (coordinates,
forces, vector ﬁeld, etc)

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Graph Representation Learning
p1 p2 p3

Representation
Learning
Topology Node Features
Edge Features
We can seek for a good representation vector that can be computed from a molecular graph,
which is expected to be superior to any man-made descriptors!
A relatively low-dimensional
good representation vector

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Beyond man-made descriptors
• 0-Dimensional Descriptors
• Constitutional descriptors
• Count descriptors
• List of structural fragments
• Fingerprints
• Graph invariants
• 3D MoRSE, WHIM, GETAWAY, ...
• Quantum-chemical descriptors
• Size, steric, surface, volume, …
• GRID, CoMFA, Volsurf, ...
"Dragon calculates 5,270 molecular
descriptors"
"Vol 1 contains an alphabetical
listing of more than 3,300 descriptors"

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Message Passing: The inner workings of GNNs
N O
C
C
C
C
H
H
H
H
H
N O
C
C
C
C
H
H
H
H
H
GNN Layer
Message Passing
q1 q2 q3

Classiﬁcation /
Regression Head
Update features by
aggregating features
around each node
ԮMessage
Permutation equivariant
operations
• NN such as MLPs
• Edge features usable
• Sum, Mean or Max
• Attentive pooling
ԯAggregate
Permutation invariant
operations
԰Update
• NN such as MLPs
N O
C
C
C
C
H
H
H
H
H
Readout • Sum, Mean or Max
• Attentive pooling
Permutation invariant
operations

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Use Case 1: Virtual Screening (QSAR/QSPR)
ML
Activity (Active or Inactive)
GI50: concentration required
for 50% inhibition of growth
NCI Human Tumor Cell
Line Growth Inhibition
Assay (PubChem AID 1)
Active (2,814) Inactive (48,922)
LogGI50 value
• Classiﬁcation Task
• Regression Task
Very Noisy, Complex Relationship…

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Use Case 1: Virtual Screening (QSAR/QSPR)
Activity (Active or Inactive)
LogGI50 value
• Classiﬁcation Task
• Regression Task
ChemProp
(Directed MPNN)
ExtraTrees
w/ ECFP6(1024)
Standard ML GNN
ChemProp (Yang et al, 2019)
from MIT MLPDS (Machine Learning for Pharmaceutical
Discovery and Synthesis) Consortium
95.079% 95.604%
RMSE 0.6076
RMSE 0.7970

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Use Case 2: Molecule Generation
Encoder Decoder
Discriminator
Generator
Faez F, Ommi Y, Baghshah MS, Rabiee HR.
Deep Graph Generators: A Survey.
IEEE Access. 2021;9: 106675–106702.
• Autoregressive
• Reinforcement-learning-based
Generated
or
Actual?
• Autoencoder-based / Flow-based
• Adversarial
Generator Generator
GNNs are an important
building block to design
generation modules.
The design patterns to
generate images, sounds,
texts, are quite useful!

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Use Case 3: Fast Approximation for QM Calculations
input output
gdb_21014
1000 sec
Density Functional Theory (DFT)
B3LYP/6-31G(2df, p) level
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
ˆ
H = E
by solving a one-electron Schrödinger
equation (Kohn–Sham equation)
ML
0.01 sec
≈
100,000 times faster!
Quantum mechanical
calculations
• Internal energy
• Free energy
• Zero point vibrational
energy
• Energy of HOMO
• Energy of LUMO
• Isotropic polarizabiliity
• Dipole moment
• Electronic spatial
extent
• Enthalpy
• Heat capacity
https://qcarchive.molssi.org/apps/ml_datasets/
…

View Slide

Use Case 3: Fast Approximation for QM Calculations
Predictions for Test Data by SchNet (Schütt et al, 2017) Predictions for Test Data by DimeNet (Klicpera et al, 2020)
Dipole Moment Energy U
HOMO
LUMO Heat Capacity
Enthalpy H Dipole Moment Energy U
HOMO
LUMO Heat Capacity
Enthalpy H
GNN predictions are strikingly accurate, in particular, for predicting enegies of a molecule of a
conformation or forces at each atom to transition towards a more stable conformation!
y_true
y_pred
y_true
y_pred
y_true
y_pred
y_true
y_pred
y_true
y_pred
y_true
y_pred
y_true
y_pred
y_true
y_pred
y_true
y_pred
y_true
y_pred
y_true
y_pred
y_true
y_pred

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Graph Regression: to predict the DFT-calculated HOMO-LUMO from 2D molecular graphs
Dataset: 3,803,453 graphs from PubChemQC (cf. QM9 = 133,885 graphs)
Rank Test MAE Models
1 0.1200 (eV) 10 × GNNs (12-layer Graphormer) + 8 × ExpC*s (5-layer ExpandingConv)
2 0.1204 (eV) 73 × GNNs (11-layer LiteGEMConv ʴ SSL pretraining)
3 0.1205 (eV) 20 × GNNs (32-layer GNN ʴ Noisy Nodes)
https://ogb.stanford.edu/kddcup2021/results/
OGB Large-Scale Challenge (KDDCup 2021)

View Slide

Pretrained models drive applied DL (ImageNet, BERT, …)
Many practical applications lack large data, and the use of pretrained models are critical.
Especially, the models that are pre-trained on broad data at scale and are adaptable to
a wide range of downstream tasks.
Call them
"foundation models"?

View Slide

Strategies for Pre-training
Graph Neural Networks
Hu, Liu, Gomes, Zitnik, Liang,
Pande, Leskovec (ICLR 2020)
Self-Supervised Graph
Transformer on Large-Scale
Molecular Data
Rong, Bian, Xu, Xie, Wei, Huang,
Huang (NeurIPS 2020)
https://arxiv.org/abs/
2007.02835
Large-scale pretraining by self-supervised learning tasks
Representation
learning module
Representation
learning module
Head for
pretraining
Head for
target task
Target downstream task
(small-data problem)
Pretraining
Large-scale Pretext task
(often self-supervised)
Transfer / Calibrate (Fine-Tune)
SSL tasks
for molecules

View Slide

• Euclidean group E(3)ɿ translations, rotations, reﬂections in 3D
• Special Euclidean group SE(3)ɿ translations, rotations in 3D
Schütt et al, SchNet. (2017) https://arxiv.org/abs/1706.08566
Satorras et al, E(n) Equivariant Graph Neural Networks. (2021) https://arxiv.org/abs/2102.09844
Anderson et al, Cormorant. (2019) https://arxiv.org/abs/1906.04015
Unke et al, PhysNet. (2019) https://arxiv.org/abs/1902.08408
Klicpera et al, DimeNet++. (2020) https://arxiv.org/abs/2011.14115
Fuchs et al, SE(3)-Transformers. (2021) https://arxiv.org/abs/2006.10503
Köhler et al, Equivariant Flows (Radial Field). (2020) https://arxiv.org/abs/2006.02425
Thomas et al, Tensor Field Networks. (2018) https://arxiv.org/abs/1802.08219
E(3)-equivariant
E(3)-invariant
SE(3)-equivariant
*OWBSJBOU
&RVJWBSJBOU
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
f(g · x) = g · f(x)
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
f(g · x) = f(x)
Geometric symmetry: Invariance and equivariance
Fundamental Requirements for Geometric GNNs:
The xyz coordinates cannot be directly used as node features.
We need to consider the invariance and equivariance under the motion group

View Slide

Edge-aware Message Passing Neural Networks (MPNNs)
Gilmer J, Schoenholz SS, Riley PF, Vinyals O, Dahl GE.
Neural Message Passing for Quantum Chemistry.
ICML 2017
Faber FA, Hutchison L, Huang B, Gilmer J, Schoenholz SS, Dahl GE, et al.
Prediction Errors of Molecular Machine Learning Models Lower than Hybrid DFT Error.
J Chem Theory Comput. 2017;13: 5255–5264.
Atom features
Atom type H, C, N, O, F (one-hot)
Atomic number # of protonns (int)
Acceptor 0 or 1 (binary)
Donor 0 or 1 (binary)
Aromatic 0 or 1 (binary)
Hybridization sp, sp2, sp3 (one-hot or null
# of hydrogens (integer)
Bond features
Euclidean distace between atom pair (real)
Bond types
single, double, triple,
aromatic (one-hot)
E(3)-invariant
xyz are used only as distances

View Slide

SchNet (Schütt et al, 2017): Standard Geometric GNN
gdb_3
Graph
0
1 2
0 1
2
edges w/
cutoff (10Å)
H2
O atom features

0 1 2
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x2
0
0 1
1
0 2
2
1 2
bond features
0.9620 0.9622 1.5133
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rij := kri rj
k
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w12
Jørgensen PB, Jacobsen KW,
Schmidt MN. Neural Message
Passing with Edge Updates for
Predicting Properties of
Molecules and Materials.
arXiv [stat.ML]. 2018.
http://arxiv.org/abs/1806.03146
SchNet-edge-update

View Slide

nn.Embedding
128
x2
gdb_3
Graph
0
1 2
0 1
2
edges w/
cutoff (10Å)
H2
O atom features

0 1 2
0
0 1
1
0 2
2
1 2
bond features
0.9620 0.9622 1.5133
rij := kri rj
k
w12
SchNet-edge-update

View Slide

nn.Embedding
128
x2
gdb_3
Graph
0
1 2
0 1
2
edges w/
cutoff (10Å)
H2
O atom features

0 1 2
0
0 1
1
0 2
2
1 2
bond features
0.9620 0.9622 1.5133
rij := kri rj
k
Gaussian Smearing
MLP (+ cutoff function)
w12
128
50
SchNet-edge-update

View Slide

nn.Embedding
128
x2
gdb_3
Graph
0
1 2
0 1
2
edges w/
cutoff (10Å)
H2
O atom features

0 1 2
0
0 1
1
0 2
2
1 2
bond features
0.9620 0.9622 1.5133
rij := kri rj
k
Gaussian Smearing
MLP (+ cutoff function)
w12
128
50
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xi xi +
0
@
X
j2Ni
(xj) !ij
1
A
Message Passing with
residual connections
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xi
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xj 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
xk
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
wij 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
wik
Element-wise
multiplication
NN (MLP etc)
Neighboring
nodes
SchNet-edge-update

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QSAR/QSPR, QM Approximation, Molecule Generations, …
(FP.PM
(FN/FU
Klicpera et al (NeurIPS2021)
Ganea et al (NeurIPS2021)
%JNF/FU
Klicpera et al (NeurIPS WS2022)
3BEJBM#BTJT 2D Spherical (Fourier-Bessel) Basis
Bond angles
Bond angles
Torsion angles
(Dihedral angles)
generates distributions of low-energy
molecular 3D conformers

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ML ⁇ QM: ML Potentials, Force fields, Density functionals
Machine Learning at the Atomic Scale (Chem. Rev.)
https://pubs.acs.org/toc/chreay/121/16
Data Science Meets Chemistry (Acc. Chem. Res.)
https://pubs.acs.org/page/achre4/data-science-meets-chemistry

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SchNOrb (Schütt et al, Nat Commn, 2019)

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DM21 Density functional (Kirkpatrick et al, Science, 2021)

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"Learn to simulate"

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Learn to simulate long-time evolution of a glassy sytem
https://deepmind.com/blog/article/Towards-understanding-glasses-with-graph-neural-networks
Bapst V, Keck T, Grabska-Barwińska A, Donner C, Cubuk ED, Schoenholz SS, et al.
Unveiling the predictive power of static structure in glassy systems.
Nature Physics. 2020;16: 448–454.

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Annu. Rev. Phys. Chem. 71:361–90 (2020)
PNAS (2020)
Acc. Chem. Res. 54(7):1575–1585 (2021)
DL/GNNs ⁇ Simulations
How to fuse ML (empiricism) and simulations (rationalism) is one of the recent hot topics.

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AtomicNum
TotalDegree
TotalNumHs
FormalCharge
deltaMass
IsInRing
Toward more effective inductive bias?
Water molecule H2
O
0
1 2
0 1
8
2
0
0
0
0
1
1
0
0
0
0
0
0 1
0
0
0
0
BondType
Stereo
1
1
0
0
0
0
A molecular graph (RDKit)
Atom
Invariants
Bond
Invariants
1 2
bond angle
104.45°
atom-atom
distance
95.84 pm
O
H H
H
O
H
1s2 2s2 2p4
1s1 1s1
8 + 1 + 1 = 10 electrons
+8
+ +
-
-
-
-
-
-
-
-
-
-
covalent bonds
δ+
δ+
δ-
δ-
- -
-
-
O
H
H
sp3 hybridization molecular orbitals
O
H H
sp3 sp3 sp3 sp3
2px 2px 2px
2s
1s
1s
O H H
LUMO
HOMO

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Toward more effective inductive bias?
https://doi.org/10.1038/ s42254-021-00314-5

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https://uclnlp.github.io/nampi/
Neural Abstract Machines & Program Induction
• Differentiable Neural Computers /
Neural Turing Machines (Graves+ 2014)
• Memory Networks (Weston+ 2014)
• Pointer Networks (Vinyals+ 2015)
• Neural Stacks (Grefenstette+ 2015, Joulin+ 2015)
• Hierarchical Attentive Memory
(Andrychowicz+ 2016)
• Neural Program Interpreters (Reed+ 2016)
• Neural Programmer (Neelakantan+ 2016)
• DeepCoder (Balog+ 2016)
:
DL/GNNs ⁇ Symbolic Tasks, Logical Inference, Planning
Now we can use machine learning also for symbolic, logical, algorithmic tasks!
Can we also use explicit chemical knowledges?

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https://www.ipam.ucla.edu/dlc2021
DL/GNNs ⁇ Combinatorial Optimization and Reasoning
https://doi.org/10.1016/j.patter.2021.100273
https://youtu.be/QOBoZaDZYUI

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One final remark on "the true dark side" …

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Object recognition
Game play
ˑ֮׶ָהֲ˒
J’aime la
musique I love music
Speech recognition
Machine translation
The huge gap between prediction and understanding
Prediction does not directly bring us Understanding nor Discovery.
Current ML already provides practical applications below, but how we recognize objects and
speech sounds, and how we aquire and use languages is still not well understood…

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Weight (kg)
Height
(cm)
Height and Weight of Pro baseball players
(2016 NPB Website)
To ﬁnd out what happens to a system when you interfere with it,
you have to interfere with it (not just passively observe it). George Box
Observational vs experimental (interventional) studies
We see correlation, but these data never tell us
"increase weight" does not imply "grow in height"
Applied Stats 101
Correlation does not imply causation
We need experiments! Passively observing
data and applying ML to it is alway insuﬃcient.
An Inconvenient Truth
All we can directly access is correlation

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Toward causal representation learning

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˖ %FTJHOQMBOBOE
DPOEVDUFYQFSJNFOT
˖ &WBMVBUFPCTFSWBUJPOT
˖ 8PSLXJUIFYQFSUT
From machine learning to machine discovery
The hard problems are happening at the interface between inside and outside of ML.
ML models
inside
outside
Input information
of the outside
Get information back
to the outside
˖ *EFOUJGZJOQVUWBSJBCMFT
˖ %FTJHO.-UBTLT
˖ 1SFQBSFHPPEUSBJOJOHEBUB
˖ 6TFFYJTUJOHEBUBLOPXMFEHF
Representing Intervening

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The lesson: Science is a human activity, after all
We need to seriously take all "human factors" into consideration. All diﬃculty is our
fault. We want "understanding" and "discovery", but neither machines nor nature do.
• Interpretability
All information needs to be simple enough so that we feel like we understand it
within our (poor) cognitive capability.
• Partiality of information
We cannot observe everything, nor model everything. Any data is some ﬁnite,
partial, and inevitably biased snapshot.
• Finitude of time
Discovery needs to be done within the time limit of one's life (or the extinction
of mankind)

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Summary

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Machine Learning for Molecules: Lessons and Challenges of Data-Centric Chemistry

Machine Learning for Molecules: Lessons and Challenges of Data-Centric Chemistry

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