TOWARDS EQUIVARIANT GRAPH CONTRASTIVE LEARNING VIA CROSS-GRAPH AUGMENTATION

Abstract

Leading graph contrastive learning (GCL) frameworks conform to the invariance mechanism by encouraging insensitivity to different augmented views of the same graph. Despite the promising performance, invariance worsens representation when augmentations cause aggressive semantics shifts. For example, dropping the super-node can dramatically change a social network's topology. In this case, encouraging invariance to the original graph can bring together dissimilar patterns and hurt the task of instance discrimination. To resolve the problem, we get inspiration from equivariant self-supervised learning and propose Equivariant Graph Contrastive Learning (E-GCL) to encourage the sensitivity to global semantic shifts. Viewing each graph as a transformation to others, we ground the equivariance principle as a cross-graph augmentation -graph interpolationto simulate global semantic shifts. Without using annotation, we supervise the representation of cross-graph augmented views by linearly combining the representations of their original samples. This simple but effective equivariance principle empowers E-GCL with the ability of cross-graph discrimination. It shows significant improvements over the state-of-the-art GCL models in unsupervised learning and transfer learning. Further experiments demonstrate E-GCL's generalization to various graph pre-training frameworks.

1. INTRODUCTION

Graph contrastive learning (GCL) (You et al., 2020; Suresh et al., 2021; Xu et al., 2021) is a prevailing paradigm for self-supervised learning (Chen et al., 2020; Zbontar et al., 2021) on graph-structured data. It typically pre-trains a graph neural network (GNN) (Dwivedi et al., 2020) without labeled data, in an effort to learn generalizable representations and boost the fine-tuning on downstream tasks. The common theme across recent GCL studies is instance discrimination (Dosovitskiy et al., 2014; Purushwalkam & Gupta, 2020 ) -viewing each graph as a class of its own, and differing it from other graphs. It galvanizes representation learning to capture discriminative characteristics of graphs. Towards this end, leading GCL works usually employ two key modules: graph augmentation and contrastive learning. Specifically, graph augmentation adopts the "intra-graph" strategy to create multiple augmented views of each graph, such as randomly dropping nodes (You et al., 2020) or adversarially perturbing edges (Suresh et al., 2021) . The views stemming from the same graph constitute the positive samples of this class, while the views of other graphs are treated as negatives. Consequently, contrastive learning encourages the agreement between positive samples and the discrepancy between negatives. This procedure essentially imposes "invariance" (Purushwalkam & Gupta, 2020; Dangovski et al., 2022) upon representations -making the anchor graph's representation invariant to its intra-graph augmentations (Figure 1a ). Formally, let g be the anchor graph, P be the groups of intra-graph augmentations, and ϕ(•) be the GNN encoder. The "invariance to intra-graph augmentations" mechanism states ϕ(g) = ϕ(T p (g)), ∀p ∈ P -the representation ϕ(g) is insensitive to the changes in augmentation p, where T p (g) is the action of augmentation p on graph g. We refer to works adopting this mechanism as Invariant Graph Contrastive Learning (I-GCL). 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U e V n 0 + g T d G K U P g p j a Z 7 Q a K r + 3 s h w p N Q 4 C s x k n l E t e r n 4 n 9 d N d X j p Z 0 w k q a a C z A 6 F K U c 6 R n k P q M 8 k J Z q P D c F E M p M V k S G W m G j T V t G U 4 C 5 + e Z m 0 z q r u e b V 2 W y v X f + o o w B E c Q w V c u I A 6 3 E A D m k D g A Z 7 g B V 6 t R + v Z e r P e Z 6 M r 1 n z n E P 7 A + v g G M 0 6 T / w = = < / l a t e x i t > (G) < l a t e x i t s h a 1 _ b a s e 6 4 = " S n V d 6 K 1 r Y J m h z h d a A Z P z C w 8 C m 4 k = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x K i D k G v H h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o L J 3 d z v P K H S P J Y P Z p q g H 9 G R 5 C F n 1 F i p O R o U S 2 7 Z X Y B s E m 9 F S n V Y o j E o f v W H M U s j l I Y J q n X P c x P j Z 1 Q Z z g T O C v 1 U Y 0 L Z h I 6 w Z 6 m k E W o / W x w 6 I 1 d W G Z I w V r a k I Q v 1 9 0 R G I 6 2 n U W A 7 I 2 r G e t 2 b i / 9 5 v d S E N T / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0 r 4 p e 9 V y p V k p 1 W u r O P J w A Z d w D R 7 c Q h 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B y N w j S o = < / l a t e x i t > g < l a t e x i t s h a 1 _ b a s e 6 4 = " L X e m w C 7 q S X v D x r m N f w D p J q p 9 6 h w = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e y G o B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0 q 6 U v Z t y t V k p 1 a q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + r 9 j Q A = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " L X e m w C 7 q S X v D x r m N f w D p J q p 9 6 h w  = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e y G o B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0 q 6 U v Z t y t V k p 1 a q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + r 9 j Q A = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " I i Y n i 4 S M w 6 / K m 5 O r c F + N k o G z n N o = " > A A A B 8 n i c b V D L S g N B E J z 1 G e M r 6 t H L Y h B y C r s h q M d A L j l G M A / Y L G F 2 0 k m G z M 4 s M 7 1 i W P I Z X j w o 4 t W v 8 e b f O H k c N L G g o a j q p r s r S g Q 3 6 H n f z t b 2 z u 7 e f u 4 g f 3 h 0 f H J a O D t v G 5 V q B i 2 m h N L d i B o Q X E I L O Q r o J h p o H A n o R J P 6 3 O 8 8 g j Z c y Q e c J h D G d C T 5 k D O K V g p 6 C E + Y 1 R u z f q V f K H p l b w F 3 k / g r U q y R J Z r 9 w l d v o F g a g 0 Q m q D G B 7 y U Y Z l Q j Z w J m + V 5 q I K F s Q k c Q W C p p D C b M F i f P 3 G u r D N y h 0 r Y k u g v 1 9 0 R G Y 2 O m c W Q 7 Y 4 p j s + 7 N x f + 8 I M X h X Z h x m a Q I k i 0 X D V P h o n L n / 7 s D r o G h m F p C m e b 2 V p e N q a Y M b U p 5 G 4 K / / v I m a V f K / k 2 5 e l 8 t 1 k q r O H L k k l y R E v H J L a m R B m m S F m F E k W f + N k o G z n N o = " > A A A B 8 n i c b V D L S g N B E J z 1 G e M r 6 t H L Y h B y C r s h q M d A L j l G M A / Y L G F 2 0 k m G z M 4 s M 7 1 i W P I Z X j w o 4 t W v 8 e b f O H k c N L G g o a j q p r s r S g Q 3 6 H n f z t b 2 z u 7 e f u 4 g f 3 h 0 f H J a O D t v G 5 V q B i 2 m h N L d i B o Q X E I L O Q r o J h p o H A n o R J P 6 3 O 8 8 g j Z c y Q e c J h D G d C T 5 k D O K V g p 6 C E + Y 1 R u z f q V f K H p l b w F 3 k / g r U q y R J Z r 9 w l d v o F g a g 0 Q m q D G B 7 y U Y Z l Q j Z w J m + V 5 q I K F s Q k c Q W C p p D C b M F i f P 3 G u r D N y h 0 r Y k u g v 1 9 0 R G Y 2 O m c W Q 7 Y 4 p j s + 7 N x f + 8 I M X h X Z h x m a Q I k i 0 X D V P h o n L n / 7 s D r o G h m F p C m e b 2 V p e N q a Y M b U p 5 G 4 K / / v I m a V f K / k 2 5 e l 8 t 1 k q r O H L k k l y R E v H J L a m R B m m S F m F E k W f + N k o G z n N o = " > A A A B 8 n i c b V D L S g N B E J z 1 G e M r 6 t H L Y h B y C r s h q M d A L j l G M A / Y L G F 2 0 k m G z M 4 s M 7 1 i W P I Z X j w o 4 t W v 8 e b f O H k c N L G g o a j q p r s r S g Q 3 6 H n f z t b 2 z u 7 e f u 4 g f 3 h 0 f H J a O D t v G 5 V q B i 2 m h N L d i B o Q X E I L O Q r o J h p o H A n o R J P 6 3 O 8 8 g j Z c y Q e c J h D G d C T 5 k D O K V g p 6 C E + Y 1 R u z f q V f K H p l b w F 3 k / g r U q y R J Z r 9 w l d v o F g a g 0 Q m q D G B 7 y U Y Z l Q j Z w J m + V 5 q I K F s Q k c Q W C p p D C b M F i f P 3 G u r D N y h 0 r Y k u g v 1 9 0 R G Y 2 O m c W Q 7 Y 4 p j s + 7 N x f + 8 I M X h X Z h x m a Q I k i 0 X D V P h o n L n / 7 s D r o G h m F p C m e b 2 V p e N q a Y M b U p 5 G 4 K / / v I m a V f K / k 2 5 e l 8 t 1 k q r O H L k k l y R E v H J L a m R B m m S F m F E k W f + N k o G z n N o = " > A A A B 8 n i c b V D L S g N B E J z 1 G e M r 6 t H L Y h B y C r s h q M d A L j l G M A / Y L G F 2 0 k m G z M 4 s M 7 1 i W P I Z X j w o 4 t W v 8 e b f O H k c N L G g o a j q p r s r S g Q 3 6 H n f z t b 2 z u 7 e f u 4 g f 3 h 0 f H J a O D t v G 5 V q B i 2 m h N L d i B o Q X E I L O Q r o J h p o H A n o R J P 6 3 O 8 8 g j Z c y Q e c J h D G d C T 5 k D O K V g p 6 C E + Y 1 R u z f q V f K H p l b w F 3 k / g r U q y R J Z r 9 w l d v o F g a g 0 Q m q D G B 7 y U Y Z l Q j Z w J m + V 5 q I K F s Q k c Q W C p p D C b M F i f P 3 G u r D N y h 0 r Y k u g v 1 9 0 R G Y 2 O m c W Q 7 Y 4 p j s + 7 N x f + 8 I M X h X Z h x m a Q I k i 0 X D V P h o n L n / 7 s D r o G h m F p C m e b 2 V p e N q a Y M b U p 5 G 4 K / / v I m a V f K / k 2 5 e l 8 t 1 k q r O H L k k l y R E v H J L a m R B m m S F m F E k W f y S t 4 c d F 6 c d + d j 2 b r l r G Y u y B 8 4 n z 9 q + 5 F M < / l a t e x i t > CH2 < l a t e x i t s h a 1 _ b a s e 6 4 = " L X e m w C 7 q S X v D x r m N f w D p J q p 9 6 h w = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e y G o B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0 q 6 U v Z t y t V k p 1 a q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + r 9 j Q A = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " L X e m w C 7 q S X v D x r m N f w D p J q p 9 6 h w = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e y G o B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0 q 6 U v Z t y t V k p 1 a q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + r 9 j Q A = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " L X e m w C 7 q S X v D x r m N f w D p J q p 9 6 h w = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e y G o B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0 q 6 U v Z t y t V k p 1 a q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + r 9 j Q A = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " W K u z w C v 4 n Z V m B X c u Z 1 7 e K f h I 4 3 4 = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x K i B 4 D X j x J A u Y B y R J m J 7 3 J m N n Z Z W Z W C E u + w I s H R b z 6 S d 7 8 G y e P g y Y W N B R V 3 X R 3 B Y n g 2 r j u t 5 P b 2 N z a 3 s n v F v b 2 D w 6 P i s c n L R 2 n i m G T x S J W n Y B q F F x i 0 3 A j s J M o p F E g s B 2 M b 2 d + + w m V 5 r F 8 M J M E / Y g O J Q 8 5 o 8 Z K j f t + s e S W 3 T n I O v G W p F S D B e r 9 4 l d v E L M 0 Q m m Y o F p 3 P T c x f k a V 4 U z g t N B L N S a U j e k Q u 5 Z K G q H 2 s / m h U 3 J h l Q E J Y 2 V L G j J X f 0 9 k N N J 6 E g W 2 M 6 J m p F e 9 m f i f 1 0 1 N e O N n X C a p Q c k W i 8 J U E B O T 2 d d k w B U y I y a W U K a 4 v Z W w E V W U G Z t N w Y b g r b 6 8 T l p X Z a 9 a r j Q q p V p l G U c e z u A c L s G D a 6 j B H d S h C Q w Q n u E V 3 p x H 5 8 V 5 d z 4 W r T l n O X M K f + B 8 / g D 8 S Y 0 N < / l a t e x i t > N < l a t e x i t s h a 1 _ b a s e 6 4 = " I i Y n i 4 S M w 6 / K m 5 O r c F + N k o G z n N o = " > A A A B 8 n i c b V D L S g N B E J z 1 G e M r 6 t H L Y h B y C r s h q M d A L j l G M A / Y L G F 2 0 k m G z M 4 s M 7 1 i W P I Z X j w o 4 t W v 8 e b f O H k c N L G g o a j q p r s r S g Q 3 6 H n f z t b 2 z u 7 e f u 4 g f 3 h 0 f H J a O D t v G 5 V q B i 2 m h N L d i B o Q X E I L O Q r o J h p o H A n o R J P 6 3 O 8 8 g j Z c y Q e c J h D G d C T 5 k D O K V g p 6 C E + Y 1 R u z f q V f K H p l b w F 3 k / g r U q y R J Z r 9 w l d v o F g a g 0 Q m q D G B 7 y U Y Z l Q j Z w J m + V 5 q I K F s Q k c Q W C p p D C b M F i f P 3 G u r D N y h 0 r Y k u g v 1 9 0 R G Y 2 O m c W Q 7 Y 4 p j s + 7 N x f + 8 I M X h X Z h x m a Q I k i 0 X D V P h o n L n / 7 s D r o G h m F p C m e b 2 V p e N q a Y M b U p 5 G 4 K / / v I m a V f K / k 2 5 e l 8 t 1 k q r O H L k k l y R E v H J L a m R B m m S F m F E k W f y S t 4 c d F 6 c d + d j 2 b r l r G Y u y B 8 4 n z 9 q + 5 F M < / l a t e x i t > CH2 < l a t e x i t s h a 1 _ b a s e 6 4 = " I i Y n i 4 S M w 6 / K m 5 O r c F + N k o G z n N o = " > A A A B 8 n i c b V D L S g N B E J z 1 G e M r 6 t H L Y h B y C r s h q M d A L j l G M A / Y L G F 2 0 k m G z M 4 s M 7 1 i W P I Z X j w o 4 t W v 8 e b f O H k c N L G g o a j q p r s r S g Q 3 6 H n f z t b 2 z u 7 e f u 4 g f 3 h 0 f H J a O D t v G 5 V q B i 2 m h N L d i B o Q X E I L O Q r o J h p o H A n o R J P 6 3 O 8 8 g j Z c y Q e c J h D G d C T 5 k D O K V g p 6 C E + Y 1 R u z f q V f K H p l b w F 3 k / g r U q y R J Z r 9 w l d v o F g a g 0 Q m q D G B 7 y U Y Z l Q j Z w J m + V 5 q I K F s Q k c Q W C p p D C b M F i f P 3 G u r D N y h 0 r Y k u g v 1 9 0 R G Y 2 O m c W Q 7 Y 4 p j s + 7 N x f + 8 I M X h X Z h x m a Q I k i 0 X D V P h o n L n / 7 s D r o G h m F p C m e b 2 V p e N q a Y M b U p 5 G 4 K / / v I m a V f K / k 2 5 e l 8 t 1 k q r O H L k k l y R E v H J L a m R B m m S F m F E k W f y S t 4 c d F 6 c d + d j 2 b r l r G Y u y B 8 4 n z 9 q + 5 F M < / l a t e x i t >

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< l a t e x i t s h a 1 _ b a s e 6 4 = " L X e m w C 7 q S X v D x r m N f w D p J q p 9 6 h w = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e y G o B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0 q 6 U v Z t y t V k p 1 a q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + r 9 j Q A = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " L X e m w C 7 q S X v D x r m N f w D p J q p 9 6 h w = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e y G o B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0 q 6 U v Z t y t V k p 1 a q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + r 9 j Q A = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " L X e m w C 7 q S X v D x r m N f w D p J q p 9 6 h w  = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e y G o B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0 q 6 U v Z t y t V k p 1 a q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + r 9 j Q A = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " W K u z w C v 4 n Z V m B X c u Z 1 7 e K f h I 4 3 4 = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x K i B 4 D X j x J A u Y B y R J m J 7 3 J m N n Z Z W Z W C E u + w I s H R b z 6 S d 7 8 G y e P g y Y W N B R V 3 X R 3 B Y n g 2 r j u t 5 P b 2 N z a 3 s n v F v b 2 D w 6 P i s c n L R 2 n i m G T x S J W n Y B q F F x i 0 3 A j s J M o p F E g s B 2 M b 2 d + + w m V 5 r F 8 M J M E / Y g O J Q 8 5 o 8 Z K j f t + s e S W 3 T n I O v G W p F S D B e r 9 4 l d v E L M 0 Q m m Y o F p 3 P T c x f k a V 4 U z g t N B L N S a U j e k Q u 5 Z K G q H 2 s / m h U 3 J h l Q E J Y 2 V L G j J X f 0 9 k N N J 6 E g W 2 M 6 J m p F e 9 m f i f 1 0 1 N e O N n X C a p Q c k W i 8 J U E B O T 2 d d k w B U y I y a W U K a 4 v Z W w E V W U G Z t N w Y b g r b 6 8 T l p X Z a 9 a r j Q q p V p l G U c e z u A c L s G D a 6 j B H d S h C Q w Q n u E V 3 p x H 5 8 V 5 d z 4 W r T l n O X M K f + B 8 / g D 8 S Y 0 N < / l a t e x i t > N < l a t e x i t s h a 1 _ b a s e 6 4 = " I i Y n i 4 S M w 6 / K m 5 O r c F + N k o G z n N o = " > A A A B 8 n i c b V D L S g N B E J z 1 G e M r 6 t H L Y h B y C r s h q M d A L j l G M A / Y L G F 2 0 k m G z M 4 s M 7 1 i W P I Z X j w o 4 t W v 8 e b f O H k c N L G g o a j q p r s r S g Q 3 6 H n f z t b 2 z u 7 e f u 4 g f 3 h 0 f H J a O D t v G 5 V q B i 2 m h N L d i B o Q X E I L O Q r o J h p o H A n o R J P 6 3 O 8 8 g j Z c y Q e c J h D G d C T 5 k D O K V g p 6 C E + Y 1 R u z f q V f K H p l b w F 3 k / g r U q y R J Z r 9 w l d v o F g a g 0 Q m q D G B 7 y U Y Z l Q j Z w J m + V 5 q I K F s Q k c Q W C p p D C b M F i f P 3 G u r D N y h 0 r Y k u g v 1 9 0 R G Y 2 O m c W Q 7 Y 4 p j s + 7 N x f + 8 I M X h X Z h x m a Q I k i 0 X D V P h o n L n / 7 s D r o G h m F p C m e b 2 V p e N q a Y M b U p 5 G 4 K / / v I m a V f K / k 2 5 e l 8 t 1 k q r O H L k k l y R E v H J L a m R B m m S F m F E k W f y S t 4 c d F 6 c d + d j 2 b r l r G Y u y B 8 4 n z 9 q + 5 F M < / l a t e x i t > CH2 < l a t e x i t s h a 1 _ b a s e 6 4 = " I i Y n i 4 S M w 6 / K m 5 O r c F + N k o G z n N o = " > A A A B 8 n i c b V D L S g N B E J z 1 G e M r 6 t H L Y h B y C r s h q M d A L j l G M A / Y L G F 2 0 k m G z M 4 s M 7 1 i W P I Z X j w o 4 t W v 8 e b f O H k c N L G g o a j q p r s r S g Q 3 6 H n f z t b 2 z u 7 e f u 4 g f 3 h 0 f H J a O D t v G 5 V q B i 2 m h N L d i B o Q X E I L O Q r o J h p o H A n o R J P 6 3 O 8 8 g j Z c y Q e c J h D G d C T 5 k D O K V g p 6 C E + Y 1 R u z f q V f K H p l b w F 3 k / g r U q y R J Z r 9 w l d v o F g a g 0 Q m q D G B 7 y U Y Z l Q j Z w J m + V 5 q I K F s Q k c Q W C p p D C b M F i f P 3 G u r D N y h 0 r Y k u g v 1 9 0 R G Y 2 O m c W Q 7 Y 4 p j s + 7 N x f + 8 I M X h X Z h x m a Q I k i 0 X D V P h o n L n / 7 s D r o G h m F p C m e b 2 V p e N q a Y M b U p 5 G 4 K / / v I m a V f K / k 2 5 e l 8 t 1 k q r O H L k k l y R E v H J L a m R B m m S F m F E k W f y S t 4 c d F 6 c d + d j 2 b r l r G Y u y B 8 4 n z 9 q + 5 F M < / l a t e x i t > CH2 < l a t e x i t s h a 1 _ b a s e 6 4 = " I i Y n i 4 S M w 6 / K m 5 O r c F + N k o G z n N o = " > A A A B 8 n i c b V D L S g N B E J z 1 G e M r 6 t H L Y h B y C r s h q M d A L j l G M A / Y L G F 2 0 k m G z M 4 s M 7 1 i W P I Z X j w o 4 t W v 8 e b f O H k c N L G g o a j q p r s r S g Q 3 6 H n f z t b 2 z u 7 e f u 4 g f 3 h 0 f H J a O D t v G 5 V q B i 2 m h N L d i B o Q X E I L O Q r o J h p o H A n o R J P 6 3 O 8 8 g j Z c y Q e c J h D G d C T 5 k D O K V g p 6 C E + Y 1 R u z f q V f K H p l b w F 3 k / g r U q y R J Z r 9 w l d v o F g a g 0 Q m q D G B 7 y U Y Z l Q j Z w J m + V 5 q I K F s Q k c Q W C p p D C b M F i f P 3 G u r D N y h 0 r Y k u g v 1 9 0 R G Y 2 O m c W Q 7 Y 4 p j s + 7 N x f + 8 I M X h X Z h x m a Q I k i 0 X D V P h o n L n / 7 s D r o G h m F p C m e b 2 V p e N q a Y M b U p 5 G 4 K / / v I m a V f K / k 2 5 e l 8 t 1 k q r O H L k k l y R E v H J L a m R B m m S F m F E k W f y S t 4 c d F 6 c d + d j 2 b r l r G Y u y B 8 4 n z 9 q + 5 F M < / l a t e x i t > CH2 < l a t e x i t s h a 1 _ b a s e 6 4 = " I i Y n i 4 S M w 6 / K m 5 O r c F + N k o G z n N o = " > A A A B 8 n i c b V D L S g N B E J z 1 G e M r 6 t H L Y h B y C r s h q M d A L j l G M A / Y L G F 2 0 k m G z M 4 s M 7 1 i W P I Z X j w o 4 t W v 8 e b f O H k c N L G g o a j q p r s r S g Q 3 6 H n f z t b 2 z u 7 e f u 4 g f 3 h 0 f H J a O D t v G 5 V q B i 2 m h N L d i B o Q X E I L O Q r o J h p o H A n o R J P 6 3 O 8 8 g j Z c y Q e c J h D G d C T 5 k D O K V g p 6 C E + Y 1 R u z f q V f K H p l b w F 3 k / g r U q y R J Z r 9 w l d v o F g a g 0 Q m q D G B 7 y U Y Z l Q j Z w J m + V 5 q I K F s Q k c Q W C p p D C b M F i f P 3 G u r D N y h 0 r Y k u g v 1 9 0 R G Y 2 O m c W Q 7 Y 4 p j s + 7 N x f + 8 I M X h X Z h x m a Q I k i 0 X D V P h o n L n / 7 s D r o G h m F p C m e b 2 V p e N q a Y M b U p 5 G 4 K / / v I m a V f K / k 2 5 e l 8 t 1 k q r O H L k k l y R E v H J L a m R B m m S F m F E k W f d t f V i 6 / t r 6 x W d g q b u / s 7 u 2 X D g 4 7 S i Q S k z Y W T M h e g B R h l J O 2 p p q R X i w J i g J G u s H 4 O s u 7 d 0 Q q K n h L T 2 L i R W j I a U g x 0 s Z y W 3 4 a + 8 6 0 O j w r + q W K X b N n g q v g L K D S K H + X 8 w 8 f 9 0 2 / 9 N k f C J x E h G v M k F K u Y 8 f a S 5 H U F D M y L f Y T R W K E x 2 h I X I M c R U R 5 6 W z k K T w 1 z g C G Q p r H N Z y 5 v z t S F C k 1 i Q J T G S E 9 U s t Z Z v 6 X u Y k O 6 1 5 K e Z x o w v H 8 o z B h U A u Y 7 Q 8 H V B K s 2 c Q A w p K a W S E e I Y m w N l f K j u A s r 7 w K n f O a c 1 m 7 u H U q j T q Y q w C O w Q m o A g d c g Q a 4 A U 3 Q B h g I 8 A i e w Y u l r S f r 1 X q b l + a s R c 8 R + C P r / Q d N 3 J O Y < / l a t e x i t > T p1 (g) q 5 j h 1 r L 0 V S U 8 z I t N B P F I k R H q M h c Q 1 y F B H l p b O R p / D M O A M Y C m k e 1 3 D m / u 5 I U a T U J A p M Z Y T 0 S C 1 n m f l f 5 i Y 6 r H s p 5 X G i C c f z j 8 K E Q S 1 g t j 8 c U E m w Z h M D C E t q Z o V 4 h C T C 2 l w p O 4 K z v P I q d G p V 5 7 J 6 c e u U G 3 U w V x 6 c g F N Q A Q 6 4 A g 1 w A 5 q g D T A Q 4 B E 8 g x d L W 0 / W q / U 2 L 1 2 z F j 3 H 4 I + s 9 x 9 P Z Z O Z < / l a t e x i t > T p2 (g) < l a t e x i t s h a 1 _ b a s e 6 4 = " H L 3 8 i i Y q w q N 0 y 3 3 k a R b G 0 v 0 o w f o = " > A A A B 7 3 i c b Z C 7 S g N B F I b P J l 5 i v E U t b S Y G w S r s B t G U A R v L C L l B E p b Z y W w y Z H Z 2 n Z k V w h I 7 X 8 D G Q h F b X 8 Q H s P N R 7 J x N U m j i D w M f / 3 8 O c 8 7 x I s 6 U t u 0 v K 5 N d W 9 / Y z G 3 l t 3 d 2 9 / Y L B 4 c t F c a S 0 C Y J e S g 7 H l a U M 0 G b m m l O O 5 G k O P A 4 b X v j q z R v 3 1 G p W C g a e h L R f o C H g v m M Y G 2 s T s N N I r c y z b u F k l 2 2 Z 0 K r 4 C y g V C t + F 7 M P H / d 1 t / D Z G 4 Q k D q j Q h G O l u o 4 d 6 X 6 C p W a E 0 2 m + F y s a Y T L G Q 9 o 1 K H B A V T + Z z T t F p 8 Y Z I D + U 5 g m N Z u 7 v j g Q H S k 0 C z 1 Q G W I / U c p a a / 2 X d W P v V f s J E F G s q y P w j P + Z I h y h d H g 2 Y p E T z i Q F M J D O z I j L C E h N t T p Q e w V l e e R V a l b J z U T 6 / c U q 1 K s y V g 2 M 4 g T N w 4 B J q c A 1 1 a A I B D o / w D C / W r f V k v V p v 8 9 K M t e g 5 g j + y 3 n 8 A w B i S w w = = < / l a t e x i t > T p2 < l a t e x i t s h a 1 _ b a s e 6 4 = " c Q k V A / s j v o 1 J + O K m / l V m F 7 U C J L g = " > A A A B 7 3 i c b Z C 7 S g N B F I b P G i 8 x 3 q K W N h O D Y B V 2 R T R l w M Y y Q m 6 Q L M v s Z D Y Z M j u 7 z s w K Y Y m d L 2 B j o Y i t L + I D 2 P k o d s 4 m K T T x h 4 G P / z + H O e f 4 M W d K 2 / a X t Z J b X V v f y G 8 W t r Z 3 d v e K + w c t F S W S 0 C a J e C Q 7 P l a U M 0 G b m m l O O 7 G k O P Q 5 b f u j q y x v 3 1 G p W C Q a e h x T N 8 Q D w Q J G s D Z W p + G l s e d M C l 6 x b F f s q d A y O H M o 1 0 r f p d z D x 3 3 d K 3 7 2 + h F J Q i o 0 4 V i p r m P H 2 k 2 x 1 I x w O i n 0 E k V j T E Z 4 Q L s G B Q 6 p c t P p v B N 0 Y p w + C i J p n t B o 6 v 7 u S H G o 1 D j 0 T W W I 9 V A t Z p n 5 X 9 Z N d F B 1 U y b i R F N B Z h 8 F C U c 6 Q t n y q M 8 k J Z q P D W A i m Z k V k S G W m G h z o u w I z u L K y 9 A 6 q z g X l f M b p 1 y r w k x 5 O I J j O A U H L q E G 1 1 C H J h D g 8 A j P 8 G L d W k / W q / U 2 K 1 2 x 5 j 2 H 8 E f W + w + + k p L C < / l a t e x i t > T p1 (a) Invariance. < l a t e x i t s h a 1 _ b a s e 6 4 = " O J 5 d y R 2 Y 8 M v / B / j c S K 0 r q j b h J i M = " > A A A B 8 H i c b V D L S g N B E O y N U W N 8 R T 1 6 G Q 1 C v I R d E c 1 F C H j x G M G 8 S J Y w O 5 l N h s z M L j O z Q l j y F V 4 8 K O L V r / A b v P k 3 T h 4 H T S x o K K q 6 6 e 4 K Y s 6 0 c d 1 v J 7 O W X d / Y z G 3 l t 3 d 2 9 / Y L B 4 c N H S W K 0 D q J e K R a A d a U M 0 n r h h l O W 7 G i W A S c N o P R 7 d R v P l K l W S Q f z D i m v s A D y U J G s L F S u x s P W W n Q 8 8 5 7 h a J b d m d A q 8 R b k G I V 3 c j s Z / u k 1 i t 8 d f s R S Q S V h n C s d c d z Y + O n W B l G O J 3 k u 4 m m M S Y j P K A d S y U W V P v p 7 O A J O r N K H 4 W R s i U N m q m / J 1 I s t B 6 L w H Y K b I Z 6 2 Z u K / 3 m d x I Q V P 2 U y T g y V Z L 4 o T D g y E Z p + j / p M U W L 4 2 B J M F L O 3 I j L E C h N j M 8 r b E L z l l 1 d J 4 6 L s X Z U v 7 2 0 a F Z g j B 8 d w C i X w 4 B q q c A c 1 q A M B A U / w A q + O c p 6 d N + d 9 3 p p x F j N H 8 A f O x w / Z p Z H 9 < / l a t e x i t > (g 1 ) < l a t e x i t s h a 1 _ b a s e 6 4 = " 0 k i B n 4 B s d N m H r L D j Q d 2 3 x 7 E A o G 8 = " > A A A B 8 n i c b V D L S g M x F L 1 T X 7 W + q i 7 d B I v g q s x I U Z c F F 7 q s Y B / Q D i W T Z t r Q T G Z I 7 g h l 6 G e 4 c a G I W 7 / G n X 9 j p q 2 g r Q c C h 3 P u J e e e I J H  C o O t + O Y W 1 9 Y 3 N r e J 2 a W d 3 b / + g f H j U M n G q G W + y W M a 6 E 1 D D p V C 8 i Q I l 7 y S a 0 y i Q v B 2 M b 3 K / / c i 1 E b F 6 w E n C / Y g O l Q g F o 2 i l b i + i O G J U Z r f T f r n i V t 0 Z y C r x F q R S h z k a / f J n b x C z N O I K m a T G d D 0 3 Q T + j G g W T f F r q p Y Y n l I 3 p k H c t V T T i x s 9 m k a f k z C o D E s b a P o V k p v 7 e y G h k z C Q K 7 G Q e 0 S x V Z f d D J a C q 5 K I a J c F N y 4 r m r b Q h j K Z T t K h k 0 m Y m Q g l d O f W j Q t F 3 P o t f o A 7 / Q C / w A 9 w + l h o 6 4 E L h 3 P u 5 d 5 7 / I Q z p W 3 7 w 8 q t r K 6 t b + Q 3 C 1 v b O 7 t 7 x f 2 D p o p T S a h L Y h 7 L t o 8 V 5 U x Q V z P N a T u R F E c + p y 1 / e D H x W 7 d U K h a L G z 1 K q B f h U L C A E a y N d B 3 2 n F 6 x b F f t K d A y c e a k X C 9 V 7 r 7 f v j 4 b v e J 7 t x + T N K J C E 4 6 V 6 j h 2 o r 0 M S 8 0 I p + N C N 1 U 0 w W S I Q 9 o x V O C I K i + b n j p G F a P 0 U R B L U 0 K j q f p 7 I s O R U q P I N 5 0 R 1 g O 1 6 E 3 E / 7 x O q o O a l z G R p J o K M l s U p B z p G E 3 + R n 0 m K d F 8 Z A g m k p l b E R l g i Y k 2 6 R R M C M 7 i y 8 u k e V J 1 z q q n V y a N G s y Q h x I c w T E 4 c A 5 1 u I Q G u E A g h H t 4 h C e L W w / W s / U y a 8 1 Z 8 5 l D + A P r 9 Q f 3 E J I I < / l a t e x i t > g 1 < l a t e x i t s h a 1 _ b a s e 6 4 = " N 0 o q i 0 e H B r x y X d j R h T S l z H w u 9 W c = " > A A A B 6 n i c b V C 7 S g N B F L 0 b X z G + o p Z p B k P A K u w G i S k D N p Y R z Q O S J c x O Z j d D Z m e X m V k h L O l s b S w U s f V b / A A 7 / Q C / w A 9 w 8 i g 0 8 c C F w z n 3 c u 8 9 X s y Z 0 r b 9 Y W X W 1 j c 2 t 7 L b u Z 3 d v f 2 D / O F R S 0 W J J L R J I h 7 J j o c V 5 U z Q p m a a 0 0 4 s K Q 4 9 T t v e 6 G L q t 2 + p V C w S N 3 o c U z f E g W A + I 1 g b 6 T r o V / r 5 o l 2 2 Z 0 C r x F m Q Y r 1 Q u v t + + / p s 9 P P v v U F E k p A K T T h W q u v Y s X Z T L D U j n E 5 y v U T R G J M R D m j X U I F D q t x 0 d u o E l Y w y Q H 4 k T Q m N Z u r v i R S H S o 1 D z 3 S G W A / V s j c V / / O 6 i f Z r b s p E n G g q y H y R n 3 C k I z T 9 G w 2 Y p E T z s S G Y S G Z u R W S I J S b a p J M z I T j L L 6 + S V q X s V M t n V y a N G s y R h Q K c w C k 4 c A 5 1 u I Q G N I F A A P f w C E 8 W t x 6 s Z + t l 3 p q x F j P H 8 A f W 6 w / 4 l J I J < / l a t e x i t > g 2 < l a t e x i t s h a 1 _ b a s e 6 4 = " N j 7 K U R J s e F l r u 7 t U 2 j T M s d 8 d  K t U = " > A A A B 8 H i c b V B L S g N B E K 2 J v x h / U Z f Z N I a A q z A j o l k G 3 L i M Y D 6 S h T i V h D Z J z G P Z C b C i n A n a 1 E x z 2 k k k x V H A a T s Y X U 3 9 9 j 2 V i s X i V o 8 T 6 k d 4 I F j I C N Z G 6 t k l L x m y i q c Z 7 9 N s M D n p 2 W W n 6 s y A / h J 3 Q c p 1 d C n y H 3 e H j Z 7 9 6 f V j k k Z U a M K x U l 3 X S b S f Y a k Z 4 X R S 9 F J F E 0 x G e E C 7 h g o c U e V n s 8 M n 6 N g o f R T G 0 p T Q a K b + n M h w p N Q 4 C k x n h P V Q L X t T 8 T + v m + q w 5 m d M J K m m g s w X h S l H O k b T F F C f S U o 0 H x u C i W T m V k S G W G K i T V Z F E 4 K 7 / P J f 0 j q t u u f V s x u T R g 3 m K M A B H E E F X L i A O l x D A 5 p A I I V H e I Y X 6 8 F 6 s l 6 t t 3 l r z l r M 7 M M v W O / f l u O V Q A = = < / l a t e x i t > (g) < l a t e x i t s h a 1 _ b a s e 6 4 = " r n r t w e 4 F q V + Z d W V 9 b 9 / p I d n F n 3 w = " > A A A B 8 H i c b V D L S g N B E O z V q D G + o h 6 9 j A Y h X s J u E M 1 F C H j x G M G 8 S J Y w O 5 l N h s z M L j O z Q l j y F V 4 8 K O L V r / A b v P k 3 T h 4 H T S x o K K q 6 6 e 4 K Y s 6 0 c d 1 v Z 2 0 9 s 7 G 5 l d 3 O 7 e z u 7 R / k D 4 8 a O k o U o X U S 8 U i 1 A q w p Z 5 L W D T O c t m J F s Q g 4 b Q a j 2 6 n f f K R K s 0 g + m H F M f Y E H k o W M Y G O l d j c e s u K g V 7 7 o 5 Q t u y Z 0 B r R J v Q Q p V d C M z n + 3 T W i / / 1 e 1 H J B F U G s K x 1 h 3 P j Y 2 f Y m U Y 4 X S S 6 y a a x p i M 8 I B 2 L J V Y U O 2 n s 4 M n 6 N w q f R R G y p Y 0 a K b + n k i x 0 H o s A t s p s B n q Z W 8 q / u d 1 E h N W / J T J O D F U k v m i M O H I R G j 6 P e o z R Y n h Y 0 s w U c z e i s g Q K 0 y M z S h n Q / C W X 1 4 l j X L J u y p d 3 t s 0 K j B H F k 7 g D I r g w T V U 4 Q 5 q U A c C A p 7 g B V 4 d 5 T w 7 b 8 7 7 v H X N W c w c w x 8 4 H z / b K p H + < / l a t e x i t > (g 2 ) < l a t e x i t s h a 1 _ b a s e 6 4 = " e 9 J H + q u w P h 7 j X s c Q C T Y j 8 W l e 8 M U = " > A A A B 8 H i c b V D L S g M x F L 1 T X 7 W + q i 7 d B I v g x j I j R b s s u H F Z w d Z K O 5 R M J t O G 5 j E k G a E M / Q o 3 L h R x 6 + e 4 8 2 9 M H w t t P R A 4 n H M u u f d E K W f G + v 6 3 V 1 h b 3 9 j c K m 6 X d n b 3 9 g / K h 0 d t o z J N a I s o r n Q n w o Z y J m n L M s t p J 9 U U i 4 j T h 2 h 0 M / U f n q g 2 T M l 7 O 0 5 p K P B A s o Q R b J 3 0 G F z 0 u A v H u F + u + F V / B r R K g g W p N G C O Z r / 8 1 Y s V y Q S V l n B s T D f w U x v m W F t G O J 2 U e p m h K S Y j P K B d R y U W 1 I T 5 b O E J O n N K j B K l 3 Z M W z d T f E z k W x o x F 5 J I C 2 6 F Z 9 q b i f 1 4 3 s 0 k 9 z J l M M 0 s l m X + U Z B x Z h a b X o 5 h p S i w f O 4 K J Z m 5 X R I Z Y Y 2 J d R y V X Q r B 8 8 i p p X 1 a D q 2 r t r l Z p 1 B d 1 F O E E T u E c A r i G B t x C E 1 p A Q M A z v M K b p 7 0 X 7 9 3 7 m E c L 3 m L m G P 7 A + / w B b t 2 Q L g = = < / l a t e x i t > 1 < l a t e x i t s h a 1 _ b a s e 6 4 = " e 9 J H + q u w P h 7 j X s c Q C T Y j 8 W l e 8 M U = " >  A A A B 8 H i c b V D L S g M x F L 1 T X 7 W + q i 7 d B I v g x j I j R b s s u H F Z w d Z K O 5 R M J t O G 5 j E k G a E M / Q o 3 L h R x 6 + e 4 8 2 9 M H w t t P R A 4 n H M u u f d E K W f G + v 6 3 V 1 h b 3 9 j c K m 6 X d n b 3 9 g / K h 0 d t o z J N a I s o r n Q n w o Z y J m n L M s t p J 9 U U i 4 j T h 2 h 0 M / U f n q g 2 T M l 7 O 0 5 p K P B A s o Q R b J 3 0 G F z 0 u A v H u F + u + F V / B r R K g g W p N G C O Z r / 8 1 Y s V y Q S V l n B s T D f w U x v m W F t G O J 2 U e p m h K S Y j P K B d R y U W 1 I T 5 b O E J O n N K j B K l 3 Z M W z d T f E z k W x o x F 5 J I C 2 6 F Z 9 q b i f 1 4 3 s 0 k 9 z J l M M 0 s l m X + U Z B x Z h a b X o 5 h p S i w f O 4 K J Z m 5 X R I Z Y Y 2 J d R y V X Q r B 8 8 i p p X 1 a D q 2 r t r l Z p 1 B d 1 F O E E T u E c A r i G B t x C E 1 p A Q M A z v M K b p 7 0 X 7 9 3 7 m E c L 3 m L m G P 7 A + / w B b t 2 Q L g = = < / l a t e x i t > 1 < l a t e x i t s h a 1 _ b a s e 6 4 = " b t j G N 3 7 o d a f v N 8 8 L S f Y F F + P v y V Q = " > A A A B 7 n i c b V D L S g M x F L 1 T X 7 W + q i 7 d B I v g q s x I q V 0 W 3 L i s Y B / Q D i + P v y V Q = " > A A A B 7 n i c b V D L S g M x F L 1 T X 7 W + q i 7 d B I v g q s x I q V 0 W 3 L i s Y B / Q D i W T y b S h m c y Q 3 B H K 0 I 9 w 4 0 I R t 3 6 P O / / G 9 L H Q 1 g O B w z n n k n t P k E p h 0 H W / n c L W 9 s 7 u X n G / d H B 4 d H x S P j 3 r m C T T j L d Z I h P d C 6 j h U i j e R o G S 9 1 L N a R x I 3 g 0 m d 3 O / + 8 S 1 E Y l 6 x G n K / Z i O l I g E o 2 i l 7 k D a a E i H 5 Y p b d R c g m 8 R b k U o T l m g N y 1 + D M G F Z z B U y S Y 3 p e 2 6 K f k 4 1 C i b 5 r D T I D E 8 p m 9 A R 7 1 u q a M y N n y / W n Z E r q 4 Q k S r R 9 C s l C / T 2 R 0 9 i Y a R z Y Z E x x b N a 9 u f i f 1 8 8 w a v i 5 U G m G X L H l R 1 E m C S Z k f j s J h e Y M G 0 X C y d t h V v Z S M 9 a D f 4 r V D B q n 8 A Q = " > A A A B 6 3 i c b V C 7 S g N B F L 0 b X z G + o p Z p B k P A K u y K a M q A j W U E 8 4 A k y O x k N j t k Z n a Z m R X C k s 7 a x k I R W 3 / F D 7 D T D / A L / A B n k x S a e O D C 4 Z x 7 u f c e P + Z M G 9 f 9 c H I r q 2 v r G / n N w t b 2 z u 5 e c f + g p a N E E d o k E Y 9 U x 8 e a c i Z p 0 z D D a S d W F A u f 0 7 Y / u s j 8 9 i 1 V m k X y 2 o x j 2 h d 4 K F n A C D a Z 1 I t D d l M s u 1 V 3 C r R M v D k p 1 0 u V u + + 3 r 8 / G T f G 9 N 4 h I I q g 0 h G O t u 5 4 b m 3 6 K l W G E 0 0 m h l 2 g a Y z L C Q 9 q 1 V G J B d T + d 3 j p B F a s M U B A p W 9 K g q f p 7 I s V C 6 7 H w b a f A J t S L X i b + 5 3 U T E 9 T 6 K Z N x Y q g k s 0 V B w p G J U P Y 4 G j B F i e F j S z B R z N 6 K S I g V J s b G U 7 A h e I s v L 5 P W S d U 7 q 5 5 e 2 T R q M E M e S n A E x + D B O d T h E h r Q B A I h 3 M M j P D n C e X C e n Z d Z a 8 6 Z z x z C H z i v P x j d k r g = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " G 0 X C y d t h V v Z S M 9 a D f 4 r V D B q n 8 A Q = " > A A A B 6 3 i c b V C 7 S g N B F L 0 b X z G + o p Z p B k P A K u y K a M q A j W U E 8 4 A k y O x k N j t k Z n a Z m R X C k s 7 a x k I R W 3 / F D 7 D T D / A L / A B n k x S a e O D C 4 Z x 7 u f c e P + Z M G 9 f 9 c H I r q 2 v r G / n N w t b 2 z u 5 e c f + g p a N E E d o k E Y 9 U x 8 e a c i Z p 0 z D D a S d W F A u f 0 7 Y / u s j 8 9 i 1 V m k X y 2 o x j 2 h d 4 K F n A C D a Z 1 I t D d l M s u 1 V 3 C r R M v D k p 1 0 u V u + + 3 r 8 / G T f G 9 N 4 h I I q g 0 h G O t u 5 4 b m 3 6 K l W G E 0 0 m h l 2 g a Y z L C Q 9 q 1 V G J B d T + d 3 j p B F a s M U B A p W 9 K g q f p 7 I s V C 6 7 H w b a f A J t S L X i b + 5 3 U T E 9 T 6 K Z N x Y q g k s 0 V B w p G J U P Y 4 G j B F i e F j S z B R z N 6 K S I g V J s b G U 7 A h e I s v L 5 P W S d U 7 q 5 5 e 2 T R q M E M e S n A E x + D B O d T h E h r Q B A I h 3 M M j P D n C e X C e n Z d Z a 8 6 Z z x z C H z i v P x j d k r g = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " G 0 X C y d t h V v Z S M 9 a D f 4 r V D B q n 8 A Q = " > A A A B 6 3 i c b V C 7 S g N B F L 0 b X z G + o p Z p B k P A K u y K a M q A j W U E 8 4 A k y O x k N j t k Z n a Z m R X C k s 7 a x k I R W 3 / F D 7 D T D / A L / A B n k x S a e O D C 4 Z x 7 u f c e P + Z M G 9 f 9 c H I r q 2 v r G / n N w t b 2 z u 5 e c f + g p a N E E d o k E Y 9 U x 8 e a c i Z p 0 z D D a S d W F A u f 0 7 Y / u s j 8 9 i 1 V m k X y 2 o x j 2 h d 4 K F n A C D a Z 1 I t D d l M s u 1 V 3 C r R M v D k p 1 0 u V u + + 3 r 8 / G T f G 9 N 4 h I I q g 0 h G O t u 5 4 b m 3 6 K l W G E 0 0 m h l 2 g a Y z L C Q 9 q 1 V G J B d T + d 3 j p B F a s M U B A p W 9 K g q f p 7 I s V C 6 7 H w b a f A J t S L X i b + 5 3 U T E 9 T 6 K Z N x Y q g k s 0 V B w p G J U P Y 4 G j B F i e F j S z B R z N 6 K S I g V J s b G U 7 A h e I s v L 5 P W S d U 7 q 5 5 e 2 T R q M E M e S n A E x + D B O d T h E h r Q B A I h 3 M M j P D n C e X C e n Z d Z a 8 6 Z z x z C H z i v P x j d k r g = < / l a t e x i t > view1 view2 < l a t e x i t s h a 1 _ b a s e 6 4 = " m q q g z K I D 3 H s h 2 y D A V t A 3 / P J A g X c = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x K i B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0 r 4 p e 9 V y p V k p 1 S q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + u d j Q I = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " m q q g z K I D 3 H s h 2 y D A V t A 3 / P J A g X c = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x K i B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0 r 4 p e 9 V y p V k p 1 S q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + u d j Q I = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " m q q g z K I D 3 H s h 2 y D A V t A 3 / P J A g X c = " >  Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0 r 4 p e 9 V y p V k p 1 S q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + u d j Q I = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " m q q g z K I D 3 H s h 2 y D A V t A 3 / P J A g X c = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x K i B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y  x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0 x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o L J / d z v P K H S P J Y P Z p q g H 9 G R 5 C F n 1 F i p W R 8 U S 2 7 Z X Y B s E m 9 F S j V Y o j E o f v W H M U s j l I Y J q n X P c x P j Z 1 Q Z z g T O C v 1 U Y 0 L Z h I 6 w Z 6 m k E W o / W x w 6 I 1 d W G Z I w V r a k I Q v 1 9 0 R G I 6 2 n U W A 7 I 2 r G e t 2 b i / 9 5 v d S E d 3 7 G Z Z I a l G y 5 K E w F M T G Z f 0 2 G X C E z Y m o J Z Y r b W w k b U 0 W Z s d k U b A j e + s u b p H 1 T 9 q r l S r N S q l V W c e T h A i 7 h G j y 4 h R r U o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B / M x j Q c = < / l a t e x i t > H < l a t e x i t s h a 1 _ b a s e 6 4 = " 0 1 L 3 k m Z f y Z L N j U n T c L U S 8 o U 0 M C M = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x K i B 4 D X n J M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o L J / d z v P K H S P J Y P Z p q g H 9 G R 5 C F n 1 F i p W R 8 U S 2 7 Z X Y B s E m 9 F S j V Y o j E o f v W H M U s j l I Y J q n X P c x P j Z 1 Q Z z g T O C v 1 U Y 0 L Z h I 6 w Z 6 m k E W o / W x w 6 I 1 d W G Z I w V r a k I Q v 1 9 0 R G I 6 2 n U W A 7 I 2 r G e t 2 b i / 9 5 v d S E d 3 7 G Z Z I a l G y 5 K E w F M T G Z f 0 2 G X C E z Y m o J Z Y r b W w k b U 0 W Z s d k U b A j e + s u b p H 1 T 9 q r l S r N S q l V W c e T h A i 7 h G j y 4 h R r U o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B / M x j Q c = < / l a t e x i t > H < l a t e x i t s h a 1 _ b a s e 6 4 = " m q q g z K I D 3 H s h 2 y D A V t A 3 / P J A g X c = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x K i B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0 r 4 p e 9 V y p V k p 1 S q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + u d j Q I = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " m q q g z K I D 3 H s h 2 y D A V t A 3 / P J A g X c = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x K i B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0 r 4 p e 9 V y p V k p 1 S q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + u d j Q I = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " m q q g z K I D 3 H s h 2 y D A V t A 3 / P J A g X c = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x K i B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0 r 4 p e 9 V y p V k p 1 S q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + u d j Q I = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " m q q g z K I D 3 H s h 2 y D A V t A 3 / P J A g X c = " > After randomly dropping some nodes, one view could hold a cyano group (-C≡N) that determines the property of molecule hypertoxic, while another could corrupt this functional group. Thus, intra-graph augmentations are inadequate for presenting a holistic view of the anchor graph. • Worse still, aggressive augmentations easily make two positive views far from each other, but the invariance mechanism blindly forces their representations to be invariant. Considering the molecule graph's views again (cf. Figure 1a ), invariance-guided contrastive learning simply maximizes their representation agreement, regardless of the changes in the hypertoxic property. Therefore, it might amplify the negative impact of aggressive intra-graph augmentations and restrain representations from reflecting the instance semantics faithfully. To mitigate these negative influences, we get inspiration from the recent work on equivariant selfsupervised learning (E-SSL) (Dangovski et al., 2022) . It splits the augmentations into two parts, to which representations should be insensitive and sensitive, and then establishes the invariance and equivariance mechanisms correspondingly. The idea of "equivariance" is our focus, which makes representations aware of semantic changes caused by certain augmentations H. Here we formulate it as ϕ(T h (g)) = T ′ h (ϕ(g)), ∀h ∈ H, where T h (g) and T ′ h (ϕ(g)) are the actions of augmentation h on graph g and representation ϕ(g), respectively. Jointly learning equivariance to sensitive augmentations H and invariance to insensitive augmentations P is promising to shield representations from the harms of aggressive augmentations. Nonetheless, it is hard, without domain knowledge (Dangovski et al., 2022; Chuang et al., 2022) or extensive testing (Dangovski et al., 2022) , to tell apart sensitive and insensitive augmentations. To embody equivariance in GCL, we propose a simple but effective approach of Equivariant Graph Contrastive Learning (E-GCL). E-GCL is an instantiation of E-SSL for graphs. Unlike previous E-SSL works, E-GCL leaves existing intra-graph augmentations untouched, and creates new augmentations through the "cross-graph" strategy. Concretely, inspired by mixup (Guo & Mao, 2021; Zhang et al., 2018) , the cross-graph augmentation interpolates the raw features of two graphs (i.e., T h ), while employing the same interpolation strategy on the graph labels that are portrayed by graph representations (i.e., T ′ h ). The augmentations across graphs not only maintain the holistic information on self-discrimination, but also are orthogonal to the intra-graph augmentations. On the top of intraand cross-graph of augmentations, E-GCL separately builds the invariance and equivariance principles to guide the representation learning. The equivariance to cross-graph augmentations diminishes the harmful invariance to aggressive augmentations that change global semantics. Integrating two principles enables representations to be sensitive to global semantic shifts across different graphs and insensitive to local substructure perturbations of single graphs. Experiments show that E-GCL achieves promising performances to surpass current state-of-the-art GCL models, across diverse settings. We also demonstrate E-GCL's generalization to various SSL frameworks, including BarlowTwins (Zbontar et al., 2021 ), GraphCL (You et al., 2020) and SimSiam (Chen & He, 2021).



y S t 4 c d F 6 c d + d j 2 b r l r G Y u y B 8 4 n z 9 q + 5 F M < / l a t e x i t > CH2 < l a t e x i t s h a 1 _ b a s e 6 4 = " I i Y n i 4 S M w 6 / K m 5 O r c F

y S t 4 c d F 6 c d + d j 2 b r l r G Y u y B 8 4 n z 9 q + 5 F M < / l a t e x i t > CH2 < l a t e x i t s h a 1 _ b a s e 6 4 = " I i Y n i 4 S M w 6 / K m 5 O r c F

y S t 4 c d F 6 c d + d j 2 b r l r G Y u y B 8 4 n z 9 q + 5 F M < / l a t e x i t > CH2 < l a t e x i t s h a 1 _ b a s e 6 4 = " I i Y n i 4 S M w 6 / K m 5 O r c F

y S t 4 c d F 6 c d + d j 2 b r l r G Y u y B 8 4 n z 9 q + 5 F M < / l a t e x i t > CH2 < l a t e x i t s h a 1 _ b a s e 6 4 = " d G i X g C e j l q 2 K I b q K m w W P m j 3 / G Z g = " > A A A B 8 n i c b Z D L S g M x F I Y z r Z d a b 1 W X b l K L U D d l R k S 7 L L h x W a E 3 m A 5 D J s 2 0 o Z l k S D J C G e r O R 3 D j Q h G 3 P o c P 4 M 5 H c W e m 7 U J b f w h 8 / P 8 5 5 J w T x I w q b

< l a t e x i t s h a 1 _ b a s e 6 4 = " D 6 t B + X I n L z e v V 7 d 2 A I 7 P 4 3 r 1 S t U = " > A A A B 8 n i c b Z D L S g M x F I Y z 1 k u t t 6 p L N 6 l F q J s y U 0 S 7 L L h x W a E 3 m A 5 D J s 2 0 o Z l k S D J C G e r O R 3 D j Q h G 3 P o c P 4 M 5 H c W e m 7 U J b f w h 8 / P 8 5 5 J w T x I w q b d t f 1 l p u f W N z K 7 9 d 2 N n d 2 z 8 o H h 5 1 l E g k J m 0 s m J C 9 A C n C K C d t T T U j v V g S F A W M d I P x d Z Z 3 7 4 h U V P C W n s T E i 9 C Q 0 5 B i p I 3 l t v w 0 9 m v T y v C 8 4 B f L d t W e C a 6 C s 4 B y o / R d y j 1 8 3 D f 9 4 m d / I H A S E a 4 x Q 0

7 u f i f 1 0 0 x v P Y z o Z I U u W L z j 8 J U E o x J f j 8 Z C M 0 Z y o k l l G l h s x I 2 o p o y t C 2 V b A n e 8 s m r p H V R 9 S 6 r t f t a p f 5 T R x F O 4 B T O w Y M r q M M d N K A J D G J 4 g h d 4 d d B 5 d t 6 c 9 / l o w V n s H M M f O B / f 0 s C R p A = = < / l a t e x i t > G < l a t e x i t s h a 1 _ b a s e 6 4 = " 1 CP g Z h Y A Q v 3 u k E 0 + W F h r N l G H 2 F o = " > A A A B + n i c b V D L S s N A F L 3 x W e s r 1 a W b w S L U T U m k q M u C C 1 1 W s A 9 o Q p l M J + 3 Q y S T M T J Q S +y l u X C j i 1 i 9 x 5 9 8 4 a S t o 6 4 G B w z n 3 c s + c I O F M a c f 5 s l Z W 1 9 Y 3 N g t b x e 2 d 3 b 1 9 u 3 T Q U n E q C W 2 S m M e y E 2 B F O R O 0 q Z n m t J N I i q O A 0 3 Y w u s r 9 9 j 2 V i s X i T o 8 T 6 k d 4 I F j I C N Z G 6 t k l L x m y i h d h P S S Y Z 9 e T 0 5 5 d d q r O F G i Z u H N S r s M M j Z 7 9 6 f V j k k Z U a M K x U l 3 X S b S f Y a k Z 4 X R S 9 F J F E 0 x G e E C 7 h g o c U e V n 0 + g T d G K U P g p j a Z 7 Q a K r + 3 s h w p N Q 4 C s x k n l E t e r n 4 n 9 d N d X j p Z 0 w k q a a C z A 6 F K U c 6 R n k P q M 8 k J Z q P D c F E M p M V k S G W m G j T V t G U 4 C 5 + e Z m 0 z q r u e b V 2 W y v X f + o o w B E c Q w V c u I A 6 3 E A D m k D g A Z 7 g B V 6 t R + v Z e r P e Z 6 M r 1 n z n E P 7 A + v g G M 0 6 T / w = = < / l a t e x i t > (G) < l a t e x i t s h a 1 _ b a s e 6 4 = " p p 9 x f B m g F z w s + / H X d V c i s w v 0 9 E s = " > A A A B 6 n i c b V D L S s N A F L 2 p r 1 p f

N D T 0 5 M 0 6 e 4 Z u n u E M G T n D d y 4 U M S t B / E A 7 v Q A n s A D 2 P k s N P F B w e O 9 K q r q + T F n 2 r j u h 5 N Z W V 1 b 3 8 h u 5 r a 2 d 3 b 3 8 v s H D R 0 l i t A 6 i X i k W j 7 W l D N J 6 4 Y Z T l u x o l j 4 n D b 9 4 c X E b 9 5 S p V k k r 8 0 o p l 2 B + 5 K F j G B j p Z u O Y T y g a X / c y x f d s j s F W i b e n B S r h d L d 9 9 v X Z 6 2 X f + 8 E E U k E l Y Z w r H X b c 2 P T T b E y j H A 6 z n U S T W N M h r h P 2 5 Z K L K j u p t O D x 6 h k l Q C F k b I l D Z q q v y d S L L Q e C d 9 2 C m w G e t G b i P 9 5 7 c S E l W 7 K Z J w Y K s l s U Z h w Z C I 0 + R 4 F T F F i + M g S T B S z t y I y w A o T Y z P K 2 R C 8 x Z e X S e O k 7 J 2 V T 6 9 s G h W Y I Q s F O I J j 8 O A c q n A J N a g D A Q H 3 8 A h P j n I e n G f n Z d a a c e Y z h / A H z u s P L t 2 V G g = = < / l a t e x i t > g < l a t e x i t s h a 1 _ b a s e 6 4 = " 6 I 3 R K 5 2 8 P g j Z r B b q 6 M s 5 b E p J 1 L E = " > A A A B + H i c b V D L S s N A F L 2 p V W t 9 N O r S z W g R 6 q Y k I t q N U H D j s o J 9 S B P K Z D p p h 0 4 m Y W Y i 1 N A v c e N C E b d + g d / g z r 9 x + l h o 9 c C F w z n 3 c u 8 9 Q c K Z 0 o 7 z Z e V W 8 q t r 6 4 W N 4 u b W 9 k 7 J 3 t 1 r q

W T y b S h m c y Q 3 B H K 0 I 9 w 4 0 I R t 3 6 P O / / G 9 L H Q 1 g O B w z n n k n t P k E p h 0 H W / n c L W 9 s 7 u X n G / d H B 4 d H x S P j 3 r m C T T j L d Z I h P d C 6 j h U i j e R o G S 9 1 L N a R x I 3 g 0 m d 3 O / + 8 S 1 E Y l 6 x G n K / Z i O l I g E o 2 i l 7 k D a a E i H 5 Y p b d R c g m 8 R b k U o T l m g N y 1 + D M G F Z z B U y S Y 3 p e 2 6 K f k 4 1 C i b 5 r D T I D E 8 p m 9 A R 7 1 u q a M y N n y / W n Z E r q 4 Q k S r R 9 C s l C / T 2 R 0 9 i Y a R z Y Z E x x b N a 9 u f i f 1 8 8 w a v i 5 U G m G X L H l R 1 E m C S Z k f j s J h e Y M 5 d Q S y r S w u x I 2 p p o y t A 2 V b A n e + s m b p H N T 9 e r V 2 k O t 0 m y s 6 i j C B V z C N X h w C 0 2 4 h x a 0 g c E E n u E V 3 p z U e X H e n Y 9 l t O C s Z s 7 h D 5 z P H 5 O x j 7 w = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " b t j G N 3 7 o d a f v N 8 8 L S f Y F F

5 d Q S y r S w u x I 2 p p o y t A 2 V b A n e + s m b p H N T 9 e r V 2 k O t 0 m y s 6 i j C B V z C N X h w C 0 2 4 h x a 0 g c E E n u E V 3 p z U e X H e n Y 9 l t O C s Z s 7 h D 5 z P H 5 O x j 7 w = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = "

A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x K i B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e VN 0 r 4 p e 9 V y p V k p 1 S q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + u d j Q I = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " m q q g z K I D 3 H s h 2 y D A V t A 3 / P J A g X c = " >A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x K i B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0r 4 p e 9 V y p V k p 1 S q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + u d j Q I = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " m q q g z K I D 3 H s h 2 y D A V t A 3 / P J A g X c = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x K i B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W MS q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e VN 0 r 4 p e 9 V y p V k p 1 S q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + u d j Q I = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " m q q g z KI D 3 H s h 2 y D A V t A 3 / P J A g X c = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x K i B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3 Q j + h I 8 p A z a q z U r A + K J b f s L k A 2 i b c i p R o s 0 R g U v / r D m K U R S s M E 1 b r n u Y n x M 6 o M Z w J n h X 6 q M a F s Q k f Y s 1 T S C L W f L Q 6 d k S u r D E k Y K 1 v S k I X 6 e y K j k d b T K L C d E T V j v e 7 N x f + 8 X m r C O z / j M k k N S r Z c F K a C m J j M v y Z D r p A Z M b W E M s X t r Y S N q a L M 2 G w K N g R v / e V N 0r 4 p e 9 V y p V k p 1 S q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + u d j Q I = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " m q q g z K I D 3 H s h 2 y D A V t A 3 / P J A g X c = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x K i B 4 D u X h M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o J J f e 5 3 n l B p H s s H M 0 3

r 4 p e 9 V y p V k p 1 S q r O P J w A Z d w D R 7 c Q g 3 u o Q E t Y I D w D K / w 5 j w 6 L 8 6 7 8 7 F s z T m r m X P 4 A + f z B + u d j Q I = < / l a t e x i t > C < l a t e x i t s h a 1 _ b a s e 6 4 = " 0 1 L 3 k m Z f y Z L N j U n T c L U S 8 o U 0 M C M = " > A A A B 6 H i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x K i B 4 D X n J M w D w g W c L s p D c Z M z u 7 z M w K Y c k X e P G g i F c / y Z t / 4 + R x 0 M S C h q K q m + 6 u I B F c G 9 f 9 d n J b 2 z u 7 e / n 9 w s H h 0 f F J 8 f S s r e N U M W y

Figure 1: (a) invariance to intra-graph augmentations; (b) equivariance to cross-graph augmentations. • Limiting the augmentations to local substructures of an individual graph is aggressive (Purushwalkam & Gupta, 2020; Wang et al., 2022) insofar as the augmented views fragmentarily or even wrongly describe the characteristics of the anchor graph. Take a molecule graph as an example.After randomly dropping some nodes, one view could hold a cyano group (-C≡N) that determines the property of molecule hypertoxic, while another could corrupt this functional group. Thus, intra-graph augmentations are inadequate for presenting a holistic view of the anchor graph. • Worse still, aggressive augmentations easily make two positive views far from each other, but the invariance mechanism blindly forces their representations to be invariant. Considering the molecule graph's views again (cf. Figure1a), invariance-guided contrastive learning simply maximizes their representation agreement, regardless of the changes in the hypertoxic property. Therefore, it might amplify the negative impact of aggressive intra-graph augmentations and restrain representations from reflecting the instance semantics faithfully.

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