id	sid	tid	token	lemma	pos
gh93gx4504k	1	1	the	the	DET
gh93gx4504k	1	2	goal	goal	NOUN
gh93gx4504k	1	3	of	of	ADP
gh93gx4504k	1	4	this	this	DET
gh93gx4504k	1	5	thesis	thesis	NOUN
gh93gx4504k	1	6	is	be	AUX
gh93gx4504k	1	7	to	to	PART
gh93gx4504k	1	8	explore	explore	VERB
gh93gx4504k	1	9	the	the	DET
gh93gx4504k	1	10	fundamental	fundamental	ADJ
gh93gx4504k	1	11	role	role	NOUN
gh93gx4504k	1	12	of	of	ADP
gh93gx4504k	1	13	geometry	geometry	NOUN
gh93gx4504k	1	14	in	in	ADP
gh93gx4504k	1	15	learning	learn	VERB
gh93gx4504k	1	16	and	and	CCONJ
gh93gx4504k	1	17	inference	inference	NOUN
gh93gx4504k	1	18	across	across	ADP
gh93gx4504k	1	19	various	various	ADJ
gh93gx4504k	1	20	statistical	statistical	ADJ
gh93gx4504k	1	21	and	and	CCONJ
gh93gx4504k	1	22	machine	machine	NOUN
gh93gx4504k	1	23	learning	learning	NOUN
gh93gx4504k	1	24	problems	problem	NOUN
gh93gx4504k	1	25	.	.	PUNCT
gh93gx4504k	2	1	as	as	SCONJ
gh93gx4504k	2	2	complex	complex	ADJ
gh93gx4504k	2	3	data	datum	NOUN
gh93gx4504k	2	4	becomes	become	VERB
gh93gx4504k	2	5	increasingly	increasingly	ADV
gh93gx4504k	2	6	prevalent	prevalent	ADJ
gh93gx4504k	2	7	in	in	ADP
gh93gx4504k	2	8	modern	modern	ADJ
gh93gx4504k	2	9	applications	application	NOUN
gh93gx4504k	2	10	,	,	PUNCT
gh93gx4504k	2	11	geometry	geometry	NOUN
gh93gx4504k	2	12	is	be	AUX
gh93gx4504k	2	13	inherently	inherently	ADV
gh93gx4504k	2	14	embedded	embed	VERB
gh93gx4504k	2	15	within	within	ADP
gh93gx4504k	2	16	it	it	PRON
gh93gx4504k	2	17	,	,	PUNCT
gh93gx4504k	2	18	either	either	CCONJ
gh93gx4504k	2	19	known	know	VERB
gh93gx4504k	2	20	or	or	CCONJ
gh93gx4504k	2	21	to	to	PART
gh93gx4504k	2	22	be	be	AUX
gh93gx4504k	2	23	discovered	discover	VERB
gh93gx4504k	2	24	.	.	PUNCT
gh93gx4504k	3	1	efficient	efficient	ADJ
gh93gx4504k	3	2	and	and	CCONJ
gh93gx4504k	3	3	reliable	reliable	ADJ
gh93gx4504k	3	4	learning	learning	NOUN
gh93gx4504k	3	5	and	and	CCONJ
gh93gx4504k	3	6	inference	inference	NOUN
gh93gx4504k	3	7	should	should	AUX
gh93gx4504k	3	8	consider	consider	VERB
gh93gx4504k	3	9	this	this	DET
gh93gx4504k	3	10	geometry	geometry	NOUN
gh93gx4504k	3	11	.	.	PUNCT
gh93gx4504k	4	1	in	in	ADP
gh93gx4504k	4	2	this	this	DET
gh93gx4504k	4	3	thesis	thesis	NOUN
gh93gx4504k	4	4	,	,	PUNCT
gh93gx4504k	4	5	we	we	PRON
gh93gx4504k	4	6	demonstrate	demonstrate	VERB
gh93gx4504k	4	7	how	how	SCONJ
gh93gx4504k	4	8	geometry	geometry	NOUN
gh93gx4504k	4	9	can	can	AUX
gh93gx4504k	4	10	be	be	AUX
gh93gx4504k	4	11	utilized	utilize	VERB
gh93gx4504k	4	12	to	to	PART
gh93gx4504k	4	13	address	address	VERB
gh93gx4504k	4	14	crucial	crucial	ADJ
gh93gx4504k	4	15	issues	issue	NOUN
gh93gx4504k	4	16	in	in	ADP
gh93gx4504k	4	17	statistics	statistic	NOUN
gh93gx4504k	4	18	and	and	CCONJ
gh93gx4504k	4	19	machine	machine	NOUN
gh93gx4504k	4	20	learning	learn	VERB
gh93gx4504k	4	21	for	for	ADP
gh93gx4504k	4	22	effective	effective	ADJ
gh93gx4504k	4	23	learning	learning	NOUN
gh93gx4504k	4	24	and	and	CCONJ
gh93gx4504k	4	25	inference	inference	NOUN
gh93gx4504k	4	26	.	.	PUNCT
gh93gx4504k	5	1	specifically	specifically	ADV
gh93gx4504k	5	2	,	,	PUNCT
gh93gx4504k	5	3	we	we	PRON
gh93gx4504k	5	4	first	first	ADV
gh93gx4504k	5	5	present	present	ADJ
gh93gx4504k	5	6	both	both	CCONJ
gh93gx4504k	5	7	intrinsic	intrinsic	ADJ
gh93gx4504k	5	8	and	and	CCONJ
gh93gx4504k	5	9	extrinsic	extrinsic	ADJ
gh93gx4504k	5	10	deep	deep	ADJ
gh93gx4504k	5	11	neural	neural	ADJ
gh93gx4504k	5	12	network	network	NOUN
gh93gx4504k	5	13	(	(	PUNCT
gh93gx4504k	5	14	dnn	dnn	PROPN
gh93gx4504k	5	15	)	)	PUNCT
gh93gx4504k	5	16	architectures	architecture	NOUN
gh93gx4504k	5	17	as	as	ADP
gh93gx4504k	5	18	versatile	versatile	ADJ
gh93gx4504k	5	19	deep	deep	ADJ
gh93gx4504k	5	20	learning	learning	NOUN
gh93gx4504k	5	21	frameworks	framework	NOUN
gh93gx4504k	5	22	for	for	ADP
gh93gx4504k	5	23	manifold	manifold	ADJ
gh93gx4504k	5	24	-	-	PUNCT
gh93gx4504k	5	25	valued	value	VERB
gh93gx4504k	5	26	data	datum	NOUN
gh93gx4504k	5	27	.	.	PUNCT
gh93gx4504k	6	1	these	these	DET
gh93gx4504k	6	2	frameworks	framework	NOUN
gh93gx4504k	6	3	harness	harness	VERB
gh93gx4504k	6	4	the	the	DET
gh93gx4504k	6	5	geometry	geometry	NOUN
gh93gx4504k	6	6	of	of	ADP
gh93gx4504k	6	7	the	the	DET
gh93gx4504k	6	8	underlying	underlying	ADJ
gh93gx4504k	6	9	manifolds	manifold	NOUN
gh93gx4504k	6	10	,	,	PUNCT
gh93gx4504k	6	11	and	and	CCONJ
gh93gx4504k	6	12	we	we	PRON
gh93gx4504k	6	13	derive	derive	VERB
gh93gx4504k	6	14	convergence	convergence	NOUN
gh93gx4504k	6	15	rates	rate	NOUN
gh93gx4504k	6	16	for	for	ADP
gh93gx4504k	6	17	estimators	estimator	NOUN
gh93gx4504k	6	18	based	base	VERB
gh93gx4504k	6	19	on	on	ADP
gh93gx4504k	6	20	the	the	DET
gh93gx4504k	6	21	proposed	propose	VERB
gh93gx4504k	6	22	dnn	dnn	NOUN
gh93gx4504k	6	23	models	model	NOUN
gh93gx4504k	6	24	.	.	PUNCT
gh93gx4504k	7	1	we	we	PRON
gh93gx4504k	7	2	also	also	ADV
gh93gx4504k	7	3	establish	establish	VERB
gh93gx4504k	7	4	an	an	DET
gh93gx4504k	7	5	extrinsic	extrinsic	ADJ
gh93gx4504k	7	6	bayesian	bayesian	ADJ
gh93gx4504k	7	7	optimization	optimization	NOUN
gh93gx4504k	7	8	framework	framework	NOUN
gh93gx4504k	7	9	for	for	ADP
gh93gx4504k	7	10	addressing	address	VERB
gh93gx4504k	7	11	general	general	ADJ
gh93gx4504k	7	12	optimization	optimization	NOUN
gh93gx4504k	7	13	problems	problem	NOUN
gh93gx4504k	7	14	on	on	ADP
gh93gx4504k	7	15	manifolds	manifold	NOUN
gh93gx4504k	7	16	.	.	PUNCT
gh93gx4504k	8	1	additionally	additionally	ADV
gh93gx4504k	8	2	,	,	PUNCT
gh93gx4504k	8	3	we	we	PRON
gh93gx4504k	8	4	propose	propose	VERB
gh93gx4504k	8	5	neural	neural	ADJ
gh93gx4504k	8	6	-	-	PUNCT
gh93gx4504k	8	7	network	network	NOUN
gh93gx4504k	8	8	-	-	PUNCT
gh93gx4504k	8	9	based	base	VERB
gh93gx4504k	8	10	numerical	numerical	ADJ
gh93gx4504k	8	11	schemes	scheme	NOUN
gh93gx4504k	8	12	that	that	PRON
gh93gx4504k	8	13	preserve	preserve	VERB
gh93gx4504k	8	14	variational	variational	ADJ
gh93gx4504k	8	15	structures	structure	NOUN
gh93gx4504k	8	16	when	when	SCONJ
gh93gx4504k	8	17	solving	solve	VERB
gh93gx4504k	8	18	surface	surface	NOUN
gh93gx4504k	8	19	pdes	pde	NOUN
gh93gx4504k	8	20	and	and	CCONJ
gh93gx4504k	8	21	geometric	geometric	ADJ
gh93gx4504k	8	22	flows	flow	NOUN
gh93gx4504k	8	23	.	.	PUNCT
gh93gx4504k	9	1	lastly	lastly	ADV
gh93gx4504k	9	2	,	,	PUNCT
gh93gx4504k	9	3	we	we	PRON
gh93gx4504k	9	4	investigate	investigate	VERB
gh93gx4504k	9	5	high	high	ADJ
gh93gx4504k	9	6	-	-	PUNCT
gh93gx4504k	9	7	dimensional	dimensional	ADJ
gh93gx4504k	9	8	data	datum	NOUN
gh93gx4504k	9	9	distribution	distribution	NOUN
gh93gx4504k	9	10	estimation	estimation	NOUN
gh93gx4504k	9	11	using	use	VERB
gh93gx4504k	9	12	adaptive	adaptive	ADJ
gh93gx4504k	9	13	bayesian	bayesian	ADJ
gh93gx4504k	9	14	deep	deep	ADJ
gh93gx4504k	9	15	generative	generative	ADJ
gh93gx4504k	9	16	models	model	NOUN
gh93gx4504k	9	17	,	,	PUNCT
gh93gx4504k	9	18	emphasizing	emphasize	VERB
gh93gx4504k	9	19	lower	lower	ADV
gh93gx4504k	9	20	-	-	PUNCT
gh93gx4504k	9	21	dimensional	dimensional	ADJ
gh93gx4504k	9	22	manifold	manifold	ADJ
gh93gx4504k	9	23	-	-	PUNCT
gh93gx4504k	9	24	supported	support	VERB
gh93gx4504k	9	25	distributions	distribution	NOUN
gh93gx4504k	9	26	of	of	ADP
gh93gx4504k	9	27	uncertain	uncertain	ADJ
gh93gx4504k	9	28	smoothness	smoothness	NOUN
gh93gx4504k	9	29	.	.	PUNCT
gh93gx4504k	10	1	each	each	DET
gh93gx4504k	10	2	chapter	chapter	NOUN
gh93gx4504k	10	3	is	be	AUX
gh93gx4504k	10	4	devoted	devoted	ADJ
gh93gx4504k	10	5	to	to	ADP
gh93gx4504k	10	6	a	a	DET
gh93gx4504k	10	7	separate	separate	ADJ
gh93gx4504k	10	8	topic	topic	NOUN
gh93gx4504k	10	9	.	.	PUNCT