Multi-task learning shows strikingly inconsistent results -- sometimes joint training helps substantially, sometimes it actively harms performance -- yet the field lacks a principled framework for predicting these outcomes. We identify a fundamental but unstated assumption underlying gradient-based task analysis: tasks must share training instances for gradient conflicts to reveal genuine relationships. When tasks are measured on the same inputs, gradient alignment reflects shared mechanistic structure; when measured on disjoint inputs, any apparent signal conflates task relationships with distributional shift. We discover this sample overlap requirement exhibits a sharp phase transition: below 30% overlap, gradient-task correlations are statistically indistinguishable from noise; above 40%, they reliably recover known biological structure. Comprehensive validation across multiple datasets achieves strong correlations and recovers biological pathway organization. Standard benchmarks systematically violate this requirement -- MoleculeNet operates at <5% overlap, TDC at 8-14% -- far below the threshold where gradient analysis becomes meaningful. This provides the first principled explanation for seven years of inconsistent MTL results.
Figures & tables
Figure 1: Sample overlap determines gradient interpretability. (a) When tasks share samples, gradients ∇θLA and ∇θLB are computed on the same input, and their angle θ reflects the true mechanistic relationship. (b) When tasks have disjoint samples, gradients are computed on different inputs from potentially different distributions, making cosθ spurious.
Dataset Statistics
Validation Results
Dataset
Domain
Tasks
Type
Compounds
Pairs
Overlap ( ↑ )
r(G,E) ( ↑ )
ρ(G,E) ( ↑ )
Tox21
Toxicity
12
Clf
7,831
66
100%
0.65
0.62
ToxCast
Toxicity
17
Clf
8,576
136
∼ 80%
0.86
0.83
SIDER
Side Effects
27
Clf
1,427
351
100%
0.94
0.97
Tox21+ADME
Cross-Domain
16
Mixed
3,410
120
100%
0.61
0.58
Kinase Panel
Selectivity
21
Reg
5,039
210
∼ 20%
0.67
0.68
Table 1: Comprehensive dataset statistics and validation results. ( ↑ ) indicates higher is better. Bold / underline mark best/second-best. All correlations significant at p<0.001 .
Figure 2: Main validation results. (A) Gradient similarity vs empirical correlation across datasets; each dataset shows strong positive correlation with per-dataset regression lines. (B) Phase transition at ∼ 30% compound overlap; green points indicate p<0.01 , red indicates non-significant. Shaded regions show unreliable ( < 30%) vs reliable ( > 30%) regimes. (C) Cross-domain analysis: within-domain pairs (Tox21, ADME) show high r(G,E) while cross-domain pairs show weak correlation, confirming hierarchical structure recovery. (D) Training dynamics on Tox21: gradient matrix stabilizes by epoch 20, enabling early estimation.
Figure 3: Practical utility. (A) Gradient similarity predicts MTL benefit ( r=0.71 , p<10−8 ); high- G pairs show positive transfer while low- G pairs show negative transfer. (B) Gradient-based task grouping outperforms random assignment by 1.4–4.2% ( p=0.023 , n=3 groups).
Category
Pairs
Gˉ
Eˉ
r(G,E)
Within-Tox
28
0.054
0.18
0.95
Within-ADME
28
0.044
0.15
0.66
Cross-Domain
64
0.008
0.02
0.23
Table 2: Cross-domain analysis on Tox21+ADME.
Appendix figures & tables12 assets
Supplementary material from the paper’s appendix.
Appendix
Component
Specification
Encoder type
GCN
Message-passing layers
3
Hidden dimensions
[256, 256, 256]
Graph pooling
Global mean
Activation
ReLU
Dropout rate
0.3
Appendix
Table 3: Full architecture specification for GCN encoder.
Hyperparameter
Value
Optimizer
AdamW
Learning rate
10−3
Weight decay
10−2
Batch size
32
Max epochs
100
Early stopping
25 epochs
Appendix
Table 4: Training configuration.
Figure 4: Supplementary: Full gradient and empirical matrices for Tox21. (A) Gradient similarity matrix G showing task relationships learned during training. (B) Empirical correlation matrix E computed directly from property measurements. Tasks are reordered by hierarchical clustering to reveal structure.
Task Pair
Gij
Eij
Most Synergistic
Hepatobiliary – Gastrointestinal
0.142
0.312
Cardiac – Vascular
0.128
0.287
Nervous system – Psychiatric
0.119
0.264
Skin – Immune system
0.107
0.198
Most Conflicting
Appendix
Table 5: SIDER: Most synergistic and conflicting task pairs.
Annotation Level
Clusters
ARI
NMI
Broad (NR vs SR)
2
0.177
0.198
Mechanistic
5
0.059
0.549
Detailed Pathways
9
0.651
0.946
Appendix
Table 6: Pathway recovery performance at different annotation granularities.
Table 8: Gradient matrix correlations across training epochs. By epoch 20, correlation with final matrix reaches r=0.73 , enabling early task relationship estimation.
GCN
GAT
1D-CNN
ECFP
GCN
1.00
0.81
0.73
0.46
GAT
0.81
1.00
0.71
0.42
1D-CNN
0.73
0.71
1.00
0.38
ECFP
0.46
0.42
0.38
1.00
Appendix
Table 9: Pairwise correlations between gradient matrices from different architectures on Tox21.
Metric
Value
Pearson r (G vs Benefit)
0.71
Spearman ρ
0.68
p -value
<10−8
High- G pairs ( G>0.05 )
Mean benefit
+2.3%
Positive benefit (%)
78%
Appendix
Table 10: MTL benefit prediction results.
Groups
Gradient
Random
Improvement
2
74.2%
72.8%
+1.4%
3
76.1%
73.4%
+2.7%
4
78.3%
74.1%
+4.2%
Appendix
Table 11: Task grouping comparison (average AUC).
Method
r with E
p -value
Gradient similarity
0.65
<10−8
Task2Vec (diagonal Fisher)
0.03
0.81
Task2Vec (full Fisher)
−0.08
0.52
Appendix
Table 12: Task2Vec vs gradient similarity comparison.
Threshold
Neg. avoided
Beneficial kept
F1
G≥0.05
62%
91%
0.74
G≥0.10
77%
85%
0.81
G≥0.15
85%
72%
0.78
Appendix
Table 13: Negative transfer avoidance at different thresholds.