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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)

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passage_offset
int64
num_passages
int64
num_embeddings
int64
embedding_offset
int64
text
string
0
6,133
892,641
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Lecture 03 Shallow Networks DL4DS – Spring 2024 DS598 B1 Gardos – Understanding Deep Learning, Other Content Cited
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• Univariate regression problem (one output, real value) • Fully connected network Recap: Regression 2
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Recap: 1D Linear regression loss function <latexit sha1_base64="/hMh896NPSehdG/Bg07J5FjBuSo=">AW9HiclZhbc9Q2FI A3lLY0LTS07z0xdMHdpCJsvQywszkBAgJDQJuUKc7Mhe2Ssiy4vyQaP/0nfOn3t/+lLf0uPbO8Kn6M8dGfCivN9uh1JtdeIkWLy39M3Pto+sf/Lpjc9mP/i5q0v525/tZ/FR erzPT+WcXrosYxLofheLnLJD5OUs8iT/MA7XdH84JynmYjVb
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/i5q0v525/tZ/FR erzPT+WcXrosYxLofheLnLJD5OUs8iT/MA7XdH84JynmYjVbn6Z8OIhUoEwmc5hAZz40j1wuSkTh2vn/kuFkRDUrxqF+dlGvVXTfy4nEZVEdjCFb3XC+Ww+wSgtLVNe5f6vAPJw9cd 9ZSGZRBuVT91BT6Vd3ItM5gbmFpcan+OLTQbwsLvfazNbj9zdAdxn4RcZX7kmXZUX8pyY9LlubCl7yadYuMJ8w/ZSE/gqJiEc+Oyz
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WbqtE1cnNRDTXUEWbtp18lTmhc17Dp1BFmwCcOuVUeQJeH6MWQRgy35QFMOHJ0xK4KhVBNuZWGnvdvhMdwXtznMB56XqrJUn/OUMZ0QE4fpbMOXzr4ST21nkpz2tcFPnZGsF jdKiwNm2lNOoFZtbGKmnWukEmzBaE0vuiaejQWlSeiO0EdwIeuSIUKPtDu1SXYsjrs3oOpoXkR/cXf+bj43JHxv9D8kmNJQVia0hHf4fDQ3hjoX3F0Tw4sUSLR4
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Recap: 1D Linear regression training This technique is known as gradient descent 4
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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
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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
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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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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,
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vOn85fzt /P2t21/bWTtWG tvnOjueZLp/VZ4 /8B0OTgog=</l atexit>y = f[x, φ] = φ0 + φ1x Example shallow network 7
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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
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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
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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
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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
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1OR/laV RmOoZbSJkKedUED NlnUo+obahCSrj Ub1m/YeslUydN4 uKk6mqI8jaTdtO ntK8qEHbqSLIgk UYtq0qgiwJN5sB ixhkuSn3YcCRoyN 2VSisCrIwt9LYa 7ed6Ahem6ME9kv bWytJ+s8YyogOwO 7T34Ipn7f1Xhq O5PknFW+LvCRM4 TJal/C0rAe1qQRG FUTG1OzyhUyabY glMbnbVP3xqLyR LQHqAN40xWpUME lbEqw
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al/C0rAe1qQRG FUTG1OzyhUyabY glMbnbVP3xqLyR LQHqAN40xWpUME lbEqwZLVYXcRhp oWkh9v/QDHx2X Xb1t9D8km1BRVi S2inT4f1Q0gMcbX l8QwZMXSzR5EKg mL5Zwf0dTx1K8s HWkmjsoCMWkyC/Q 9hehal9TRXBn4w j1FQK6XvhmQqFJ DoK2rANahm94UFs WkI8G6dj9GWcF SknNz+0niFS6fq 2mAr9sGrfUKUW2v
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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
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am36aX dtrhX9ICfblh6u 0E8YlFHorqaHlK PWJb2oC57Hjdso7 C4dlOSeid5tNoW d2qi5R/s6qOoPi bFcqCPfbF06xAWc yrmVjGOeIjEOoT FqGhb8H+s7Ah4e LStOoTFrUy0NR3A 0oBLPIQ6hMV6C7 fNJobVDYu6YVeZ TIbIrENYfMIiPOo 6hMWQiqFVPGFJg sQ6RPI4xHkc0jw mWEpsEp6RxDIjZE nZFlQ6jNuSDmBp hFob
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hMWQiqFVPGFJg sQ6RPI4xHkc0jw mWEpsEp6RxDIjZE nZFlQ6jNuSDmBp hFobWRqDHshYoQ abIJYzuvIy68pT aBUruor3bA3vXdF wzlCFOoClTbLH HfTusk8nGI4Ztm SnAhkJTSBW9jZos 7k9OcFJTnJecGF oReUnht6TumBoQ eUpoaSXwRe8NJQ8 uvEC84MPaN039B 9SgtDC0r3DN2jN DA0oPSxoY8p9Q31 KV01dJXS3FByI
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NJQ8 uvEC84MPaN039B 9SgtDC0r3DN2jN DA0oPSxoY8p9Q31 KV01dJXS3FByIo UngqG7lA4NHVJ6 aOghpa8MfUXpU0O fUvra0NeUvjP0H aUPDX1IKTOUbp m6Bql3FDy6sALVg xdodQzlPz2g71m 6BaliaEJpY8MfU TpwFDyqxieZ4aS4 w08GA2VlD4z9Bm lwlDy+80LXhj6g tLI0IjS54Y+p/St oW8pfWLoE0pDQ8 m7ATidG
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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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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
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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
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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
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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
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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
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1OR/laV RmOoZbSJkKedUED NlnUo+obahCSrj Ub1m/YeslUydN4 uKk6mqI8jaTdtO ntK8qEHbqSLIgk UYtq0qgiwJN5sB ixhkuSn3YcCRoyN 2VSisCrIwt9LYa 7ed6Ahem6ME9kv bWytJ+s8YyogOwO 7T34Ipn7f1Xhq O5PknFW+LvCRM4 TJal/C0rAe1qQRG FUTG1OzyhUyabY glMbnbVP3xqLyR LQHqAN40xWpUME lbEqw
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al/C0rAe1qQRG FUTG1OzyhUyabY glMbnbVP3xqLyR LQHqAN40xWpUME lbEqwZLVYXcRhp oWkh9v/QDHx2X Xb1t9D8km1BRVi S2inT4f1Q0gMcbX l8QwZMXSzR5EKg mL5Zwf0dTx1K8s HWkmjsoCMWkyC/Q 9hehal9TRXBn4w j1FQK6XvhmQqFJ DoK2rANahm94UFs WkI8G6dj9GWcF SknNz+0niFS6fq 2mAr9sGrfUKUW2v
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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
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am36aX dtrhX9ICfblh6u 0E8YlFHorqaHlK PWJb2oC57Hjdso7 C4dlOSeid5tNoW d2qi5R/s6qOoPi bFcqCPfbF06xAWc yrmVjGOeIjEOoT FqGhb8H+s7Ah4e LStOoTFrUy0NR3A 0oBLPIQ6hMV6C7 fNJobVDYu6YVeZ TIbIrENYfMIiPOo 6hMWQiqFVPGFJg sQ6RPI4xHkc0jw mWEpsEp6RxDIjZE nZFlQ6jNuSDmBp hFob
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hMWQiqFVPGFJg sQ6RPI4xHkc0jw mWEpsEp6RxDIjZE nZFlQ6jNuSDmBp hFobWRqDHshYoQ abIJYzuvIy68pT aBUruor3bA3vXdF wzlCFOoClTbLH HfTusk8nGI4Ztm SnAhkJTSBW9jZos 7k9OcFJTnJecGF oReUnht6TumBoQ eUpoaSXwRe8NJQ8 uvEC84MPaN039B 9SgtDC0r3DN2jN DA0oPSxoY8p9Q31 KV01dJXS3FByI
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NJQ8 uvEC84MPaN039B 9SgtDC0r3DN2jN DA0oPSxoY8p9Q31 KV01dJXS3FByIo UngqG7lA4NHVJ6 aOghpa8MfUXpU0O fUvra0NeUvjP0H aUPDX1IKTOUbp m6Bql3FDy6sALVg xdodQzlPz2g71m 6BaliaEJpY8MfU TpwFDyqxieZ4aS4 w08GA2VlD4z9Bm lwlDy+80LXhj6g tLI0IjS54Y+p/St oW8pfWLoE0pDQ8 m7ATidG
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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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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
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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
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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
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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
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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
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1OR/laV RmOoZbSJkKedUED NlnUo+obahCSrj Ub1m/YeslUydN4 uKk6mqI8jaTdtO ntK8qEHbqSLIgk UYtq0qgiwJN5sB ixhkuSn3YcCRoyN 2VSisCrIwt9LYa 7ed6Ahem6ME9kv bWytJ+s8YyogOwO 7T34Ipn7f1Xhq O5PknFW+LvCRM4 TJal/C0rAe1qQRG FUTG1OzyhUyabY glMbnbVP3xqLyR LQHqAN40xWpUME lbEqw
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al/C0rAe1qQRG FUTG1OzyhUyabY glMbnbVP3xqLyR LQHqAN40xWpUME lbEqwZLVYXcRhp oWkh9v/QDHx2X Xb1t9D8km1BRVi S2inT4f1Q0gMcbX l8QwZMXSzR5EKg mL5Zwf0dTx1K8s HWkmjsoCMWkyC/Q 9hehal9TRXBn4w j1FQK6XvhmQqFJ DoK2rANahm94UFs WkI8G6dj9GWcF SknNz+0niFS6fq 2mAr9sGrfUKUW2v
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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
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am36aX dtrhX9ICfblh6u 0E8YlFHorqaHlK PWJb2oC57Hjdso7 C4dlOSeid5tNoW d2qi5R/s6qOoPi bFcqCPfbF06xAWc yrmVjGOeIjEOoT FqGhb8H+s7Ah4e LStOoTFrUy0NR3A 0oBLPIQ6hMV6C7 fNJobVDYu6YVeZ TIbIrENYfMIiPOo 6hMWQiqFVPGFJg sQ6RPI4xHkc0jw mWEpsEp6RxDIjZE nZFlQ6jNuSDmBp hFob
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hMWQiqFVPGFJg sQ6RPI4xHkc0jw mWEpsEp6RxDIjZE nZFlQ6jNuSDmBp hFobWRqDHshYoQ abIJYzuvIy68pT aBUruor3bA3vXdF wzlCFOoClTbLH HfTusk8nGI4Ztm SnAhkJTSBW9jZos 7k9OcFJTnJecGF oReUnht6TumBoQ eUpoaSXwRe8NJQ8 uvEC84MPaN039B 9SgtDC0r3DN2jN DA0oPSxoY8p9Q31 KV01dJXS3FByI
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NJQ8 uvEC84MPaN039B 9SgtDC0r3DN2jN DA0oPSxoY8p9Q31 KV01dJXS3FByIo UngqG7lA4NHVJ6 aOghpa8MfUXpU0O fUvra0NeUvjP0H aUPDX1IKTOUbp m6Bql3FDy6sALVg xdodQzlPz2g71m 6BaliaEJpY8MfU TpwFDyqxieZ4aS4 w08GA2VlD4z9Bm lwlDy+80LXhj6g tLI0IjS54Y+p/St oW8pfWLoE0pDQ8 m7ATidG
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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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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
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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
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TM gv4MEhkh36LOdSKD4s RCH5YZpxFvuSH/ina5 ofnPMsF4naKy5TfhyzS IlQBKyA0MniSy/2k0n FpkdXx+7PbvPXDt8czg I+j4SqAmgin7p9wvXO yvZyL1yf+q7ngfHecS L+Jnb97gatXpvYeFkcb nf69c/lxZW2sKy0/4G J7c/HXmjJChjropAsjw /WumnxXHFskIEk8Xv DLnKQtOWcSPoKhYzPj qk7E1L0DkZEbJhn8U4 VbR
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Asjw /WumnxXHFskIEk8Xv DLnKQtOWcSPoKhYzPj qk7E1L0DkZEbJhn8U4 VbR18/o2Jxnl/GPpgxK 8Y5ZjpoY0dlEf54XAm VlgVXQdNQWEq3SFydVX ckMh4U8hIKLMgE9NUN xixjQG5X/AUvwiSOGa QGm91fXtatWnlkDk9D 9Np1mvHZ3J64zVJ3vz WkTBY3HFSW1oiu5Ru DRtKp4L+phIDgA0eMEJ AqmtfJ0fvzQXUEU1p0 EXD
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3vz WkTBY3HFSW1oiu5Ru DRtKp4L+phIDgA0eMEJ AqmtfJ0fvzQXUEU1p0 EXDWLyANjZ0qVgWPIC cd7QXRoJBKPulYa8SC qYw7yi4ornvH1YAXGcw CdBUOHM3BbsrUdHZew SdFle5juEWMqYiXjcB Qw6Y1CPqGqUEk4NOt Yv2Nph6rRNXJLWXc10B Fl7WdcpMpoXNeo6dQR ZsAijrlVHkCXhKjFiMY Mst+UTGHDs6ohdFQqr giz
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pc8NfU7pY0MfU/rC0 BeUXhl6Rel9Q+9Tygxl lK4buk4pN5R8OvDVU NXKfUNJe9+sNcMHVCaG pS+sDQB5SODCVvxXA /M5Q83sCN0VBJ6RNDn1 AqDCXvb374zNBnlMaG xpQ+NfQpa8MfUXpI0M fURoZSr4NwNOJobuUm q9AVU7ptqHblJ4Zemb/ LsDn0+jbFuaWqWCL0s TQhNINQ8mbAjxKGHpKn idD1V7VZl+byHUtVHN uYW3GZ2
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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 .
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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
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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
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