hiwire progress report technical university of crete speech processing and dialog systems group...
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HIWIRE Progress Report
Technical University of CreteSpeech Processing and
Dialog Systems Group
Presenter: Alex Potamianos (WP1)Vassilis Diakoloukas (WP2)
Technical University of CreteSpeech Processing and
Dialog Systems Group
Presenter: Alex Potamianos (WP1)Vassilis Diakoloukas (WP2)
Outline
Work package 1• Baseline: Aurora 2, Aurora 3, Aurora 4 (lattices)• Audio-Visual ASR: Baseline• Feature extraction and combination• Segment models for ASR• Blind Source Separation for multi-microphone ASR
Work package 2• Adaptation• Data collection
Outline
Work package 1• Baseline: Aurora 2, Aurora 3, Aurora 4 (lattices)• Audio-Visual ASR: Baseline• Feature extraction and combination• Segment models for ASR• Blind Source Separation for multi-microphone ASR
Work package 2• Adaptation• Data collection
Baseline
Baseline Performance Completed• Aurora 2 on HTK• Aurora 3 on HTK• Aurora 4 on HTK
Lattices for Aurora 4 Baseline Performance Ongoing
• WSJ1 (Decipher)• DMHMMs (Decipher)
Aurora 2 Database
Based on TIdigits downsampled to 8KHz Noise artificially added at several SNRs 3 sets of noises
• A: subway, babble, car, exhib. hall• B: restaurant, street, airport, train station• C: subway, street (with different freq.
characteristics)
Two training conditions• Training on clean data• Multi-condition Training on noisy data
Aurora 2 Database
8440 training sentences 1001 test sentences / test set Three front-end configurations
• HTK default• WI007 (Aurora 2 distribution)• WI008 (Thanks to Prof. Segura)
Aurora 2: Clean training
HTK default Front-End
Accuracy vs SNR (Clean Training)
0
10
20
30
40
50
60
70
80
90
100
Clean 20 dB 15 dB 10 dB 5 dB 0 dB -5 dB
Test Set A
Test Set B
Test Set C
Overall
Aurora 2: Multi-Condition training
HTK default Front-End
Accuracy vs SNR (Multi-Condition Training)
0
10
20
30
40
50
60
70
80
90
100
Clean 20 dB 15 dB 10 dB 5 dB 0 dB -5 dB
Test Set A
Test Set B
Test Set C
Overall
Aurora 2: Clean vs Multi-Condition Training
Overall Aurora 2 Accuracy vs SNR
0
10
20
30
40
50
60
70
80
90
100
Clean 20 dB 15 dB 10 dB 5 dB 0 dB -5 dB
Multi-Condition TrainingClean Training
Aurora 2 Front End Comparison: Clean Training
Accuracy vs SNR (Clean Training)
0102030405060708090
100
Clean 20 dB 15 dB 10 dB 5 dB 0 dB -5 dB
WI008 FE
WI007 FE
HTK FE
Front End Comparison: Multi-Condition Training
Accuracy vs SNR (Multi-Condition Training)
0102030405060708090
100
Clean 20 dB 15 dB 10 dB 5 dB 0 dB -5 dB
WI008 FE
WI007 FE
HTK FE
Aurora 3 Database
5 languages• Finnish • German• Italian• Spanish• Danish
3 noise conditions• quiet• low noisy (low)• high noisy (high)
2 recording modes• close-talking microphone (ch0)• hands-free microphone (ch1)
Aurora 3 Database
3 experimental setups• Well-Matched (WM)
• 70% of all utts in “quiet, low, high” conditions were used for training
• remaining 30% were used for testing
• Medium Mismatched (MM)• 100% hands-free recordings from “quiet” and “low”
for training• 100% hands-free recordings from “high” for testing
• High Mismatched (HM)• 70% of close-talking recordings from all noise
conditions for training• 30% of hands-free recordings from “low” and “high”
for testing
Baseline Aurora 3 performance
AURORA 3 Performance (Spanish + Italian)
0
10
20
30
40
50
60
70
80
90
100
SPAN_WM SPAN_MM SPAN_HM ITAL_WM ITAL_MM ITAL_HM
WI007
WI008
Baseline Aurora 3 performance
AURORA 3 Performance
0
10
20
30
40
50
60
70
80
90
100
WI007
WI008
Baseline Aurora 3 with WI007 FE ( TUC - UGR comparison )
FINNISH SPANISH GERMAN
FRONT-END WM MM HM WM MM HM WM MM HM
WI007-TUC 90,53 72,5 30,35 86,88 73,72 42,23 90,58 79,06 74,24
WI007-UGR 92,74 80,51 40,53 92,94 80,31 51,55 91,2 81,04 73,17
TRAIN(#sent.) 1778 561 889 3392 1607 1696 2032 997 1007
TEST(#sent.) 770 146 283 1522 850 631 867 241 394
DANISH ITALIAN
FRONT-END WM MM HM WM MM HM
WI007-TUC 79,62 49,29 33,15 93,64 82,02 39,84
WI007-UGR 87,28 67,32 39,37 93,64 82,02 39,84
TRAIN(#sent.) 3440 1254 1720 2951 1245 1720
TEST(#sent.) 1474 204 658 1309 405 626
Baseline Aurora 3 with WI007 FE ( TUC - UGR comparison )
AURORA 3 Baseline accuracyTUC-UGR comparison
0
10
20
30
40
50
60
70
80
90
100
WI007-TUC
WI007-UGR
Baseline Aurora 3 with WI008 FE ( TUC - UGR comparison )
AURORA 3 RESULTS
0
20
40
60
80
100
120WI008-TUC
WI008-UGR
Aurora 4 Database
Based on the WSJ phase 0 collection 5000 word vocabulary 7138 training data (ARPA evaluation) 2 recording microphones 6 different noises artificially added
• Car, Babble, Restaurant, Street, Airport, TrainSt
Aurora 4 Training Data Sets 3 Training Conditions
• (Clean – MultiCondition – Noisy)
7138 utterances(as in the ARPA
evaluation)
7138 utterances
3569 utterances(Sennheiser)
3569 utterances(2nd mic)
893 (no noise added)
2676 (1 out of 6 noises added at SNRs between 10 and 20 dB)
Clean training Multicondition training
2676 (1 out of 6 noises added at SNRs between 10 and 20 dB)
893 (no noise added)
Aurora 4 Test Sets
14 Test Sets 2 sizes: small (166 utts) and large (330 utts)
330 utt.(Sennheiser microphone)
SET 1
330 utt.(Sennheiser mic; Noise 1 added at SNRs between 5
and 15 dB)
SET 2
…330 utt.
(Sennheiser mic; Noise 2 added at SNRs between 5
and 15 dB)
SET 3
330 utt.(Sennheiser mic; Noise 6 added at SNRs between 5
and 15 dB)
SET 7
330 utt.(2nd
microphone)
SET 8
330 utt.(2nd mic; Noise 1
added at SNRs between 5 and
15 dB)
SET 9
…330 utt.
(2nd mic; Noise 2 added at SNRs between 5 and
15 dB)
SET 10
330 utt.(2nd mic; Noise 6
added at SNRs between 5 and
15 dB)
SET 14
Lattices
Obtained from SONIC recognizer • real time decoding for WSJ 5k task
• State-of-the-art performance (8% WERR)
Lattices obtained from clean models
Three sizes lattices: small, medium, large
Fixed branching factor for each lattice size (small=2.5, medium=4, large=5.5)
Speed-up factor compared to HTK decoding: x100, x50, x10
Baseline Aurora 4 with Lattices
AURORA 4 (Small Lattice)
0
10
20
30
40
50
60
70
80
90
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Test Sets
Accu
racy
Clean
Multi
Noisy
Baseline Aurora 4 with Lattices
AURORA 4 (Medium Lattice)
0
10
20
30
40
50
60
70
80
90
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Test Sets
Accu
racy
Clean
Multi
Noisy
Baseline Aurora 4 (Comparing Lattices)
Clean Training comparisonNo vs Small vs Medium Lattices
0
20
40
60
80
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 Avg.Test Sets
Accu
racy
No Lattices
Small Lattices
Medium Lattices
Aurora4 BaselineConclusions on Lattices
Lattices speed up recognition
• Medium Size Lattice is ~ 60 times faster
• Small Size Lattice is ~ 108 times faster
Problem: improved performance in noisy test
Careful when using lattices in mismatched
conditions (clean training-noisy data)!
Solution:
• two sets of lattices lattices: matched, mismatched
Audio-Visual ASR: Database
Subset of CUAVE database used:• 36 speakers (30 training, 6 testing)
• 5 sequences of 10 connected digits per speaker
• Training set: 1500 digits (30x5x10)
• Test set: 300 digits (6x5x10)
CUAVE database also contains more complex data sets: speaker moving around, speaker shows profile, continuous digits, two speakers (to be used in future evaluations)
CUAVE Database Speakers
Audio-Visual ASR: Feature Extraction Lip region of interest (ROI) tracking
• A fixed size ROI is detected using template matching
• ROI minimizes RGB-Euclidean distance with a given ROI template
• ROI template is selected from 1st frame of each speaker
• Continuity constraint: search within a 20x20 pixel window of previous frame ROI (does not work for rapid speaker movements)
Audio-Visual ASR: Feature Extraction Features extracted from ROI
• ROI is transformed to grayscale• ROI is decimated to a 16x16 pixel region• 2D separable DCT is applied to 16x16 pixel region• Upper-left 6x6 region is kept (excluding first coef.)• 35 feature vector is resampled in time from 29.97
fps (NTSC) to 100 fps • First and second derivatives in time are computed
using a 6 frame window (feature size 105)
Sanity check: unsupervised k-means clustering of ROI results in …
Experiments
Recognition experiment:
• Open loop digit grammar (50 digits per utterance,
no endpointing)
Classification experiment:
• Single digit grammar (endpointed digits based on
provided segmentation)
Models
Features: • Audio: 39 features (MFCC_D_A)• Visual: 105 features (ROIDCT_D_A)• Audio-Visual: 39+35 feats (MFCC_D_A+ROIDCT)
HMM models• 8 state, left-to-right HMM whole-digit models with
no state skipping• Single Gaussian mixture• Audio-Visual HMM uses separate audio and video
feature streams with equal weights (1,1)
Results (Word Accuracy]
Data• Training: 1500 digits (30 speakers)• Testing: 300 digits (6 speakers)
Audio Visual AudioVisual
Recognition 98% 26% 78%
Classification 99% 46% 85%
Future Work
Multi-mixture models Front-end (NTUA)
• Tracking algorithms • Feature extraction
Feature Combination• Feature integration• Feature weighting
Outline
Work package 1• Baseline: Aurora 2, Aurora 3, Aurora 4 (lattices)• Audio-Visual ASR: Baseline• Feature extraction and combination• Segment models for ASR• Blind Source Separation for multi-microphone ASR
Work package 2• Adaptation• Data collection
Feature extraction and combination
Noise Robust Features (NTUA) – m12
AM-FM Features (NTUA) – m12
Feature combination – m12
Supra-segmental features (see also segment
models) – m18
Outline
Work package 1• Baseline: Aurora 2, Aurora 3, Aurora 4 (lattices)• Audio-Visual ASR: Baseline• Feature extraction and combination• Segment models for ASR• Blind Source Separation for multi-microphone ASR
Work package 2• Adaptation• Data collection
Segment Models
Baseline system
Supra-segmental features
• Phone Transition modeling – m12
• Prosody modeling – m18
• Stress modeling – m18
Parametric modeling of feature trajectories
Dynamical system modeling
Combine with HMMs
Outline
Work package 1• Baseline: Aurora 2, Aurora 3, Aurora 4 (lattices)• Audio-Visual ASR: Baseline• Feature extraction and combination• Segment models for ASR• Blind Source Separation for multi-microphone ASR
Work package 2• Adaptation• Data collection
Blind Source Separation (Mokios, Sidiropoulos] Based on PARallel FACtor (PARAFAC) analysis, i.e., low-
rank decomposition of multi-dimensional tensorial data Collecting spatial covariance matrix estimates which are
sufficiently separated in time:
Assumptions• uncorrelated speaker signals and noise• D(t) is a diagonal matrix of speaker powers for
measurement period t• denotes noise power (estimated from silence
intervals)
2( ) ( ) , k 1,..., (2) Hk kR t AD t A K
2
Outline
Work package 1• Baseline: Aurora 2, Aurora 3, Aurora 4 (lattices)• Audio-Visual ASR: Baseline• Feature extraction and combination• Segment models for ASR• Blind Source Separation for multi-microphone ASR
Work package 2• Adaptation• Data collection
Acoustic Model Adaptation
Adaptation Method: • Bayes’ Optimal Classification
Acoustic Models:• Discrete Mixture HMMs
Bayes optimal classification
Classifier decision for a test data vector xtest:
Choose the class that results in the highest value:
),...,,|(maxarg)( 21jN
jjtest
jtest xxxxpcxc
dxxxpxpxxxxp jN
jjtest
jN
jjtest ),...,,|()|(),...,,|( 2121
Bayes optimal versus MAP
Assumption: the posterior is sufficiently peaked around the most probable point
MAP approximation:
θMAP is the set of parameters that maximize:
)|(),...,,|( 21 MAPtestjN
jjtest xpxxxxp
)}()|,...,,({maxarg),...,,|(maxarg 2121
pxxxpxxxp NNMAP
Why Bayes optimal classification
Optimal classification criterion The prediction of all the parameter hypotheses
is combined Better discrimination Less training data Faster asymptotic convergence to the ML
estimate
Why Bayes optimal classification
However:
• Computationally more expensive
• Difficult to find analytical solutions
• ....hence some approximations should still be considered
Discrete-Mixture HMMs (Digalakis et. al. 2000)
It is based on sub-vector quantization
Introduces a new form of observation distributions
DMHMMs benefits (Digalakis et. al. 2000)
Speech Recognition performance driven quantization scheme
Quantization of the acoustic space in sufficient detail
Mixtures capture the correlation between sub-vectors
Well-matched in client-server applications
Comparable performance to continuous HMMs
Faster decoding speeds
DMHMM parameters that could be adapted
Partitioning into sub-vectors• How many sub-vectors
• Which MFCCs to form each sub-vector
Bit-allocation• Optimize bit-allocation based on adaptation data
Discrete Mixture Weights
Centroids of codebooks
Centroid observation probabilities
Outline
Work package 1• Baseline: Aurora 2, Aurora 3, Aurora 4 (lattices)• Audio-Visual ASR: Baseline• Feature extraction and combination• Segment models for ASR• Blind Source Separation for multi-microphone ASR
Work package 2• Adaptation• Data collection
TUC Non-Native Recordings
10 Speakers (6 male – 4 female)
Fluency in English:• 4 excellent
• 5 good – very good
• 1 satisfactory
Speaker pronunciation:• 1 from Cyprus
• 3 from Northern Greece
• 1 from Ionian Islands
• 2 Athens area
• 1 from Crete
• 1 from Central Greece
EXTRA SLIDES
Prior Work Overview
MLST.Constr. Est. Adapt.
MAP (Bayes) Adapt.
GenonesSegment Models
VTLN
Combinations
Robust Features
HIWIRE Work Proposal
AdaptationBayes optimal class.
Audio Visual ASRBaseline experiments
Microphone ArraysSpeech/Noise Separation
Feature SelectionAM-FM Features
Acoustic ModelingSegment Models
Aurora 2 Performance with HTK FE (Clean Training)
A B C
Subway Babble Car Exhibit Avg. Restr Street Airport Station Avg. Sub.M. Str.M. Avg. Overall
Clean 98,83 98,97 98,81 99,14 98,94 98,83 98,97 98,81 99,14 98,94 99,02 98,97 99 98,95
20 dB 96,96 89,96 96,84 96,2 94,99 89,19 95,77 90,07 94,38 92,35 94,47 95,19 94,83 93,9
15 dB 92,91 73,43 89,53 91,85 86,93 74,39 88,27 76,89 83,62 80,79 87,63 89,69 88,66 84,82
10 dB 78,72 49,06 66,24 75,1 67,28 52,72 66,75 53,15 59,61 58,06 75,19 75,27 75,23 65,18
5 dB 53,39 27,03 32,8 43,51 39,18 29,57 38,15 30,69 29,71 32,03 52,84 48,85 50,85 38,65
0 dB 27,3 11,73 13,27 15,98 17,07 11,7 18,68 15,84 12,25 14,62 26,01 21,64 23,83 17,44
-5 dB 12,62 4,96 8,35 7,65 8,4 5,04 10,07 8,08 8,49 7,92 12,1 10,7 11,4 8,81
Avg. 65,82 50,73 57,98 61,35 58,97 51,63 59,52 53,36 55,31 54,96 63,89 62,9 63,4 58,25
Aurora 2 Performance with HTK FE (Multi-Condition Training)
A B C
Subway Babble Car Exhibit Avg. Restr Street Airport Station Avg. Sub.M. Str.M. Avg. Overall
Clean 98,59 98,52 98,48 98,55 98,54 98,59 98,52 98,48 98,55 98,54 98,65 98,52 98,59 98,55
20 dB 97,64 97,61 97,85 96,98 97,52 96,56 97,46 97,17 96,64 96,96 97,05 96,43 96,74 97,14
15 dB 96,75 96,8 97,64 96,58 96,94 94,72 95,92 95,62 95,25 95,38 95,46 95,5 95,48 96,02
10 dB 94,38 95,22 95,65 93,12 94,59 90,97 94,2 92,78 92,35 92,58 92,35 91,9 92,13 93,29
5 dB 88,42 87,67 86,17 86,95 87,3 81,85 85,34 84,91 82,91 83,75 81,46 81,86 81,66 84,75
0 dB 65,67 61,03 50,82 61,8 59,83 56,83 60,22 64,36 54,21 58,91 45,16 54,05 49,61 57,42
-5 dB 26,01 26,18 19,15 22,49 23,46 22,6 26,3 27,65 18,88 23,86 18,61 25,54 22,08 23,34
Avg. 88,57 87,67 85,63 87,09 87,24 84,19 86,63 86,97 84,27 85,52 82,3 83,95 83,12 85,72
Aurora 2 Performance with WI008 FE (Clean Training)
A B C
Subway Babble Car Exhibit Avg. Restr Street Airport Station Avg. Sub.M. Str.M. Avg. Overall
Clean 99,08 99,03 99,05 99,23 99,1 99,08 99,03 99,05 99,23 99,1 99,02 99,03 99,03 99,08
20 dB 97,88 98,25 98,36 97,81 98,08 98,07 97,64 98,42 98,43 98,14 97,36 97,67 97,52 97,99
15 dB 96,38 96,74 97,52 96,7 96,84 95,33 96,58 97,05 96,76 96,43 95,3 95,74 95,52 96,41
10 dB 92,26 91,99 95,29 92,59 93,03 89,87 92,74 93,26 93,86 92,43 90,33 90,75 90,54 92,29
5 dB 83,88 80,68 86,01 84,05 83,66 76,05 83,25 83,54 84,2 81,76 78,88 78,48 78,68 81,9
0 dB 61,93 51,12 66,06 63,5 60,65 50,26 59,7 60,24 62,23 58,11 52,59 52,12 52,36 57,98
-5 dB 31,07 18,95 29,82 33,2 28,26 18,39 29,23 27,32 29,56 26,13 25,15 26,12 25,64 26,88
Avg. 86,47 83,76 88,65 86,93 86,45 81,92 85,98 86,5 87,1 85,37 82,89 82,95 82,92 85,31
Aurora 2 Performance with WI008 FE(Multi-Condition Training)
A B C
Subway Babble Car Exhibit Avg. Restr Street Airport Station Avg. Sub.M. Str.M. Avg. Overall
Clean 99,02 98,82 98,99 99,14 98,99 99,02 98,82 98,99 99,14 98,99 98,99 98,85 98,92 98,98
20 dB 98,62 98,58 98,54 98,24 98,5 98,1 98,13 98,63 98,8 98,42 98,07 97,94 98,01 98,37
15 dB 97,54 97,91 98,42 97,56 97,86 96,93 97,85 98,03 97,69 97,63 97,54 97,73 97,64 97,72
10 dB 95,33 96,07 97,38 95,34 96,03 94,84 95,59 95,91 96,05 95,6 95,58 95,31 95,45 95,74
5 dB 91,43 90,21 90,93 90,1 90,67 87,14 90,39 91,44 90,16 89,78 88,92 87,52 88,22 89,82
0 dB 75,28 68,71 80,7 76 75,17 65,55 73,85 75,78 74,08 72,32 66,99 65,63 66,31 72,26
-5 dB 39,85 30,05 40,41 44,99 38,83 28,52 38,88 40,95 41,75 37,53 30,43 30,59 30,51 36,64
Avg. 91,64 90,3 93,19 91,45 91,65 88,51 91,16 91,96 91,36 90,75 89,42 88,83 89,13 90,78
Aurora 3 HTK Settings
Spanish• Parametrize.csh
• Set Options = “-F RAW –fs 8 –q –noc0 –swap”
• Config_tr• TARGETKIND = MFCC_E_D_A• DELTAWINDOW = 3• ACCWINDOW = 2• ENORMALISE = F• HNET:TRACE = 2• NATURALREADORDER = T• NATURALWRITEORDER = T
Aurora 3 HTK Settings
Italian• Sdc_it.conf
• $FE_OPTIONS = “-q -F RAW –fs 8 ”
• Config• TARGETKIND = MFCC_D_A_E• HNET:TRACE = 2• ACCWINDOW = 2• DELTAWINDOW = 3• ENORMALISE = F• NATURALREADORDER = T• NATURALWRITEORDER = T
Baseline Aurora 3 Performance
FINNISH SPANISH GERMAN
FRONT-END WM MM HM WM MM HM WM MM HM
WI007 90,53 72,5 30,35 86,88 73,72 42,23 90,58 79,06 74,24
WI008 95,62 76,68 86,11 93,47 85,41 81,02 94,49 88,73 89,55
TRAIN(#sent.) 1778 561 889 3392 1607 1696 2032 997 1007
TEST(#sent.) 770 146 283 1522 850 631 867 241 394
DANISH ITALIAN
FRONT-END WM MM HM WM MM HM
WI007 79,62 49,29 33,15 93,64 82,02 39,84
WI008 84,99 65,68 63,91 96,58 88,53 88,22
TRAIN(#sent.) 3440 1254 1720 2951 1245 1720
TEST(#sent.) 1474 204 658 1309 405 626
Baseline Aurora 3 with WI007 FE ( TUC - UGR comparison )
FINNISH SPANISH GERMAN
FRONT-END WM MM HM WM MM HM WM MM HM
WI007-TUC 90,53 72,5 30,35 86,88 73,72 42,23 90,58 79,06 74,24
WI007-UGR 92,74 80,51 40,53 92,94 80,31 51,55 91,2 81,04 73,17
TRAIN(#sent.) 1778 561 889 3392 1607 1696 2032 997 1007
TEST(#sent.) 770 146 283 1522 850 631 867 241 394
DANISH ITALIAN
FRONT-END WM MM HM WM MM HM
WI007-TUC 79,62 49,29 33,15 93,64 82,02 39,84
WI007-UGR 87,28 67,32 39,37 93,64 82,02 39,84
TRAIN(#sent.) 3440 1254 1720 2951 1245 1720
TEST(#sent.) 1474 204 658 1309 405 626
Baseline Aurora 3 with WI008 FE ( TUC - UGR comparison )
FINNISH SPANISH GERMAN
FRONT-END WM MM HM WM MM HM WM MM HM
WI008-TUC 95,62 76,68 86,11 93,47 85,41 81,02 94,49 88,73 89,55
WI008-UGR 96,09 80,92 86,61 96,64 93,92 91,55 95,11 90,84 91,25
TRAIN(#sent.) 1778 561 889 3392 1607 1696 2032 997 1007
TEST(#sent.) 770 146 283 1522 850 631 867 241 394
DANISH ITALIAN
FRONT-END WM MM HM WM MM HM
WI008-TUC 84,99 65,68 63,91 96,58 88,53 88,22
WI008-UGR 93,37 81,49 79,59 96,71 92,53 89
TRAIN(#sent.) 3440 1254 1720 2951 1245 1720
TEST(#sent.) 1474 204 658 1309 405 626
Baseline Aurora 4 with Lattices
Small Lattice Size
8 9 10 11 12 13 14 Avg.
Clean 86,56 80,77 68,43 64,75 55,31 70,98 59,7 72,37
Multi 86,85 86,52 83,98 82,5 81,33 84,64 81,84 84,88
Noisy 87 85,97 81,58 80,48 76,51 82,65 77,48 83,3
Average 86,8 84,42 78 75,91 71,05 79,42 73,01 80,19
1 2 3 4 5 6 7
Clean 88,36 85,67 74,36 73,44 66,41 74,59 63,87
Multi 86,81 86,85 85,78 85,34 85,56 85,89 84,42
Noisy 87,81 86,96 85,71 83,61 83,09 85,6 81,8
Average 87,66 86,49 81,95 80,8 78,35 82,03 76,7
Baseline Aurora 4 with Lattices
Medium Lattice Size 1 2 3 4 5 6 7
Clean 87,92 84,71 72,89 72,78 65,12 73,78 62,91
Multi 85,97 85,52 84,79 83,83 83,9 84,24 83,24
Noisy 87,33 85,78 84,42 82,28 81,58 84,16 80,88
Average 87,07 85,34 80,7 79,63 78,87 80,73 75,68
8 9 10 11 12 13 14 Avg.
Clean 85,67 79,45 66,08 63,68 53,86 69,07 58,31 71,16
Multi 86,19 84,97 82,65 81,18 80,63 82,84 80,29 83,59
Noisy 86,7 85,45 81,14 78,67 74,22 82,21 76,65 82,25
Average 86,19 83,29 76,62 74,51 69,57 78,04 71,75 79,14
Baseline Aurora 4 with Lattices
Small Lattice Size
8 9 10 11 12 13 14 Avg.
Clean 86,56 80,77 68,43 64,75 55,31 70,98 59,7 72,37
Multi 86,85 86,52 83,98 82,5 81,33 84,64 81,84 84,88
Noisy 87 85,97 81,58 80,48 76,51 82,65 77,48 83,3
Average 86,8 84,42 78 75,91 71,05 79,42 73,01 80,19
1 2 3 4 5 6 7
Clean 88,36 85,67 74,36 73,44 66,41 74,59 63,87
Multi 86,81 86,85 85,78 85,34 85,56 85,89 84,42
Noisy 87,81 86,96 85,71 83,61 83,09 85,6 81,8
Average 87,66 86,49 81,95 80,8 78,35 82,03 76,7