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XThomasBU
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Colbert_Index

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The dataset generation failed because of a cast error

Error code:   DatasetGenerationCastError
Exception:    DatasetGenerationCastError
Message:      An error occurred while generating the dataset

All the data files must have the same columns, but at some point there are 1 new columns ({'text'}) and 4 missing columns ({'num_embeddings', 'passage_offset', 'num_passages', 'embedding_offset'}).

This happened while the json dataset builder was generating data using

hf://datasets/XThomasBU/Colbert_Index/colbert/indexes/new_idx/collection.json (at revision 29f88be2d04b7d31dd63c8262c5115e3c106de89)

Please either edit the data files to have matching columns, or separate them into different configurations (see docs at https://hf.co/docs/hub/datasets-manual-configuration#multiple-configurations)
Traceback:    Traceback (most recent call last):
                File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 2011, in _prepare_split_single
                  writer.write_table(table)
                File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/arrow_writer.py", line 585, in write_table
                  pa_table = table_cast(pa_table, self._schema)
                File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/table.py", line 2302, in table_cast
                  return cast_table_to_schema(table, schema)
                File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/table.py", line 2256, in cast_table_to_schema
                  raise CastError(
              datasets.table.CastError: Couldn't cast
              text: string
              to
              {'passage_offset': Value(dtype='int64', id=None), 'num_passages': Value(dtype='int64', id=None), 'num_embeddings': Value(dtype='int64', id=None), 'embedding_offset': Value(dtype='int64', id=None)}
              because column names don't match
              
              During handling of the above exception, another exception occurred:
              
              Traceback (most recent call last):
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1577, in compute_config_parquet_and_info_response
                  parquet_operations = convert_to_parquet(builder)
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1191, in convert_to_parquet
                  builder.download_and_prepare(
                File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1027, in download_and_prepare
                  self._download_and_prepare(
                File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1122, in _download_and_prepare
                  self._prepare_split(split_generator, **prepare_split_kwargs)
                File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1882, in _prepare_split
                  for job_id, done, content in self._prepare_split_single(
                File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 2013, in _prepare_split_single
                  raise DatasetGenerationCastError.from_cast_error(
              datasets.exceptions.DatasetGenerationCastError: An error occurred while generating the dataset
              
              All the data files must have the same columns, but at some point there are 1 new columns ({'text'}) and 4 missing columns ({'num_embeddings', 'passage_offset', 'num_passages', 'embedding_offset'}).
              
              This happened while the json dataset builder was generating data using
              
              hf://datasets/XThomasBU/Colbert_Index/colbert/indexes/new_idx/collection.json (at revision 29f88be2d04b7d31dd63c8262c5115e3c106de89)
              
              Please either edit the data files to have matching columns, or separate them into different configurations (see docs at https://hf.co/docs/hub/datasets-manual-configuration#multiple-configurations)

Need help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.

passage_offset int64	num_passages int64	num_embeddings int64	embedding_offset int64	text string
0	6,133	892,641	0	null
null	null	null	null	Lecture 03 Shallow Networks DL4DS – Spring 2024 DS598 B1 Gardos – Understanding Deep Learning, Other Content Cited
null	null	null	null	• Univariate regression problem (one output, real value) • Fully connected network Recap: Regression 2
null	null	null	null	Recap: 1D Linear regression loss function <latexit sha1_base64="/hMh896NPSehdG/Bg07J5FjBuSo=">AW9HiclZhbc9Q2FI A3lLY0LTS07z0xdMHdpCJsvQywszkBAgJDQJuUKc7Mhe2Ssiy4vyQaP/0nfOn3t/+lLf0uPbO8Kn6M8dGfCivN9uh1JtdeIkWLy39M3Pto+sf/Lpjc9mP/i5q0v525/tZ/FR erzPT+WcXrosYxLofheLnLJD5OUs8iT/MA7XdH84JynmYjVb
null	null	null	null	/i5q0v525/tZ/FR erzPT+WcXrosYxLofheLnLJD5OUs8iT/MA7XdH84JynmYjVbn6Z8OIhUoEwmc5hAZz40j1wuSkTh2vn/kuFkRDUrxqF+dlGvVXTfy4nEZVEdjCFb3XC+Ww+wSgtLVNe5f6vAPJw9cd 9ZSGZRBuVT91BT6Vd3ItM5gbmFpcan+OLTQbwsLvfazNbj9zdAdxn4RcZX7kmXZUX8pyY9LlubCl7yadYuMJ8w/ZSE/gqJiEc+Oyz
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null	null	null	null	UC1V7XJ2yZyXQvUlFtYm/FJbZLzQE25hbVXp0ltcn0K1JSPyNBX96cvUiClcKUfzC308VtYWth/sNj/ZfHh9sOFx8vtG 9obvW973/Xu9vq9X3uPey96W729nt/7d+b6zM2ZW/Pn83/M/zn/V6Nem2nrfN3rfOb/g9NB/xE</latexit> L[φ] = I X i=1 (f[xi, φ] − yi)2 = I X i=1 (φ0 + φ1xi − yi)2 Loss function: “Least squares loss function” 3
null	null	null	null	Recap: 1D Linear regression training This technique is known as gradient descent 4
null	null	null	null	Shallow neural networks • 1D regression model is obviously limited • Want to be able to describe input/output that are not lines • Want multiple inputs • Want multiple outputs • Shallow neural networks • Flexible enough to describe arbitrarily complex input/output mappings • Can have as many inputs as we want • Can have as many outputs as we want 5
null	null	null	null	This lecture we’ll cover… • Example network, 1 input, 1 output • Universal approximation theorem • More than one output • More than one input • General case • Number of regions • Terminology 6
null	null	null	null	1D Linear Regression <latexit sha1_base64=" NTIf4aNnvrpa8D wPTFP8Igh9dpg=" >AXIXiclZhb 9s2FICd7talu6Q blpe9CAtaDGsW2G l3wYCbdL0lnRJ msbpQYlUzIbil J0SZwK/jXDfszeh r0N+zM7lGQzOod 5mIHU7Pk+8XJIS rS8RIos73b/mbn2 3vsfPjR9Y9nb3 zy6Wefz938Yj+L i9Tne34s4/TQYxm XQvG9XOSHyYpZ 5En+YF3sq
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null	null	null	null	Qg 02QSxndOVl1pWn 0CpWdBUPbA0Prm k4Z6hCHcDSLtl j7nDXusk8nGI4Z tmSnAhkJTSBfez 0qbM4/XlBSU5yX jAzdEbplaFXlB4 ZekRpaij5ReAFL wlv0684NLQS0 oPDT2ktDC0oHRg 6IDSwNCA0keGPq LUN9SndNPQTUpz Q8mJFJ4Ih5QOj F0QumxoceUvjT0 JaVPDH1C6YmhJ 5S+MfQNpQ8MfUA pM5RumXoFqXcU PLqw
null	null	null	null	j F0QumxoceUvjT0 JaVPDH1C6YmhJ 5S+MfQNpQ8MfUA pM5RumXoFqXcU PLqwAs2DN2g1DO U/PaDvWZon9LE0 ITSh4Y+pHRsKPl VDM8zQ8nxBh6M hkpKnxr6lFJhKP n95gXPDX1OaWRo ROkzQ59R+trQ15 Q+NvQxpaGh5N0A nE4M3afUvAUqM0 r3DN2j9MLQC/t 7Ab6cRs+2MHdNB buUxobGlG4bSn4 pwFHC0HNyngxUc 1db
null	null	null	null	0 r3DN2j9MLQC/t 7Ab6cRs+2MHdNB buUxobGlG4bSn4 pwFHC0HNyngxUc 1dbvG0i97VALbm FNRlfXE1yHqglt 7Dm7rS4mtyfAr XkE9L1rcPlixRI KdzpR6vrPfwWlh YOf+r0func27u3 fn+jeUN70/na+c b5zuk5vzr3nSdO 3xk4vOn85fzt /P2t21/bWTtWG tvnOjueZLp/VZ4 /8B0OTgog=</l atexit>y = f[x,
null	null	null	null	vOn85fzt /P2t21/bWTtWG tvnOjueZLp/VZ4 /8B0OTgog=</l atexit>y = f[x, φ] = φ0 + φ1x Example shallow network 7
null	null	null	null	Example shallow network <latexit sha1_base64=" NTIf4aNnvrpa8D wPTFP8Igh9dpg=" >AXIXiclZhb 9s2FICd7talu6Q blpe9CAtaDGsW2G l3wYCbdL0lnRJ msbpQYlUzIbil J0SZwK/jXDfszeh r0N+zM7lGQzOod 5mIHU7Pk+8XJIS rS8RIos73b/mbn2 3vsfPjR9Y9nb3 zy6Wefz938Yj+L i9Tne34s4/TQYxm XQvG9XOSHyYpZ 5En+YF3sqr
null	null	null	null	jR9Y9nb3 zy6Wefz938Yj+L i9Tne34s4/TQYxm XQvG9XOSHyYpZ 5En+YF3sqr5wRl PMxGr3fwi4cRC5 UIhM9yCPXn/ri4 fd9xIy8elcH4aL ToekEyFMeuO3v7v gulfte541SFXqO x8ZGbD3nO+mWvO 74zLfGo+OJu0z d5Uvucu1W6l2q3r 2k3tXqbH9uobvU rT4OLfSawkKn+W z1b341cAexX0Rc5 b5kWXbU6yb5cn SXPiSj
null	null	null	null	3tXqbH9uobvU rT4OLfSawkKn+W z1b341cAexX0Rc5 b5kWXbU6yb5cn SXPiSj2fdIuMJ8 09YyI+gqFjEs+Oy yufYuQWRgRPEKf yp3Kmil68oWZRl F5EHZsTyYaZDtr YUZEHPx+XQiVFz pVfNxQU0sljR0+ OMxAp93N5AQXmpw L6vhDljI/hymc dRU/9+MoYmpQui tr2+PS9XgoVMlPi 2o6x+O2s1Y5HIp XGSvPdqe1iJxH4 h
null	null	null	null	c dRU/9+MoYmpQui tr2+PS9XgoVMlPi 2o6x+O2s1Y5HIp XGSvPdqe1iJxH4 h0nlVSKruQKgYfj suRL4RIGgMQS5 yAWPEM6tT58QKn hygsXwm4rNcFLEj n5ZhUrXIeQk5a2 muiQSGRfNSyVok FUxm1lB1QHOeWow HPU5gF6Cp8cTQH OwlT48l1OR/laV RmOoZbSJkKedUED NlnUo+obahCSrj Ub1m/YeslUydN4 uKk6mqI8ja
null	null	null	null	1OR/laV RmOoZbSJkKedUED NlnUo+obahCSrj Ub1m/YeslUydN4 uKk6mqI8jaTdtO ntK8qEHbqSLIgk UYtq0qgiwJN5sB ixhkuSn3YcCRoyN 2VSisCrIwt9LYa 7ed6Ahem6ME9kv bWytJ+s8YyogOwO 7T34Ipn7f1Xhq O5PknFW+LvCRM4 TJal/C0rAe1qQRG FUTG1OzyhUyabY glMbnbVP3xqLyR LQHqAN40xWpUME lbEqw
null	null	null	null	al/C0rAe1qQRG FUTG1OzyhUyabY glMbnbVP3xqLyR LQHqAN40xWpUME lbEqwZLVYXcRhp oWkh9v/QDHx2X Xb1t9D8km1BRVi S2inT4f1Q0gMcbX l8QwZMXSzR5EKg mL5Zwf0dTx1K8s HWkmjsoCMWkyC/Q 9hehal9TRXBn4w j1FQK6XvhmQqFJ DoK2rANahm94UFs WkI8G6dj9GWcF SknNz+0niFS6fq 2mAr9sGrfUKUW2v
null	null	null	null	FJ DoK2rANahm94UFs WkI8G6dj9GWcF SknNz+0niFS6fq 2mAr9sGrfUKUW2v cNLqdXQRkeDmf8 is9lFGvzqcXF2 rAUpTMkZ7S0Rs3y 2GL2XZ/NeV10Wq F/HS9aQ/6BbNT+ D4/7a/j+QiJR2J 6oKTkbUuSxLe1 DXdLle7lm5/uY7 srRDi2s3Jam36aX dtrhX9ICfblh6u 0E8YlFHorqaHlK PWJb2oC57Hjdso7 C4dlOSeid5t
null	null	null	null	am36aX dtrhX9ICfblh6u 0E8YlFHorqaHlK PWJb2oC57Hjdso7 C4dlOSeid5tNoW d2qi5R/s6qOoPi bFcqCPfbF06xAWc yrmVjGOeIjEOoT FqGhb8H+s7Ah4e LStOoTFrUy0NR3A 0oBLPIQ6hMV6C7 fNJobVDYu6YVeZ TIbIrENYfMIiPOo 6hMWQiqFVPGFJg sQ6RPI4xHkc0jw mWEpsEp6RxDIjZE nZFlQ6jNuSDmBp hFob
null	null	null	null	hMWQiqFVPGFJg sQ6RPI4xHkc0jw mWEpsEp6RxDIjZE nZFlQ6jNuSDmBp hFobWRqDHshYoQ abIJYzuvIy68pT aBUruor3bA3vXdF wzlCFOoClTbLH HfTusk8nGI4Ztm SnAhkJTSBW9jZos 7k9OcFJTnJecGF oReUnht6TumBoQ eUpoaSXwRe8NJQ8 uvEC84MPaN039B 9SgtDC0r3DN2jN DA0oPSxoY8p9Q31 KV01dJXS3FByI
null	null	null	null	NJQ8 uvEC84MPaN039B 9SgtDC0r3DN2jN DA0oPSxoY8p9Q31 KV01dJXS3FByIo UngqG7lA4NHVJ6 aOghpa8MfUXpU0O fUvra0NeUvjP0H aUPDX1IKTOUbp m6Bql3FDy6sALVg xdodQzlPz2g71m 6BaliaEJpY8MfU TpwFDyqxieZ4aS4 w08GA2VlD4z9Bm lwlDy+80LXhj6g tLI0IjS54Y+p/St oW8pfWLoE0pDQ8 m7ATidG
null	null	null	null	A2VlD4z9Bm lwlDy+80LXhj6g tLI0IjS54Y+p/St oW8pfWLoE0pDQ8 m7ATidGLpDqXkL VGaUbhu6Tempoaf 29wJ8Oo2ebWFum go2KY0NjSldN5T 8UoCjhKEn5DwZqO auNnbRO5rgZpy C2syPrma5DxQU2 5hzd1pcjW5PwVqy oek62v70xcpkFK 40/fnFnr4LSwt7 C8v9X5curd9b+HB SvOG9nrn6843nW 87vc5PnQedp52t z
null	null	null	null	K 40/fnFnr4LSwt7 C8v9X5curd9b+HB SvOG9nrn6843nW 87vc5PnQedp52t zl7Hn7kx05v5Zeb X+d/n/5z/a/7vW r0201zZaf1mf/ 3P5u9C70=</late xit>y = f[x, φ] = φ0 + φ1a[✓10 + ✓11x] + φ2a[✓20 + ✓21x] + φ3a[✓30 + ✓31x] 8
null	null	null	null	Example shallow network <latexit sha1_base64=" NTIf4aNnvrpa8D wPTFP8Igh9dpg=" >AXIXiclZhb 9s2FICd7talu6Q blpe9CAtaDGsW2G l3wYCbdL0lnRJ msbpQYlUzIbil J0SZwK/jXDfszeh r0N+zM7lGQzOod 5mIHU7Pk+8XJIS rS8RIos73b/mbn2 3vsfPjR9Y9nb3 zy6Wefz938Yj+L i9Tne34s4/TQYxm XQvG9XOSHyYpZ 5En+YF3sqr
null	null	null	null	jR9Y9nb3 zy6Wefz938Yj+L i9Tne34s4/TQYxm XQvG9XOSHyYpZ 5En+YF3sqr5wRl PMxGr3fwi4cRC5 UIhM9yCPXn/ri4 fd9xIy8elcH4aL ToekEyFMeuO3v7v gulfte541SFXqO x8ZGbD3nO+mWvO 74zLfGo+OJu0z d5Uvucu1W6l2q3r 2k3tXqbH9uobvU rT4OLfSawkKn+W z1b341cAexX0Rc5 b5kWXbU6yb5cn SXPiSj
null	null	null	null	3tXqbH9uobvU rT4OLfSawkKn+W z1b341cAexX0Rc5 b5kWXbU6yb5cn SXPiSj2fdIuMJ8 09YyI+gqFjEs+Oy yufYuQWRgRPEKf yp3Kmil68oWZRl F5EHZsTyYaZDtr YUZEHPx+XQiVFz pVfNxQU0sljR0+ OMxAp93N5AQXmpw L6vhDljI/hymc dRU/9+MoYmpQui tr2+PS9XgoVMlPi 2o6x+O2s1Y5HIp XGSvPdqe1iJxH4 h
null	null	null	null	c dRU/9+MoYmpQui tr2+PS9XgoVMlPi 2o6x+O2s1Y5HIp XGSvPdqe1iJxH4 h0nlVSKruQKgYfj suRL4RIGgMQS5 yAWPEM6tT58QKn hygsXwm4rNcFLEj n5ZhUrXIeQk5a2 muiQSGRfNSyVok FUxm1lB1QHOeWow HPU5gF6Cp8cTQH OwlT48l1OR/laV RmOoZbSJkKedUED NlnUo+obahCSrj Ub1m/YeslUydN4 uKk6mqI8ja
null	null	null	null	1OR/laV RmOoZbSJkKedUED NlnUo+obahCSrj Ub1m/YeslUydN4 uKk6mqI8jaTdtO ntK8qEHbqSLIgk UYtq0qgiwJN5sB ixhkuSn3YcCRoyN 2VSisCrIwt9LYa 7ed6Ahem6ME9kv bWytJ+s8YyogOwO 7T34Ipn7f1Xhq O5PknFW+LvCRM4 TJal/C0rAe1qQRG FUTG1OzyhUyabY glMbnbVP3xqLyR LQHqAN40xWpUME lbEqw
null	null	null	null	al/C0rAe1qQRG FUTG1OzyhUyabY glMbnbVP3xqLyR LQHqAN40xWpUME lbEqwZLVYXcRhp oWkh9v/QDHx2X Xb1t9D8km1BRVi S2inT4f1Q0gMcbX l8QwZMXSzR5EKg mL5Zwf0dTx1K8s HWkmjsoCMWkyC/Q 9hehal9TRXBn4w j1FQK6XvhmQqFJ DoK2rANahm94UFs WkI8G6dj9GWcF SknNz+0niFS6fq 2mAr9sGrfUKUW2v
null	null	null	null	FJ DoK2rANahm94UFs WkI8G6dj9GWcF SknNz+0niFS6fq 2mAr9sGrfUKUW2v cNLqdXQRkeDmf8 is9lFGvzqcXF2 rAUpTMkZ7S0Rs3y 2GL2XZ/NeV10Wq F/HS9aQ/6BbNT+ D4/7a/j+QiJR2J 6oKTkbUuSxLe1 DXdLle7lm5/uY7 srRDi2s3Jam36aX dtrhX9ICfblh6u 0E8YlFHorqaHlK PWJb2oC57Hjdso7 C4dlOSeid5t
null	null	null	null	am36aX dtrhX9ICfblh6u 0E8YlFHorqaHlK PWJb2oC57Hjdso7 C4dlOSeid5tNoW d2qi5R/s6qOoPi bFcqCPfbF06xAWc yrmVjGOeIjEOoT FqGhb8H+s7Ah4e LStOoTFrUy0NR3A 0oBLPIQ6hMV6C7 fNJobVDYu6YVeZ TIbIrENYfMIiPOo 6hMWQiqFVPGFJg sQ6RPI4xHkc0jw mWEpsEp6RxDIjZE nZFlQ6jNuSDmBp hFob
null	null	null	null	hMWQiqFVPGFJg sQ6RPI4xHkc0jw mWEpsEp6RxDIjZE nZFlQ6jNuSDmBp hFobWRqDHshYoQ abIJYzuvIy68pT aBUruor3bA3vXdF wzlCFOoClTbLH HfTusk8nGI4Ztm SnAhkJTSBW9jZos 7k9OcFJTnJecGF oReUnht6TumBoQ eUpoaSXwRe8NJQ8 uvEC84MPaN039B 9SgtDC0r3DN2jN DA0oPSxoY8p9Q31 KV01dJXS3FByI
null	null	null	null	NJQ8 uvEC84MPaN039B 9SgtDC0r3DN2jN DA0oPSxoY8p9Q31 KV01dJXS3FByIo UngqG7lA4NHVJ6 aOghpa8MfUXpU0O fUvra0NeUvjP0H aUPDX1IKTOUbp m6Bql3FDy6sALVg xdodQzlPz2g71m 6BaliaEJpY8MfU TpwFDyqxieZ4aS4 w08GA2VlD4z9Bm lwlDy+80LXhj6g tLI0IjS54Y+p/St oW8pfWLoE0pDQ8 m7ATidG
null	null	null	null	A2VlD4z9Bm lwlDy+80LXhj6g tLI0IjS54Y+p/St oW8pfWLoE0pDQ8 m7ATidGLpDqXkL VGaUbhu6Tempoaf 29wJ8Oo2ebWFum go2KY0NjSldN5T 8UoCjhKEn5DwZqO auNnbRO5rgZpy C2syPrma5DxQU2 5hzd1pcjW5PwVqy oek62v70xcpkFK 40/fnFnr4LSwt7 C8v9X5curd9b+HB SvOG9nrn6843nW 87vc5PnQedp52t z
null	null	null	null	K 40/fnFnr4LSwt7 C8v9X5curd9b+HB SvOG9nrn6843nW 87vc5PnQedp52t zl7Hn7kx05v5Zeb X+d/n/5z/a/7vW r0201zZaf1mf/ 3P5u9C70=</late xit>y = f[x, φ] = φ0 + φ1a[✓10 + ✓11x] + φ2a[✓20 + ✓21x] + φ3a[✓30 + ✓31x] Activation function 9
null	null	null	null	Example shallow network <latexit sha1_base64=" NTIf4aNnvrpa8D wPTFP8Igh9dpg=" >AXIXiclZhb 9s2FICd7talu6Q blpe9CAtaDGsW2G l3wYCbdL0lnRJ msbpQYlUzIbil J0SZwK/jXDfszeh r0N+zM7lGQzOod 5mIHU7Pk+8XJIS rS8RIos73b/mbn2 3vsfPjR9Y9nb3 zy6Wefz938Yj+L i9Tne34s4/TQYxm XQvG9XOSHyYpZ 5En+YF3sqr
null	null	null	null	jR9Y9nb3 zy6Wefz938Yj+L i9Tne34s4/TQYxm XQvG9XOSHyYpZ 5En+YF3sqr5wRl PMxGr3fwi4cRC5 UIhM9yCPXn/ri4 fd9xIy8elcH4aL ToekEyFMeuO3v7v gulfte541SFXqO x8ZGbD3nO+mWvO 74zLfGo+OJu0z d5Uvucu1W6l2q3r 2k3tXqbH9uobvU rT4OLfSawkKn+W z1b341cAexX0Rc5 b5kWXbU6yb5cn SXPiSj
null	null	null	null	3tXqbH9uobvU rT4OLfSawkKn+W z1b341cAexX0Rc5 b5kWXbU6yb5cn SXPiSj2fdIuMJ8 09YyI+gqFjEs+Oy yufYuQWRgRPEKf yp3Kmil68oWZRl F5EHZsTyYaZDtr YUZEHPx+XQiVFz pVfNxQU0sljR0+ OMxAp93N5AQXmpw L6vhDljI/hymc dRU/9+MoYmpQui tr2+PS9XgoVMlPi 2o6x+O2s1Y5HIp XGSvPdqe1iJxH4 h
null	null	null	null	c dRU/9+MoYmpQui tr2+PS9XgoVMlPi 2o6x+O2s1Y5HIp XGSvPdqe1iJxH4 h0nlVSKruQKgYfj suRL4RIGgMQS5 yAWPEM6tT58QKn hygsXwm4rNcFLEj n5ZhUrXIeQk5a2 muiQSGRfNSyVok FUxm1lB1QHOeWow HPU5gF6Cp8cTQH OwlT48l1OR/laV RmOoZbSJkKedUED NlnUo+obahCSrj Ub1m/YeslUydN4 uKk6mqI8ja
null	null	null	null	1OR/laV RmOoZbSJkKedUED NlnUo+obahCSrj Ub1m/YeslUydN4 uKk6mqI8jaTdtO ntK8qEHbqSLIgk UYtq0qgiwJN5sB ixhkuSn3YcCRoyN 2VSisCrIwt9LYa 7ed6Ahem6ME9kv bWytJ+s8YyogOwO 7T34Ipn7f1Xhq O5PknFW+LvCRM4 TJal/C0rAe1qQRG FUTG1OzyhUyabY glMbnbVP3xqLyR LQHqAN40xWpUME lbEqw
null	null	null	null	al/C0rAe1qQRG FUTG1OzyhUyabY glMbnbVP3xqLyR LQHqAN40xWpUME lbEqwZLVYXcRhp oWkh9v/QDHx2X Xb1t9D8km1BRVi S2inT4f1Q0gMcbX l8QwZMXSzR5EKg mL5Zwf0dTx1K8s HWkmjsoCMWkyC/Q 9hehal9TRXBn4w j1FQK6XvhmQqFJ DoK2rANahm94UFs WkI8G6dj9GWcF SknNz+0niFS6fq 2mAr9sGrfUKUW2v
null	null	null	null	FJ DoK2rANahm94UFs WkI8G6dj9GWcF SknNz+0niFS6fq 2mAr9sGrfUKUW2v cNLqdXQRkeDmf8 is9lFGvzqcXF2 rAUpTMkZ7S0Rs3y 2GL2XZ/NeV10Wq F/HS9aQ/6BbNT+ D4/7a/j+QiJR2J 6oKTkbUuSxLe1 DXdLle7lm5/uY7 srRDi2s3Jam36aX dtrhX9ICfblh6u 0E8YlFHorqaHlK PWJb2oC57Hjdso7 C4dlOSeid5t
null	null	null	null	am36aX dtrhX9ICfblh6u 0E8YlFHorqaHlK PWJb2oC57Hjdso7 C4dlOSeid5tNoW d2qi5R/s6qOoPi bFcqCPfbF06xAWc yrmVjGOeIjEOoT FqGhb8H+s7Ah4e LStOoTFrUy0NR3A 0oBLPIQ6hMV6C7 fNJobVDYu6YVeZ TIbIrENYfMIiPOo 6hMWQiqFVPGFJg sQ6RPI4xHkc0jw mWEpsEp6RxDIjZE nZFlQ6jNuSDmBp hFob
null	null	null	null	hMWQiqFVPGFJg sQ6RPI4xHkc0jw mWEpsEp6RxDIjZE nZFlQ6jNuSDmBp hFobWRqDHshYoQ abIJYzuvIy68pT aBUruor3bA3vXdF wzlCFOoClTbLH HfTusk8nGI4Ztm SnAhkJTSBW9jZos 7k9OcFJTnJecGF oReUnht6TumBoQ eUpoaSXwRe8NJQ8 uvEC84MPaN039B 9SgtDC0r3DN2jN DA0oPSxoY8p9Q31 KV01dJXS3FByI
null	null	null	null	NJQ8 uvEC84MPaN039B 9SgtDC0r3DN2jN DA0oPSxoY8p9Q31 KV01dJXS3FByIo UngqG7lA4NHVJ6 aOghpa8MfUXpU0O fUvra0NeUvjP0H aUPDX1IKTOUbp m6Bql3FDy6sALVg xdodQzlPz2g71m 6BaliaEJpY8MfU TpwFDyqxieZ4aS4 w08GA2VlD4z9Bm lwlDy+80LXhj6g tLI0IjS54Y+p/St oW8pfWLoE0pDQ8 m7ATidG
null	null	null	null	A2VlD4z9Bm lwlDy+80LXhj6g tLI0IjS54Y+p/St oW8pfWLoE0pDQ8 m7ATidGLpDqXkL VGaUbhu6Tempoaf 29wJ8Oo2ebWFum go2KY0NjSldN5T 8UoCjhKEn5DwZqO auNnbRO5rgZpy C2syPrma5DxQU2 5hzd1pcjW5PwVqy oek62v70xcpkFK 40/fnFnr4LSwt7 C8v9X5curd9b+HB SvOG9nrn6843nW 87vc5PnQedp52t z
null	null	null	null	K 40/fnFnr4LSwt7 C8v9X5curd9b+HB SvOG9nrn6843nW 87vc5PnQedp52t zl7Hn7kx05v5Zeb X+d/n/5z/a/7vW r0201zZaf1mf/ 3P5u9C70=</late xit>y = f[x, φ] = φ0 + φ1a[✓10 + ✓11x] + φ2a[✓20 + ✓21x] + φ3a[✓30 + ✓31x] <latexit s ha1_base64="y0cLbs hKv4qJCV4w9psY+07H Pg=">AW2niclZhJc 9xEFICVsAWzOVD4wkW
null	null	null	null	4="y0cLbs hKv4qJCV4w9psY+07H Pg=">AW2niclZhJc 9xEFICVsAWzOVD4wkWF KxRFwdSYCsBqhI7zm YHj5exnViOq6VpaTput WQt9tiquXCjuPKT+BP 8Ba7wA3gtaj9oHpi pR+32fendrc1PpciL fv+vGzfePOt9+59e7 Ce+9/8OFHi7c/3s+TM gv4MEhkh36LOdSKD4s RCH5YZpxFvuSH/ina5 ofnPMsF4naKy5TfhyzS IlQ
null	null	null	null	TM gv4MEhkh36LOdSKD4s RCH5YZpxFvuSH/ina5 ofnPMsF4naKy5TfhyzS IlQBKyA0MniSy/2k0n FpkdXx+7PbvPXDt8czg I+j4SqAmgin7p9wvXO yvZyL1yf+q7ngfHecS L+Jnb97gatXpvYeFkcb nf69c/lxZW2sKy0/4G J7c/HXmjJChjropAsjw /WumnxXHFskIEk8Xv DLnKQtOWcSPoKhYzPj qk7E1L0DkZEbJhn8U4 VbR
null	null	null	null	Asjw /WumnxXHFskIEk8Xv DLnKQtOWcSPoKhYzPj qk7E1L0DkZEbJhn8U4 VbR18/o2Jxnl/GPpgxK 8Y5ZjpoY0dlEf54XAm VlgVXQdNQWEq3SFydVX ckMh4U8hIKLMgE9NUN xixjQG5X/AUvwiSOGa QGm91fXtatWnlkDk9D 9Np1mvHZ3J64zVJ3vz WkTBY3HFSW1oiu5Ru DRtKp4L+phIDgA0eMEJ AqmtfJ0fvzQXUEU1p0 EXD
null	null	null	null	3vz WkTBY3HFSW1oiu5Ru DRtKp4L+phIDgA0eMEJ AqmtfJ0fvzQXUEU1p0 EXDWLyANjZ0qVgWPIC cd7QXRoJBKPulYa8SC qYw7yi4ornvH1YAXGcw CdBUOHM3BbsrUdHZew SdFle5juEWMqYiXjcB Qw6Y1CPqGqUEk4NOt Yv2Nph6rRNXJLWXc10B Fl7WdcpMpoXNeo6dQR ZsAijrlVHkCXhKjFiMY Mst+UTGHDs6ohdFQqr giz
null	null	null	null	0B Fl7WdcpMpoXNeo6dQR ZsAijrlVHkCXhKjFiMY Mst+UTGHDs6ohdFQqr gizMQZb43bZTHcFrc5L Cful6xVJ/zlDGdEB2 H36KJgKeFdfS+a2O0vO e3rAp+4Y5is7iksi5p hzRqBUbWxKTXrXCGTZ gtCWXLRNXVvLCpPRXeA OoA3XZkJFb6mfV2XYM nqsPc1DUrJT/6pvcdn xXfb1t9H8km1BRXqa 2inT4f1Q0gvsSXl8QwZ OXS
null	null	null	null	XYM nqsPc1DUrJT/6pvcdn xXfb1t9H8km1BRXqa 2inT4f1Q0gvsSXl8QwZ OXSDR5EKgnL5FwfUdT xzK8sHWknjsoCMWkKC7 R9heR6p5TR3Bnkxj1F QK6XjgyodAkh2FX1gEt wxHusJYFKBs0YA5 nkZcbJxQ+tZ4jUur4sZ kLfrLoXVKmF7nWDy/l ZUIabwzm/5nQfZdRv8u knpRqxDCVzoqd08tL C9hit1fT3lTtFpw9 o24N+we
null	null	null	null	l ZUIabwzm/5nQfZdRv8u knpRqxDCVzoqd08tL C9hit1fT3lTtFpw9 o24N+weyUQcDPTjbwf ETEo5EdcEjbUuSxL e1DXfLm+3rNq4+VXZG lHFtduSlJv20u7bXGv6 QE/27T0dpN4xKORHW 1PaQesSztQV32PG7aRm Fx7aYk9c7yaLUt7txE yz/cG/OC6cekRI70Y18 ivSaExYKhVMYh4hs QlhMS67FvyNlV0BN4+u 1YSwOMhFV9
null	null	null	null	cG/OC6cekRI70Y18 ivSaExYKhVMYh4hs QlhMS67FvyNlV0BN4+u 1YSwOMhFV9MBLI24xE NoQlhstnDXbGNY3bSom 3aVyXSMzCaExUcsxqN uQliMqBhZxVOWpkhsQi SPY5zHMc1jiqXUJuEZ S0zQpaUbUFl46Qr6QC WJqi1iaUx6IFMFGqwDW I5pysvt648hVaxoqt4 aGt4eE3DBUMV6gCWtsg ec70t6ybzcYr16oly alAVkoTOM
null	null	null	null	pysvt648hVaxoqt4 aGt4eE3DBUMV6gCWtsg ec70t6ybzcYr16oly alAVkoTOMDOgDqzpz8/ rMiTnB9eGnpJ6YWhF5 QeGHpAaWYoeSPwx1Dy duJH54bek7pvqH7lJa GlpQODR1SGhoaUvrQ0I eUBoYGlK4ZukZpYSh5 IoU7gqF7lI4NHVN6aOg hpc8NfU7pY0MfU/rC0 BeUXhl6Rel9Q+9Tygxl lK4buk4pN5R8OvDVU NXKfUNJe
null	null	null	null	pc8NfU7pY0MfU/rC0 BeUXhl6Rel9Q+9Tygxl lK4buk4pN5R8OvDVU NXKfUNJe9+sNcMHVCaG pS+sDQB5SODCVvxXA /M5Q83sCN0VBJ6RNDn1 AqDCXvb374zNBnlMaG xpQ+NfQpa8MfUXpI0M fURoZSr4NwNOJobuUm q9AVU7ptqHblJ4Zemb/ LsDn0+jbFuaWqWCL0s TQhNINQ8mbAjxKGHpKn idD1V7VZl+byHUtVHN uYW3GZ2
null	null	null	null	sDn0+jbFuaWqWCL0s TQhNINQ8mbAjxKGHpKn idD1V7VZl+byHUtVHN uYW3GZ2eTnIdqzi2svT rNzibXp1DN+Zh0fX1/ /iEFUgpX+pPF5RX8FZY W9r/trXzfu7t9d/nea vuF9pbzmfO586Wz4vzg 3HMeOwNn6ATOn87fzj /Ov0ve0q9Lvy393qg3b 7TnfOJ0fkt/Acq/Gu </latexit> a[z] = ReLU[z] = ( 0 z < 0 z z ≥ 0 .
null	null	null	null	y393qg3b 7TnfOJ0fkt/Acq/Gu </latexit> a[z] = ReLU[z] = ( 0 z < 0 z z ≥ 0 . Rectified Linear Unit (one type of activation function) Activation function 10
null	null	null	null	Example shallow network <latexit sha1_base64=" NTIf4aNnvrpa8D wPTFP8Igh9dpg=" >AXIXiclZhb 9s2FICd7talu6Q blpe9CAtaDGsW2G l3wYCbdL0lnRJ msbpQYlUzIbil J0SZwK/jXDfszeh r0N+zM7lGQzOod 5mIHU7Pk+8XJIS rS8RIos73b/mbn2 3vsfPjR9Y9nb3 zy6Wefz938Yj+L i9Tne34s4/TQYxm XQvG9XOSHyYpZ 5En+YF3sqr
null	null	null	null	jR9Y9nb3 zy6Wefz938Yj+L i9Tne34s4/TQYxm XQvG9XOSHyYpZ 5En+YF3sqr5wRl PMxGr3fwi4cRC5 UIhM9yCPXn/ri4 fd9xIy8elcH4aL ToekEyFMeuO3v7v gulfte541SFXqO x8ZGbD3nO+mWvO 74zLfGo+OJu0z d5Uvucu1W6l2q3r 2k3tXqbH9uobvU rT4OLfSawkKn+W z1b341cAexX0Rc5 b5kWXbU6yb5cn SXPiSj
null	null	null	null	3tXqbH9uobvU rT4OLfSawkKn+W z1b341cAexX0Rc5 b5kWXbU6yb5cn SXPiSj2fdIuMJ8 09YyI+gqFjEs+Oy yufYuQWRgRPEKf yp3Kmil68oWZRl F5EHZsTyYaZDtr YUZEHPx+XQiVFz pVfNxQU0sljR0+ OMxAp93N5AQXmpw L6vhDljI/hymc dRU/9+MoYmpQui tr2+PS9XgoVMlPi 2o6x+O2s1Y5HIp XGSvPdqe1iJxH4 h
null	null	null	null	c dRU/9+MoYmpQui tr2+PS9XgoVMlPi 2o6x+O2s1Y5HIp XGSvPdqe1iJxH4 h0nlVSKruQKgYfj suRL4RIGgMQS5 yAWPEM6tT58QKn hygsXwm4rNcFLEj n5ZhUrXIeQk5a2 muiQSGRfNSyVok FUxm1lB1QHOeWow HPU5gF6Cp8cTQH OwlT48l1OR/laV RmOoZbSJkKedUED NlnUo+obahCSrj Ub1m/YeslUydN4 uKk6mqI8ja
null	null	null	null	1OR/laV RmOoZbSJkKedUED NlnUo+obahCSrj Ub1m/YeslUydN4 uKk6mqI8jaTdtO ntK8qEHbqSLIgk UYtq0qgiwJN5sB ixhkuSn3YcCRoyN 2VSisCrIwt9LYa 7ed6Ahem6ME9kv bWytJ+s8YyogOwO 7T34Ipn7f1Xhq O5PknFW+LvCRM4 TJal/C0rAe1qQRG FUTG1OzyhUyabY glMbnbVP3xqLyR LQHqAN40xWpUME lbEqw
null	null	null	null	al/C0rAe1qQRG FUTG1OzyhUyabY glMbnbVP3xqLyR LQHqAN40xWpUME lbEqwZLVYXcRhp oWkh9v/QDHx2X Xb1t9D8km1BRVi S2inT4f1Q0gMcbX l8QwZMXSzR5EKg mL5Zwf0dTx1K8s HWkmjsoCMWkyC/Q 9hehal9TRXBn4w j1FQK6XvhmQqFJ DoK2rANahm94UFs WkI8G6dj9GWcF SknNz+0niFS6fq 2mAr9sGrfUKUW2v
null	null	null	null	FJ DoK2rANahm94UFs WkI8G6dj9GWcF SknNz+0niFS6fq 2mAr9sGrfUKUW2v cNLqdXQRkeDmf8 is9lFGvzqcXF2 rAUpTMkZ7S0Rs3y 2GL2XZ/NeV10Wq F/HS9aQ/6BbNT+ D4/7a/j+QiJR2J 6oKTkbUuSxLe1 DXdLle7lm5/uY7 srRDi2s3Jam36aX dtrhX9ICfblh6u 0E8YlFHorqaHlK PWJb2oC57Hjdso7 C4dlOSeid5t
null	null	null	null	am36aX dtrhX9ICfblh6u 0E8YlFHorqaHlK PWJb2oC57Hjdso7 C4dlOSeid5tNoW d2qi5R/s6qOoPi bFcqCPfbF06xAWc yrmVjGOeIjEOoT FqGhb8H+s7Ah4e LStOoTFrUy0NR3A 0oBLPIQ6hMV6C7 fNJobVDYu6YVeZ TIbIrENYfMIiPOo 6hMWQiqFVPGFJg sQ6RPI4xHkc0jw mWEpsEp6RxDIjZE nZFlQ6jNuSDmBp hFob
null	null	null	null	hMWQiqFVPGFJg sQ6RPI4xHkc0jw mWEpsEp6RxDIjZE nZFlQ6jNuSDmBp hFobWRqDHshYoQ abIJYzuvIy68pT aBUruor3bA3vXdF wzlCFOoClTbLH HfTusk8nGI4Ztm SnAhkJTSBW9jZos 7k9OcFJTnJecGF oReUnht6TumBoQ eUpoaSXwRe8NJQ8 uvEC84MPaN039B 9SgtDC0r3DN2jN DA0oPSxoY8p9Q31 KV01dJXS3FByI
null	null	null	null	NJQ8 uvEC84MPaN039B 9SgtDC0r3DN2jN DA0oPSxoY8p9Q31 KV01dJXS3FByIo UngqG7lA4NHVJ6 aOghpa8MfUXpU0O fUvra0NeUvjP0H aUPDX1IKTOUbp m6Bql3FDy6sALVg xdodQzlPz2g71m 6BaliaEJpY8MfU TpwFDyqxieZ4aS4 w08GA2VlD4z9Bm lwlDy+80LXhj6g tLI0IjS54Y+p/St oW8pfWLoE0pDQ8 m7ATidG
null	null	null	null	A2VlD4z9Bm lwlDy+80LXhj6g tLI0IjS54Y+p/St oW8pfWLoE0pDQ8 m7ATidGLpDqXkL VGaUbhu6Tempoaf 29wJ8Oo2ebWFum go2KY0NjSldN5T 8UoCjhKEn5DwZqO auNnbRO5rgZpy C2syPrma5DxQU2 5hzd1pcjW5PwVqy oek62v70xcpkFK 40/fnFnr4LSwt7 C8v9X5curd9b+HB SvOG9nrn6843nW 87vc5PnQedp52t z

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