Geometric deep learning SDM 2023
Swap the drug. The number stays. The map does not.
EIR reads the target as a plain sequence of amino acids and the drug as a graph, and predicts two things together: one number for how strongly the pair binds, and a residue-by-atom map of where.
Why two answers: the paper says a score alone “could only provide one number [...] which lack sufficient information to study how and where the drug and target bind”. On its affinity table the paper reports the best value in all 12 columns (Table 1); computed from its cells, the runner-up is 0.001 to 0.036 behind.
Figure 1Illustration
Both drugs are built to read the same number in this toy, to the two decimals shown. One number cannot tell them apart. The map can.
01 The problem
Screening drug candidates by computer means predicting how a drug and a target protein bind. The paper names what holds the usual approach back: a 3D structure of the target is not always available, and a binding score alone does not say where the two meet. Switch between the three approaches and watch what goes in and what comes out.
Figure 2Illustration
Goes in
Comes out
With scripts off the board shows the first approach. Each approach below says in words what goes in and what comes out.
Goes in: a 3D structure of the target, and the drug. Comes out: one number. Not used: the target sequence alone, known interaction pairs. Not produced: a map.
Goes in: a 3D structure of the target, the drug, and the known interaction pairs of the two. Comes out: one number. Not produced: a map.
Goes in: the target as a sequence only, and the drug. Comes out: one number and a map. Not used: a 3D structure of the target, known interaction pairs.
IllustrationA drawing of inputs and outputs made for this page, with the toy target, Drug A and the start map of this page’s Figure 1 as its small pictures; the number on it is a toy number and not a result. The quotations are the paper’s. The paper makes the two points of the first tab separately (Section 1): structures as the standard input, and one number as all an affinity score gives. It also names a separate line of work that predicts interfaces. The paper does not sort its baselines into these boards, so no model is named under the first two.
02 The idea
EIR scores every meeting of a residue and an atom: that table is the map. The predicted map then decides which residues and atoms count in the one pooled number. The bench is a toy of that wiring.
Figure 3Illustration
Point at a map cell to read its toy score. Select a residue on the strip to edit it.
Even pooling is this page’s counterfactual. The paper does not test the model without the link from the map to the number.
The start pair: Drug A on the 30-residue toy target. Nothing has been changed yet.
How to read the number. One number for the whole pair: any change anywhere can move it. The toy’s constants are set by hand, so the direction in which this number moves means nothing. Watch the map, and watch where the pooling track stands.
With scripts on, this view lets you change one residue or one atom and marks every map cell that felt the change, under the full toy and under the three variants the supplement defines. The drawing of the pair is the one in the first view.
Change one residue or one atom, then open “What felt the last change”.
Both branches of the sequence module and both channels of the graph module are on.
Toy behaviour above. Measured behaviour below, in the supplement’s words.
“The proposed EIR outperforms other variants, proving that jointly handling the multi-level signals is crucial for drug-target interaction prediction.” It reports one exception itself: see EIR-G.
Supplement 8.2, the supplement’s Figure 6, IC50 only, bars without printed values“EIR-C: remove the proposed global representation learning branch in SRL module.” What is left is the convolution, which sees a window.
Toy behaviour above. Measured behaviour below, in the supplement’s words.
“The lack of long-range interaction learning in EIR-C and the insufficient local interaction representation learning in EIR-A lead to performance reduction”.
Supplement 8.2, the supplement’s Figure 6, IC50 only, bars without printed values“EIR-A: remove the local representation learning branch in the SRL module.” What is left is the additive attention, which sees every position at once. In this toy, which has no positional encoding, it cannot tell their order apart; the paper’s Figure 2 draws a positional encoding on the way into the attention blocks.
Toy behaviour above. Measured behaviour below, in the supplement’s words.
“The lack of long-range interaction learning in EIR-C and the insufficient local interaction representation learning in EIR-A lead to performance reduction”.
Supplement 8.2, the supplement’s Figure 6, IC50 only, bars without printed values“EIR-G: remove the graph-level representation branch and Update Gate Unit in GRL module.” What is left is message passing along bonds.
Toy behaviour above. Measured behaviour below, in the supplement’s words.
“the EIR model outperforms the EIR-G model in DTA prediction”, and the exception: “Although EIR-G shows a slightly better performance for DTI prediction under PIT and PPI settings, the low performance in DTA prediction makes the model lack practical use for drug discovery.” DTA is the affinity, DTI the interface, PIT is Predict Interaction of Targets and PPI is Predict Pairwise Interactions.
Supplement 8.2, the supplement’s Figure 6, IC50 only, bars without printed valuesSelect a residue on the strip or an atom in the drawing, then give it another made-up kind. From the keyboard, keys 1 to 4 do the same on the strip and keys 1 to 3 on an atom.
EIR, all parts. No edit yet. Change one residue or one atom, or press one of the two edits. Distinct columns in the map: 13 of 30.
Why reach is an honest thing to show. Which cells can change after an edit follows from the form of each operation, not from the values of the weights: a sum over all positions, a window, a sum over bonded neighbours, one shared vector. The toy keeps exactly those forms, and “bit-identical” is tested by exact equality. What a branch does to accuracy is a measured question, which only the card under the drawing answers. The toy has no ground truth, so no variant is better or worse in it.
IllustrationA hand-built toy with 30 made-up residues, 7 made-up atoms, three numbers per item and fixed constants in place of learned weights. It shows how the design is wired and what each part can reach. It is not the trained network and its numbers are not results.
In this toy a residue and an atom score high when their made-up kinds match, which is why the shapes are shared. Real binding is nothing like this simple. The point is the shape of the computation.
The interface module transforms both embeddings and multiplies them, one score for each residue and atom pair (Eq. 4.17). The affinity module then takes “the predicted interaction matrix M” and uses it to carry each side’s features across before it pools (Eq. 4.18 to 4.23). In the printed equations the map feeds the number (Eq. 4.18 to 4.23) and the number does not appear in the map (Eq. 4.17).
As this page reads Eq. 4.2 to 4.5, the global branch gives each residue one weight, sums all positions into one summary and multiplies every residue by it. Change any residue and the summary shifts, so every column of the map can move. The paper’s aim for this module is to capture “both the local patterns and long-range relations between the residues”.
The local branch is built from convolution blocks “to extract sequentially local correlations from the target sequence embeddings” (Section 4.1.2). In the toy the window is three residues wide. The paper does not give its kernel width.
Message passing sums over bonded neighbours (Eq. 4.6). The paper’s reason for adding a graph-level vector: “It is challenging for the isolated nodes with few connections to influence the whole molecule graph because the message passing operation of the GNN relies on the edge connections.” (Section 4.2.2)
03 One pair, two answers
The drawing has two lanes, the target above and the drug below. In each lane the upper track looks at the whole and the lower track at the parts: double lines carry something about the whole, single lines something about the parts. The live values are the toy’s, for the residue and the atom you last selected in the bench, with every part switched on.
Figure 4Illustration
Drawn for this page from Equations 4.1 to 4.27, not copied from the paper’s Figure 2. The repeat counts NT and ND are symbols in the paper; it does not give their values.
The target is a sequence of L residues with 20 numbers each. The drug is a graph of N atoms with atom and bond attributes. No structure of the target is needed. The paper does describe the drug as a 3D structure, and its equations use atom and bond attributes. It does not say what the 20 numbers are.
residue 19 on the toy target, and a ring around atom 2 of the toy drug. The shapes are the made-up kinds.
Additive attention, as this page reads Eq. 4.2 to 4.5: each position gets one softmax weight over the L positions, not one per pair of positions as in self-attention. The weighted positions are summed into one summary, and every residue is multiplied by it. The paper’s index notation is not consistent.
Bars: the toy’s attention weights, one per residue, all 30 summing to 1. residue 19.
Convolution blocks pick up patterns among neighbouring residues. After a linear layer the local output is added to the global one, and the sum is the updated sequence embedding T′. The paper does not give the width of its kernels; the toy’s window is three residues.
Boxed: the window of three that the toy’s convolution sees. residue 19.
Each atom combines its own features with a sum over its bonded neighbours and the bond attributes, the step the paper calls Weisfeiler-Lehman relabelling. A GRU cell then updates the atom’s state.
Ringed: atom 2. Heavy bonds and dashed rings: the bonded neighbours it hears.
A vector for the whole molecule starts as the sum of all atom features. Attention from that vector over the atoms updates it, and sigmoid gates decide how much of it flows back into each atom. The paper adds it because message passing alone makes it hard for poorly connected atoms to influence the whole graph.
Bars: the toy’s graph-level attention, one per atom. atom 2.
Both embeddings are transformed and multiplied, which gives one score for each residue and atom pair: an L by N map. This is the intrinsic output. It is trained against interface labels with a binary cross-entropy for every cell.
The toy map, a row per atom and a column per residue, shaded by toy score. residue 19, atom 2; the outlined cell is where they meet.
The predicted map carries each side’s features across to the other side. With them, attention picks which residues and which atoms count, the two pooled vectors are multiplied, a GRU cell repeats this K times, and a last linear layer gives one number per complex: the extrinsic output.
Bars: where the number looks, one per residue. Dashed line: an even share, 1 of 30. Underlined: the residues the map lights. residue 19.
Select any part of the drawing to read what it is in the paper: its name there, where it is described, what goes in and out, the live toy value, and what the paper does not say. Arrow keys move between parts.
Section 3
The target enters as a sequence of L residues with a feature matrix of 20 numbers per residue. No 3D structure of the target is used. Toy: residue 19 is kind 1, which starts as [1.00, 0.00, 0.20].
The paper does not say what the 20 features are.
The paper’s Figure 2 only
Drawn in the paper’s Figure 2: the target embedding forks, and the positional encoding is added on the fork that enters the attention blocks. The fork into the convolution blocks has none. The toy leaves it out, so its global branch cannot tell positions apart.
The paper’s text does not describe it.
whole Section 4.1.1, Eq. 4.1 to 4.5
NA multi-head additive attention blocks, each of (NB + 2) additive attention layers, then a feed-forward layer. As this page reads Eq. 4.3, one softmax weight per position rather than one per pair of positions; the paper’s index notation is not consistent. Toy: residue 19 holds 5.1% of the weight and the summary is [0.08, 0.08, 0.06].
The paper gives no value for NA or NB, and no cost measurement for this branch.
parts Section 4.1.2
NC convolution blocks “to extract sequentially local correlations from the target sequence embeddings”. Toy: one block, a window of three, which gives residue 19 the vector [0.50, −0.15, −0.10].
The paper does not give the kernel width or NC.
Section 4.1.2
“After a linear transformation layer, the output of the local representation branch is added to the global branch to get the updated sequence embeddings T′(P, S′).” Toy: residue 19 leaves as [1.52, −0.13, 0.12].
The whole module repeats NT times; the paper gives no value.
Section 3
Atoms are nodes with an attribute matrix F, bonds are edges with an attribute tensor E. Toy: atom 2 is kind 1, which starts as [1.00, 0.00, 0.10].
The paper does not list the atom and bond attributes. It calls the input a 3D structure; no coordinate appears in its equations.
parts Section 4.2.1, Eq. 4.6 to 4.9
A gated graph neural network: each atom is updated from a sum over its bonded neighbours, mixed with the graph-level vector by a gate, then passed through a GRU cell. Toy: atom 2 hears atoms 1, 3 and ends as [0.58, 0.15, 0.16].
The paper gives no hidden size and no number of rounds ND.
whole Section 4.2.2, Eq. 4.10 to 4.16
S starts as the sum of the node features. Attention with k heads over the atoms updates it through a gate and a GRU cell. Its final value S′ also enters the affinity output directly (Eq. 4.23). Toy: S is [0.58, 0.58, 0.28].
The paper gives no value for k.
Named in the paper’s Figure 2 and Supplement 8.2; read here as Eq. 4.7, 4.8 and 4.14, 4.15
Two sigmoid gates, one on each side: (1 − gate) times a side’s own features plus gate times the other scale. It is removed together with the graph-level branch in the variant EIR-G. The paper’s Figure 2 and Supplement 8.2 name the unit; the running text does not. This page reads it as the two gates of Eq. 4.7, 4.8 and 4.14, 4.15. Toy: the gate lets 61% of the graph-level vector into atom 2.
The paper reports no measurement of the gate by itself.
Section 3; Section 4.3
The interface module “first transforms the multi-level features captured from the SRL module and GRL features to construct the drug-target complex graph”. Toy: 30 + 7 nodes.
The paper does not describe the transform beyond Eq. 4.17.
parts Section 4.3, Eq. 4.17. The paper’s word: intrinsic
Each side passes through a linear layer and a non-linearity, their matrix product gives one number per pair, and a last non-linearity gives M′. Toy: residue 19 with atom 2 scores 0.83.
The paper does not name the two non-linearities.
whole Section 4.4, Eq. 4.18 to 4.23. The paper’s word: extrinsic
It uses “the predicted interaction matrix M”: the model’s own map, not the labels. K iterations of a GRU, then a linear layer. Toy: 78.44 toy units, with 85% of the target-side weight on the touched residues.
The paper does not test the model without the link from the map, and gives no value for K.
Section 4.5, Eq. 4.24 to 4.27
Mean squared error on the number, binary cross-entropy averaged over the L by N cells of the map, added with weights λE and λI. The paper: EIR is “under the co-guidance of both extrinsic representation learning [...] and intrinsic representation learning”. The toy is not trained, so it has no loss.
The paper does not report the values of λE and λI it used, and never sets one of them to zero.
IllustrationThe drawing is this page’s reading of the paper’s equations, and the live values come from the hand-built toy of this page’s Figure 3. They are not the trained network and its numbers are not results.
04 The evidence
The paper tests three ways of holding data out, on two datasets it calls KIKD and IC50. In each, a drug, a target or both have never been seen in training. First see what each setting hides from the model, then read Table 1.
Figure 5Illustration
Predict Interaction of Drugs, fold 1 of 5: drugs 1 to 3 are held out. 7 of the 60 toy pairs are tested, 53 are left for training.
Illustration15 made-up drugs, 15 made-up targets and made-up pairs. Only the fold counts are the paper’s (Supplement 8.1): five disjoint sets of drugs or of targets, and three of each for the pairwise setting. Here a set is a run of neighbouring rows or columns. The paper says it divides all drug-targets into cluster groups by hierarchical clustering on similarity and uses a threshold γ = 0.3 in its evaluation experiments (Section 6.2). It does not spell out how the cluster groups become the five or three disjoint sets. The counts are not results.
Figure 6Measured, Table 1
The bars start at zero, so every gap shows at its true size.
The datasets. Two datasets, which the paper calls KIKD and IC50 and takes from prior works [14] [4] [16] (Section 5). Its Figure 2 draws database icons labelled PDBBind and BindingDB without comment. It gives no sizes, no construction details and no affinity units, so the RMSE axis carries no unit.
The folds. The supplement describes five-fold cross-validation for PID and PIT and nine-fold for Predict Pairwise Interactions (PPI) (Supplement 8.1). The paper does not say how the folds are combined into one cell, and prints no spread and no significance test.
The machine. The paper ran everything on one Linux machine with “8x NVIDIA Tesla A100 GPU with 40 GB video memory” (Section 5). It reports no running time.
| Dataset | Dataset: KIKD | Dataset: IC50 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Setting | KIKD PID_R | KIKD PIT_R | KIKD PPI_R | KIKD PID_P | KIKD PIT_P | KIKD PPI_P | IC50 PID_R | IC50 PIT_R | IC50 PPI_R | IC50 PID_P | IC50 PIT_P | IC50 PPI_P |
| CGKronRLS | 1.493 | 1.728 | 1.846 | 0.686 | 0.537 | 0.463 | 1.203 | 1.439 | 1.516 | 0.675 | 0.505 | 0.452 |
| Tsubaki et al. | 1.763 | 1.790 | 1.940 | 0.523 | 0.500 | 0.451 | 1.400 | 1.435 | 1.793 | 0.530 | 0.511 | 0.452 |
| DeepDTA | 1.556 | 1.711 | 1.800 | 0.652 | 0.545 | 0.483 | 1.224 | 1.370 | 1.411 | 0.659 | 0.542 | 0.511 |
| DeepAffinity | 1.641 | 1.786 | 1.834 | 0.600 | 0.490 | 0.454 | 1.261 | 1.406 | 1.455 | 0.634 | 0.518 | 0.467 |
| MONN | 1.499 | 1.702 | 1.776 | 0.687 | 0.555 | 0.510 | 1.179 | 1.350 | 1.385 | 0.690 | 0.566 | 0.536 |
| GIN_Conv | 2.035 | 2.036 | 1.949 | 0.394 | 0.199 | 0.299 | 1.620 | 1.686 | 1.709 | 0.353 | 0.249 | 0.400 |
| GAT_net | 2.088 | 2.048 | 2.063 | 0.245 | 0.129 | 0.236 | 1.614 | 1.511 | 1.685 | 0.218 | 0.468 | 0.244 |
| GAT_GCN | 2.044 | 2.089 | 2.116 | 0.171 | 0.154 | 0.164 | 1.212 | 1.674 | 1.732 | 0.375 | 0.193 | 0.160 |
| GCN_net | 2.043 | 2.070 | 2.100 | 0.260 | 0.163 | 0.198 | 1.627 | 1.661 | 1.801 | 0.195 | 0.284 | 0.473 |
| GanDTI | 1.749 | 1.810 | 1.872 | 0.518 | 0.466 | 0.407 | 1.426 | 1.810 | 1.903 | 0.475 | 0.466 | 0.385 |
| EIR (Ours) | 1.457 | 1.687 | 1.773 | 0.696 | 0.556 | 0.530 | 1.177 | 1.335 | 1.371 | 0.697 | 0.576 | 0.543 |
As printed. R is root mean square error, lower is better. P is Pearson’s correlation, higher is better. PID is Predict Interaction of Drugs, PIT is Predict Interaction of Targets and PPI is Predict Pairwise Interactions. Among the values, only the EIR row is bold, as in the paper. The paper names Spearman’s ρ as a third metric and does not tabulate it. Computed by this page from the cells: EIR has the best cell in 12 of 12 columns; the runner-up is MONN in 11 of them and CGKronRLS in 1; the gaps to the runner-up run from 0.001 to 0.036. In 7 of the 11 rows the error rises and the correlation falls at each step from PID to PIT to PPI (the pairwise setting) on both datasets; none of the four GraphDTA rows follows that order throughout.
05 A second reading
Two things a careful reader checks next: how far EIR is ahead of any one baseline, cell by cell, and what stands behind the other half of the claim, the interface prediction.
Figure 7Measured, Table 1
Both marks of a row sit on one axis per metric, and the axis starts at zero, so a gap is drawn at its true size against the values. Where the two marks overlap, read the printed difference.
EIRMONNdiffer by: EIR minus MONN
RMSE, lower is better EIR is ahead where its diamond sits left of the ring
Pearson, higher is better EIR is ahead where its diamond sits right of the ring
EIR against MONN. RMSE: EIR lower in 6 of 6 columns, by 0.002 to 0.042. Pearson: EIR higher in 6 of 6 columns, by 0.001 to 0.020. RMSE: lower is better. Pearson: higher is better. Computed from Table 1.
Measured, Table 1Both values in every cell are printed cells of Table 1 (Section 6.1). The differences are plain subtractions computed by this page from Table 1. The cells come from five-fold or nine-fold cross-validation (Supplement 8.1); the paper does not say how the folds are combined, and prints no spread and no significance test, so this page draws no conclusion from the size of any gap.
This page does not chart them and reads no value off a bar. Each tab says what was varied, what the paper says, what the figure does not give, and where it is.
And six pictures. The paper’s Figure 5 shows six examples, one picked at random from each of three AUC bands for drugs and for targets. The paper: “Most of the identified active sites in the drug plots and target sequence plots matched the ground truth labels. The figure shows a few false negative and false positive observations.” (Section 5.2; Section 6.3)
The takeaway
What the paper shows for it: the best cell in every column of one affinity table, by 0.001 to 0.036 over the runner-up (computed from Table 1), with no spread printed, and interface results as charts. What it does not isolate: whether the link from the map to the number is what helps.
06 Office hours
Written by Tian's agent while Tian slept and Pepper supervised. Pepper accepts no liability either.
Each answer says where in the paper it comes from, so you can check the agent's work.
No. In this paper they are the two things predicted. Extrinsic is the binding affinity, “the extrinsic scalar of the overall complex”: one number. Intrinsic is the interface, an L by N matrix over residues and atoms. The conclusion puts it as a global property of the complex against information at the node and edge level. The paper has no network of known interactions and no notion of a molecule’s neighbours.
Source: Section 3; Section 7Only for the target, which enters as a sequence with 20 numbers per residue. Definition 3.1 starts from “a drug with 3D structure” and Definition 3.2 from “a drug with a 3D structure”, and the drug module is described as learning from the drug’s geometric 3D structure, although the printed equations use only atom and bond attributes and the paper does not list them. Training the interface output also needs interface labels; the paper does not say how they were obtained. Its Figure 2 draws database icons labelled PDBBind and BindingDB without comment.
Source: Section 3, Definitions 3.1 and 3.2; Section 4.2; the paper’s Figure 2EIR has the best cell in all 12 columns of Table 1. The runner-up is MONN in 11 of them: behind by 0.002 to 0.015 in its five RMSE columns and by 0.001 to 0.020 in the six Pearson columns. In the remaining column (KIKD, PID, RMSE) the runner-up is CGKronRLS, 0.036 behind, the largest gap to a runner-up in the table. These differences are computed from the printed cells. The cells come from five-fold or nine-fold cross-validation (Supplement 8.1); the paper does not say how folds are combined, and prints no spread, no repeated seeds and no significance test. It also names Spearman’s ρ as a metric and does not tabulate it.
Source: Table 1; Section 5.2; Supplement 8.1In the paper’s Figure 3, as bars. The measure is the average AUC over test samples, the EIR bar is the tallest in each of six panels, and no value is printed; the axes start between 0.70 and 0.80. DeepAffinity is named as an interface baseline in the text and does not appear in the figure. The qualitative figure shows six examples chosen one per AUC band, and the paper itself notes “a few false negative and false positive observations”. This page therefore charts the affinity table only.
Source: the paper’s Figure 3 and the paper’s Figure 5; Section 5.1; Section 5.2; Section 6.3The design says it should: the affinity module uses “the predicted interaction matrix M” to carry features between the two sides before pooling. The experiments do not isolate it. There is no run of EIR trained on one loss only, no sweep of λE and λI (their values are not reported), and no variant without the link from the map to the affinity module. The paper’s statement that EIR “performs better than the single-task models” compares it with other architectures, and the supplement’s ablation removes encoder branches, on one dataset, with one exception it reports itself: without the graph-level channel the interface AUC is slightly higher under two settings. The “Even” switch in the bench shows how the link is wired, not that it helps.
Source: Section 4.4; Section 4.5; Section 6.1; Supplement 8.2