Separating Style and Content with Bilinear Models
Abstract
Perceptual systems routinely separate “content” from “style,” classifying familiar words spoken in an unfamiliar accent, identifying a font or handwriting style across letters, or recognizing a familiar face or object seen under unfamiliar viewing conditions. Yet a general and tractable computational model of this ability to untangle the underlying factors of perceptual observations remains elusive (Hofstadter, 1985). Existing factor models (Mardia, Kent, & Bibby, 1979; Hinton & Zemel, 1994; Ghahramani, 1995; Bell & Sejnowski, 1995; Hinton, Dayan, Frey, & Neal, 1995; Dayan, Hinton, Neal, & Zemel, 1995; Hinton & Ghahramani, 1997) are either insufficiently rich to capture the complex interactions of perceptually meaningful factors such as phoneme and speaker accent or letter and font, or do not allow efficient learning algorithms. We present a general framework for learning to solve two-factor tasks using bilinear models, which provide sufficiently expressive representations of factor interactions but can nonetheless be fit to data using efficient algorithms based on the singular value decomposition and expectation-maximization. We report promising results on three different tasks in three different perceptual domains: spoken vowel classification with a benchmark multi-speaker database, extrapolation of fonts to unseen letters, and translation of faces to novel illuminants.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
GeAN uses a bilinear model to distil knowledge interwoven in node and edge representations.
“GeAN also uses the bilinear model [29,30] to distil the knowledge interwoven in these representations by allowing each node and edge to collaboratively modulate each other's contributions through a shared learning space.”
From TVGeAN: Tensor Visibility Graph-Enhanced Attention Network for Versatile Multivariant Time Series Learning Tasks (2024) · cites this paper as [29]
Cites
Maximum Likelihood from Incomplete Data Via the <i>EM</i> Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444 · see citing works
Neural networks for pattern recognition
Bishop, C. (1994) · Choice Reviews Online · doi:10.5860/choice.31-5500 · Cited by 18,537 · see citing works
Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (1994) · Cited by 15,411 · see citing works
Turk, M., & Pentland, A. (1991) · Journal of Cognitive Neuroscience · doi:10.1162/jocn.1991.3.1.71 · Cited by 13,733 · see citing works
Pattern classification and scene analysis
Duda, R. O., & Hart, P. E. (1973) · CERN Document Server (European Organization for Nuclear Research) · Cited by 12,895 · see citing works
Numerical recipes in Pascal: the art of scientific computing
(1990) · Choice Reviews Online · doi:10.5860/choice.27-5158 · Cited by 12,040 · see citing works
An Information-Maximization Approach to Blind Separation and Blind Deconvolution
Bell, A. J., & Sejnowski, T. J. (1995) · Neural Computation · doi:10.1162/neco.1995.7.6.1129 · Cited by 8,986 · see citing works
Shape and motion from image streams under orthography: a factorization method
Tomasi, C., & Takeo Kanade, A. (1992) · International Journal of Computer Vision · doi:10.1007/bf00129684 · Cited by 2,879 · see citing works
Matrix Differential Calculus with Applications in Statistics and Econometrics.
Magnus, J. R., & Neudecker, H. (1988) · Biometrics · doi:10.2307/2531754 · Cited by 2,734 · see citing works
Classical Electrodynamics (2nd edn)
Brereton, M. (1976) · Physics Bulletin · doi:10.1088/0031-9112/27/8/041 · Cited by 2,612 · see citing works
Application of the Karhunen-Loeve procedure for the characterization of human faces
Kirby, M. J. L., & Sirovich, L. (1990) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.41390 · Cited by 2,459 · see citing works
Optimal unsupervised learning in a single-layer linear feedforward neural network
Sanger, T. D. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90044-0 · Cited by 1,506 · see citing works
Probabilistic visual learning for object representation
Moghaddam, B., & Pentland, A. (1997) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.598227 · Cited by 1,444 · see citing works
Encoding of Spatial Location by Posterior Parietal Neurons
Andersen, R., Essick, G. K., & Siegel, R. M. (1985) · Science · doi:10.1126/science.4048942 · Cited by 1,413 · see citing works
Thrun, S., & Pratt, L. (1998) · Springer eBooks · doi:10.1007/978-1-4615-5529-2 · Cited by 1,291 · see citing works
Dayan, P., Hinton, G. E., Neal, R. M., & Zemel, R. S. (1995) · Neural Computation · doi:10.1162/neco.1995.7.5.889 · Cited by 1,207 · see citing works
(1993) · Cited by 1,173 · see citing works
Caruana, R. (1998) · Cited by 1,110 · see citing works
The "Wake-Sleep" Algorithm for Unsupervised Neural Networks
Hinton, G. E., Dayan, P., Frey, B. J., & Neal, R. M. (1995) · Science · doi:10.1126/science.7761831 · Cited by 1,070 · see citing works
Olshausen, B., Anderson, C., & Van Essen, D. (1993) · The Journal of Neuroscience · doi:10.1523/jneurosci.13-11-04700.1993 · Cited by 908 · see citing works
Gasteratos, A., Vincze, M., & Tsotsos, J. K. (2008) · Lecture notes in computer science · doi:10.1007/978-3-540-79547-6 · Cited by 848 · see citing works
NEURAL NETWORKS, PRINCIPAL COMPONENTS, AND SUBSPACES
Oja, E. (1989) · International Journal of Neural Systems · doi:10.1142/s0129065789000475 · Cited by 837 · see citing works
Discriminant adaptive nearest neighbor classification
Hastie, T., & Tibshirani, R. J. (1996) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.506411 · Cited by 833 · see citing works
RECOVERING INTRINSIC SCENE CHARACTERISTICS FROM IMAGES
Barrow, H. G., & Tenenbaum, J. M. (1978) · Cited by 725 · see citing works
Self-citationLarge-scale neuronal theories of the brain
(1995) · Choice Reviews Online · doi:10.5860/choice.32-4182 · Cited by 624 · see citing works
Talker-specific learning in speech perception
Nygaard, L. C., & Pisoni, D. B. (1998) · Perception & Psychophysics · doi:10.3758/bf03206860 · Cited by 590 · see citing works
Parametric hidden Markov models for gesture recognition
Wilson, A. D., & Bobick, A. (1999) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.790429 · Cited by 574 · see citing works
Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought
Hofstadter, D. R. (1995) · Cited by 527 · see citing works
Teo, P. C., & Heeger, D. J. (2002) · Proceedings of 1st International Conference on Image Processing · doi:10.1109/icip.1994.413502 · Cited by 471 · see citing works
Efficient Pattern Recognition Using a New Transformation Distance
Simard, P., LeCun, Y., & Denker, J. S. (1992) · neural information processing systems · Cited by 464 · see citing works
Fluid Concepts and Creative Analogies
Hofstadter, D. R. (1995) · Cited by 408 · see citing works
A model of multiplicative neural responses in parietal cortex.
Salinas, E., & Abbott, L. F. (1996) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.93.21.11956 · Cited by 319 · see citing works
Surface modeling with oriented particle systems
Szeliski, R., & Tonnesen, D. (1992) · ACM SIGGRAPH Conference (SIGGRAPH) · doi:10.1145/133994.134037 · Cited by 298 · see citing works
A low-dimensional representation of human faces for arbitrary lighting conditions
Hallinan (1994) · doi:10.1109/cvpr.1994.323941 · Cited by 293 · see citing works
Atick, J. J., Griffin, P. A., & Redlich, A. (1996) · Neural Computation · doi:10.1162/neco.1996.8.6.1321 · Cited by 272 · see citing works
Image Representations for Visual Learning
Beymer, D., & Poggio, T. (1996) · Science · doi:10.1126/science.272.5270.1905 · Cited by 272 · see citing works
Linear models of surface and illuminant spectra
Marimont, D. H., & Wandell, B. A. (1992) · Journal of the Optical Society of America A · doi:10.1364/josaa.9.001905 · Cited by 271 · see citing works
Generative models for discovering sparse distributed representations
Hinton, G. E., & Ghahramani, Z. (1997) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.1997.0101 · Cited by 225 · see citing works
Transformation-invariant clustering using the EM algorithm
Frey, B. J., & Jojić, N. (2003) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2003.1159942 · Cited by 205 · see citing works
Computation and the single neuron
Christof Koch, A. (1997) · Nature · doi:10.1038/385207a0 · Cited by 188 · see citing works
Tenenbaum, J. B., & Freeman, W. T. (1996) · Cited by 124 · see citing works
Self-citationColor constancy: surface color from changing illumination
D’Zmura, M. (1992) · Journal of the Optical Society of America A · doi:10.1364/josaa.9.000490 · Cited by 121 · see citing works
Learning bilinear models for two-factor problems in vision
Freeman, W. T., & Tenenbaum, J. B. (2002) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.1997.609380 · Cited by 109 · see citing works
Self-citationRepresentations of Vision: Trends and Tacit Assumptions in Vision Research
Goréa, A. (1991) · Cited by 100 · see citing works
Nayar, S. K., & Poggio, T. (1996) · Cited by 79 · see citing works
What's up in top-down processing?
Patrick Cavanagh, B., & Gorea, A. C. (1991) · Cited by 67 · see citing works
Factorial Learning and the EM Algorithm
Ghahramani, Z. (1994) · Cited by 67 · see citing works
The Generic Bilinear Calibration-Estimation Problem
Koenderink, J. J., & van Doorn, A. J. (1997) · International Journal of Computer Vision · doi:10.1023/a:1007971132346 · Cited by 58 · see citing works
Critic-driven ensemble classification
Miller, D. J., & Yan, L. (1999) · IEEE Transactions on Signal Processing · doi:10.1109/78.790663 · Cited by 50 · see citing works
Dayan, P., Hinton, G. E., Neal, R. M., & Zemel, R. S. (1999) · The MIT Press eBooks · doi:10.7551/mitpress/7011.003.0017 · Cited by 49 · see citing works
A Bilinear Model of the Illuminant's Effect on Color Appearance
Brainard, D. H., & Wandell, B. A. (1991) · The MIT Press eBooks · doi:10.7551/mitpress/2002.003.0020 · Cited by 34 · see citing works
A Simple Common Contexts Explanation for the Development of Abstract Letter Identities
Polk, T. A., & Farah, M. J. (1997) · Neural Computation · doi:10.1162/neco.1997.9.6.1277 · Cited by 33 · see citing works
Computation and the single neuron
滋, 篠. (1998) · The Brain & Neural Networks · doi:10.3902/jnns.5.18 · Cited by 24 · see citing works
Perceptual normalization of the vowels of a man and a child in various contexts
van Bergem, D. R., Pols, L. C. W., & Beinum, F. J. K.-V. (1988) · Speech Communication · doi:10.1016/0167-6393(88)90018-0 · Cited by 19 · see citing works
Effects of Font- and Letter-Specific Experience on the Perceptual Processing of Letters
Sanocki, T. (1992) · The American Journal of Psychology · doi:10.2307/1423197 · Cited by 19 · see citing works
Omohundro, S. M. (1995) · Cited by 16 · see citing works
Observations on Cortical Mechanisms for Object Recognition and Learning
Poggio, T., & Hurlbert, A. C. (1993) · Cited by 16 · see citing works
Recovery of 3D volume from 2-tone images of novel objects
Moore, C., & Cavanagh, P. (1999) · The MIT Press eBooks · doi:10.7551/mitpress/5089.003.0003 · Cited by 15 · see citing works
Neural Models for Part-Whole Hierarchies
Riesenhuber, M., & Dayan, P. (1996) · MPG.PuRe (Max Planck Society) · Cited by 14 · see citing works
Connectionist generalization for production: an example from GridFont
Grebert, I., Stork, D. G., Keesing, R., et al. (2002) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.1991.155321 · Cited by 6 · see citing works
Connectionist generalization for production: An example from GridFont
Grebert, I., Stork, D. G., Keesing, R., et al. (1992) · Neural Networks · doi:10.1016/s0893-6080(05)80046-2 · Cited by 4 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Zhao, W., Chellappa, R., Phillips, P. J., & Rosenfeld, A. (2003) · ACM Computing Surveys · doi:10.1145/954339.954342 · Cited by 6,174 · see citing works
“, AN be m × 3 matrices whose columns are images of object i (from the bootstrap set) that contain the same m pixels; then the bilinear energy/cost function [Freeman and Tenenbaum 2000] for an image ys of object y under illumination s is ( ys − N ∑”
BackgroundImage Style Transfer Using Convolutional Neural Networks
Gatys, L. A., Ecker, A. S., & Bethge, M. (2016) · 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2016.265 · Cited by 6,025 · see citing works
“Such factorised representations were previously achieved only for controlled subsets of natural images such as faces under different illumination conditions and characters in different font styles [29] or handwritten digits and house numbers [17].”
BackgroundA Neural Algorithm of Artistic Style
Gatys, L., Ecker, A., & Bethge, M. (2016) · Journal of Vision · doi:10.1167/16.12.326 · Cited by 2,612 · see citing works
“12,13 In our demonstration, we render a given photograph in the style of a range of well-known artworks.”
BackgroundBilinear CNN Models for Fine-Grained Visual Recognition
Lin, T., RoyChowdhury, A., & Maji, S. (2015) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2015.170 · Cited by 2,207 · see citing works
“Bilinear models were proposed by Tanenbaum and Freeman [33] to model two-factor variations, such as “style” and “content”, for images.”
MethodMultimodal Compact Bilinear Pooling for Visual Question Answering and Visual Grounding
Fukui, A., Park, D. H., Yang, D., Rohrbach, A., Darrell, T., & Rohrbach, M. (2016) · Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing · doi:10.18653/v1/d16-1044 · Cited by 1,582 · see citing works
Gao, Y., Beijbom, O., Zhang, N., & Darrell, T. (2016) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2016.41 · Cited by 912 · see citing works
“Bilinear models were first introduced by Tenenbaum and Freeman [32] to separate style and content.”
MethodMultilinear Analysis of Image Ensembles: TensorFaces
Vasilescu, M. A. O., & Terzopoulos, D. (2002) · Lecture notes in computer science · doi:10.1007/3-540-47969-4_30 · Cited by 850 · see citing works
“This is not to be confused with the classical “rank-R problem” [7].”
BackgroundGeneralized Multiview Analysis: A discriminative latent space
Sharma, A., Kumar, A., Daumé, H., & Jacobs, D. W. (2012) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2012.6247923 · Cited by 737 · see citing works
“• BLM A i = X i W i X T i , B i = I and Z i = X i i.e. same as GMPCA.”
MethodInfluentialWeighted low-rank approximations
Srebro, N., & Jaakkola, T. (2003) · International Conference on Machine Learning · Cited by 715 · see citing works
Learning photographic global tonal adjustment with a database of input/output image pairs
Bychkovsky, V., Paris, S., Chan, E., & Durand, F. (2011) · doi:10.1109/cvpr.2011.5995413 · Cited by 666 · see citing works
A Framework for Robust Subspace Learning
de la Torre, F. N., & Black, M. J. (2003) · International Journal of Computer Vision · doi:10.1023/a:1023709501986 · Cited by 601 · see citing works
“One example is the work of Tenenbaum and Freeman on factoring style and content (Tenenbaum and Freeman, 2000) using a bilinear model.”
MethodGenerative Image Modeling Using Style and Structure Adversarial Networks
Wang, X., & Gupta, A. (2016) · Lecture notes in computer science · doi:10.1007/978-3-319-46493-0_20 · Cited by 607 · see citing works
“Finally, the idea of factorizing image into two separate phenomena has been well studied in [46,47,48,49], which motivates us to decompose the generative process to structure and style.”
BackgroundParametric hidden Markov models for gesture recognition
Wilson, A. D., & Bobick, A. (1999) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.790429 · Cited by 574 · see citing works
Deep Learning of Representations: Looking Forward
Bengio, Y. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-39593-2_1 · Cited by 558 · see citing works
“…priors on the form of the model can be used to enhance disentangling, such as multiplicative interactions between the factors (Tenenbaum and Freeman, 2000; Desjardins et al., 2012) or orthogonality of the features derivative with respect to the input (Rifai et al., 2011b, 2012a; Sohn et…”
MethodLearning photographic global tonal adjustment with a database of input / output image pairs
Bychkovsky, V., Paris, S., Chan, E., & Durand, F. (2011) · doi:10.1109/cvpr.2011.5995332 · Cited by 531 · see citing works
Learning a Mahalanobis Metric from Equivalence Constraints
Bar-Hillel, A., Hertz, T., Shental, N., & Weinshall, D. (2005) · Cited by 517 · see citing works
Incremental Singular Value Decomposition of Uncertain Data with Missing Values
Brand, M. (2002) · Lecture notes in computer science · doi:10.1007/3-540-47969-4_47 · Cited by 511 · see citing works
“Examples include the combination of lighting and pose [20] and shape and motion [12,3] in image formation, mixing of sources in acoustic recordings [6], and word associations in collections of documents [1,23].”
BackgroundMultimodal intelligence: Representation learning, information fusion, and applications
Zhang, C., Yang, Z., He, X., & Deng, L. (2020) · IEEE Journal of Selected Topics in Signal Processing · doi:10.1109/jstsp.2020.2987728 · Cited by 511 · see citing works
“This method is also referred to as second-order pooling [167].”
MethodProbabilistic Linear Discriminant Analysis
Ioffe, S. (2006) · Lecture notes in computer science · doi:10.1007/11744085_41 · Cited by 499 · see citing works
“Note that if an example comes from a class represented by v , and belongs to the j th mixture component, then its expected value is m j + A j v , which is the representation used in asymmetric bi-linear models [12].”
MethodLearning Discriminative Binary Codes for Large-scale Cross-modal Retrieval
Xu, X., Shen, F., Yang, Y., Shen, H. T., & Li, X. (2017) · IEEE Transactions on Image Processing · doi:10.1109/tip.2017.2676345 · Cited by 458 · see citing works
“Despite of the above classical methods such as CCA and BLM, other subspace learning approaches leverage the valuable class label information to improve the retrieval performance.”
BackgroundAudio-driven facial animation by joint end-to-end learning of pose and emotion
Karras, T., Aila, T., Laine, S., Herva, A., & Lehtinen, J. (2017) · ACM Transactions on Graphics · doi:10.1145/3072959.3073658 · Cited by 435 · see citing works
Learning distance functions using equivalence relations
Bar-Hillel, A., Hertz, T., Shental, N., & Weinshall, D. (2003) · Cited by 433 · see citing works
How Close Are We to Understanding V1?
Olshausen, B. A., & Field, D. J. (2005) · Neural Computation · doi:10.1162/0899766054026639 · Cited by 411 · see citing works
Bypassing synthesis: PLS for face recognition with pose, low-resolution and sketch
Sharma, A., & Jacobs, D. W. (2011) · doi:10.1109/cvpr.2011.5995350 · Cited by 384 · see citing works
Multilinear subspace analysis of image ensembles
Vasilescu, M. A. O., & Terzopoulos, D. (2003) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2003.1211457 · Cited by 379 · see citing works
“It subsumes as special cases the simple linear (1-factor) analysis known as principal components analysis (PCA), as well as bilinear (2-factor) analysis [7].”
MethodLow-Rank Bilinear Pooling for Fine-Grained Classification
Kong, S., & Fowlkes, C. C. (2017) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2017.743 · Cited by 374 · see citing works
Wang, T., Zhao, J., Yatskar, M., Chang, K.-W., & Ordóñez, V. (2019) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2019.00541 · Cited by 353 · see citing works
“Building models under fairness objectives is also related to feature disentangling methods [28, 22, 17, 18, 19].”
BackgroundKernel Pooling for Convolutional Neural Networks
Cui, Y., Zhou, F., Wang, J., Liu, X., Lin, Y., & Belongie, S. (2017) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2017.325 · Cited by 353 · see citing works
“In the case of p = 2, the model is usually referred as Bilinear models, first introduced by Tenenbaum and Freeman [40].”
MethodMultilinear Discriminant Analysis for Face Recognition
Yan, S., Xu, D., Yang, Q., et al. (2006) · IEEE Transactions on Image Processing · doi:10.1109/tip.2006.884929 · Cited by 340 · see citing works
“Most traditional algorithms, such as the principal component analysis (PCA) [17], [20], [21], [24] and linear discriminant analysis (LDA)”
MethodDisentangled and Controllable Face Image Generation via 3D Imitative-Contrastive Learning
Deng, Y., Yang, J., Chen, D., Wen, F., & Tong, X. (2020) · 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr42600.2020.00520 · Cited by 329 · see citing works
“Historical attempts are based on simple bilinear models [46], restricted Boltzmann machines [10, 39], among others.”
Bilinear Convolutional Neural Networks for Fine-Grained Visual Recognition
Lin, T., RoyChowdhury, A., & Maji, S. (2017) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2017.2723400 · Cited by 403 · see citing works
“Bilinear models were used by Tanenbaum and Freeman [48] to model twofactor variations such as “style” and “content” for images.”
MethodLearning to share visual appearance for multiclass object detection
Salakhutdinov, R., Torralba, A. B., & Tenenbaum, J. B. (2011) · doi:10.1109/cvpr.2011.5995720 · Cited by 326 · see citing works
“These methods can be applied for object classes with well defined sets of transformations such as letters [20, 28], or faces [28].”
MethodSelf-citationJoint Feature Selection and Subspace Learning for Cross-Modal Retrieval
Wang, K., He, R., Wang, L., Wang, W., & Tan, T. (2015) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2015.2505311 · Cited by 318 · see citing works
“Recently, several approaches for establishing inter-modal relationships between data from different modalities generally rely on subspace learning, such as Canonical Correlation Analysis [25], [26], Partial Least Squares (PLS) [27] and Bilinear Model (BLM) [28], [29].”
BackgroundMethodMulti-view Harmonized Bilinear Network for 3D Object Recognition
Yu, T., Meng, J., & Yuan, J. (2018) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2018.00027 · Cited by 318 · see citing works
“Bilinear pooling is first proposed by Tenenbaum and Freeman [31] to separate style and content.”
Style translation for human motion
Hsu, E., Pulli, K., & Popović, J. (2005) · ACM Transactions on Graphics · doi:10.1145/1073204.1073315 · Cited by 309 · see citing works
RoNIN: Robust Neural Inertial Navigation in the Wild: Benchmark, Evaluations, & New Methods
Herath, S., Yan, H. R., & Furukawa, Y. (2020) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra40945.2020.9196860 · Cited by 304 · see citing works
“RoNIN LSTM : We use a stacked unidirectional LSTM [18] while enriching its input feature by concatenating the output of a bilinear layer [20].”
MethodNorouzi, M., & Fleet, D. J. (2013) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2013.388 · Cited by 306 · see citing works
“, [17]).”
Applications of Support Vector Machines to Speech Recognition
Ganapathiraju, A., Hamaker, J., & Picone, J. (2004) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2004.831018 · Cited by 281 · see citing works
Ensemble manifold regularized sparse low-rank approximation for multiview feature embedding
Zhang, L., Zhang, Q., Zhang, L., Tao, D., Huang, X., & Du, B. (2015) · Pattern Recognition · doi:10.1016/j.patcog.2014.12.016 · Cited by 279 · see citing works
“In this subsection, we use theWiki Text-Image data set to illustrate the effectiveness of EMR-SLRA algorithm in comparing with its competitors including the traditional multiview methods CCA, PLS and BLM. Table 1 shows the number of training and test samples of each category in the Wiki Text-Image data set.”
MethodInfluentialArtFlow: Unbiased Image Style Transfer via Reversible Neural Flows
An, J., Huang, S., Song, Y., Dou, D., Liu, W., & Luo, J. (2021) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr46437.2021.00092 · Cited by 276 · see citing works
“Following the theoretical framework of the Bilinear Model [52], we can define the unbiased style transfer as: Definition 1 Suppose we have a bilinear style transfer module f cs = C ( f c ) S ( f s ) , where C, S denote the content factor and the style factor in the bilinear model, respectively. f cs is an unbiased style…”
BackgroundMethodInfluentialDeep Cascaded Bi-Network for Face Hallucination
Zhu, S., Liu, S., Loy, C. C., & Tang, X. (2016) · Lecture notes in computer science · doi:10.1007/978-3-319-46454-1_37 · Cited by 249 · see citing works
Weakly-supervised Disentangling with Recurrent Transformations for 3D View SynthesisPreprint
Yang, J., Reed, S., Yang, M., & Lee, H. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1601.00706 · Cited by 247 · see citing works
“Bilinear models for separating style and content are developed in [25], and are shown to”
MethodDiscovering states and transformations in image collections
Isola, P., Lim, J. J., & Adelson, E. H. (2015) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2015.7298744 · Cited by 238 · see citing works
“This approach is reminiscent of Freeman and Tenenbaum’s work on separating style and content [29].”
ResultLearning Coupled Feature Spaces for Cross-Modal Matching
Wang, K., He, R., Wang, W., et al. (2013) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2013.261 · Cited by 238 · see citing works
“In [24], Tenenbaum and Freeman propose a bilinear model (BLM) to derive a common space for cross-modal face recognition, and BLM is also used for text-image retrieval in [22].”
BackgroundMethodInfluentialDeep Temporal Linear Encoding Networks
Diba, A., Sharma, V., & Gool, L. V. (2017) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2017.168 · Cited by 236 · see citing works
“Likewise, Bilinear models [20, 32] have been widely used and have achieved state-of-the-art results.”
MethodEntity-Sensitive Attention and Fusion Network for Entity-Level Multimodal Sentiment Classification
Yu, J., Jiang, J., & Xia, R. (2019) · IEEE/ACM Transactions on Audio Speech and Language Processing · doi:10.1109/taslp.2019.2957872 · Cited by 235 · see citing works
“the widely used bilinear models [35], which is expected to consider all the pairwise interactions between features.”
MethodMultimodal Neurons in Artificial Neural Networks
Goh, G., Cammarata, N., Voss, C., Carter, S., Petrov, M., Schubert, L., Radford, A., & Olah, C. (2021) · Distill · doi:10.23915/distill.00030 · Cited by 240 · see citing works
Personalized recommendation on dynamic content using predictive bilinear models
Chu, W., & Park, S.-T. (2009) · The Web Conference · doi:10.1145/1526709.1526802 · Cited by 288 · see citing works
“[39] J. B. Tenenbaum and W. T. Freeman.”
BackgroundMultilinear image analysis for facial recognition
Vasilescu, M. A. O., & Terzopoulos, D. (2003) · doi:10.1109/icpr.2002.1048350 · Cited by 231 · see citing works
Disentangling factors of variation in deep representations using adversarial trainingPreprint
Mathieu, M., Zhao, J., Sprechmann, P., Ramesh, A., & LeCun, Y. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1611.03383 · Cited by 258 · see citing works
Learning to Represent Spatial Transformations with Factored Higher-Order Boltzmann Machines
Memisevic, R., & Hinton, G. E. (2010) · Neural Computation · doi:10.1162/neco.2010.01-09-953 · Cited by 227 · see citing works
Swapping Autoencoder for Deep Image ManipulationPreprint
Park, T., Zhu, J.-Y., Wang, O., Lu, J., Shechtman, E., Efros, A. A., & Zhang, R. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2007.00653 · Cited by 253 · see citing works
“Modeling style and content is a classic computer vision and graphics problem [69, 22].”
BackgroundLearning Consistent Feature Representation for Cross-Modal Multimedia Retrieval
Kang, C., Xiang, S., Liao, S., Xu, C., & Pan, C. (2015) · IEEE Transactions on Multimedia · doi:10.1109/tmm.2015.2390499 · Cited by 222 · see citing works
“There are some other algorithms which can also deal with cross-modal problems, such as BLM [38].”
BackgroundMethodMTFH: A Matrix Tri-Factorization Hashing Framework for Efficient Cross-Modal Retrieval
Liu, X., Hu, Z., Ling, H., et al. (2019) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2019.2940446 · Cited by 221 · see citing works
“Accordingly, many reasonable extensions, e.g., bi-linear model (BLM) [9], manifold learning [9], latent subspace analysis (LSA) [1], sparse subspace learning (SSL) [5], [10], and correlated subspace learning (CSL) [2], [11], have also been developed for cross-modal retrieval task.”
BackgroundLearning with matrix factorizations
Srebro, N., & Jaakkola, T. (2004) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 217 · see citing works
Manifold based analysis of facial expression
Chang, Y. H., Hu, C., Feris, R. S., & Turk, M. (2005) · Image and Vision Computing · doi:10.1016/j.imavis.2005.08.006 · Cited by 214 · see citing works
“Tenenbaum and Freeman [33] talked about separating style and content by using symmetry or asymmetry bilinear models.”
BackgroundSynthesizing retinal and neuronal images with generative adversarial nets
Zhao, H., Li, H., Maurer‐Stroh, S., & Cheng, L. (2018) · Medical Image Analysis · doi:10.1016/j.media.2018.07.001 · Cited by 211 · see citing works
Unifying Nuclear Norm and Bilinear Factorization Approaches for Low-Rank Matrix Decomposition
Cabral, R., de la Torre, F. N., Costeira, J. P., et al. (2013) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2013.309 · Cited by 210 · see citing works
“However, this is not generalizable to several other computer vision problems modeled as lowrank factorization problems [5, 31, 34, 37].”
BackgroundTransformation-invariant clustering using the EM algorithm
Frey, B. J., & Jojić, N. (2003) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2003.1159942 · Cited by 205 · see citing works
Statistical regularities in art: Relations with visual coding and perception
Graham, D. J., & Redies, C. (2010) · Vision Research · doi:10.1016/j.visres.2010.05.002 · Cited by 207 · see citing works
“This challenge is part of the more general problem in computer vision of separating style and content (see Tenenbaum & Freeman, 2000).”
BackgroundLearning to Disentangle Factors of Variation with Manifold Interaction
Reed, S., Sohn, K., Zhang, Y., & Lee, H. (2014) · Cited by 201 · see citing works
Facial expression decomposition
Wang, H., & Ahuja (2003) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2003.1238452 · Cited by 199 · see citing works
“[1] propose using a bilinear model [2] to separate person-specific video data into expressive features and speech content, and synthesize new sequences which maintain the original speech while using a different expression.”
MethodReed, S., Zhang, Y., Zhang, Y., & Lee, H. (2015) · neural information processing systems · Cited by 197 · see citing works
Tied Factor Analysis for Face Recognition across Large Pose Differences
Prince, S. J. D., Warrell, J., Elder, J. H., et al. (2008) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2008.48 · Cited by 193 · see citing works
“Tenenbaum and Freeman [32] investigated the use of bilinear models for separating style from content.”
BackgroundInfluentialDeep Learning Techniques for Future Intelligent Cross-Media RetrievalPreprint
Rehman, S. U., Waqas, M. M., Tu, S., Koubâa, A., Rehman, O. U., Ahmad, J. E., Hanif, M. I., & Han, Z. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2008.01191 · Cited by 191 · see citing works
“Generalized Multiview Analysis (GMA) [13] can be used to combine CCA, BLM, and PLS for solving cross-media retrieval task.”
BackgroundInfluentialBilinear Models for 3-D Face and Facial Expression Recognition
Mpiperis, I., Malassiotis, S., & Strintzis, M. G. (2008) · IEEE Transactions on Information Forensics and Security · doi:10.1109/tifs.2008.924598 · Cited by 185 · see citing works
Separating style and content on a nonlinear manifold
Elgammal, A., & Lee, C.-S. (2004) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2004.1315070 · Cited by 182 · see citing works
Tensor Methods in Computer Vision and Deep Learning
Panagakis, Y., Kossaifi, J., Chrysos, G. G., Oldfield, J. P., Nicolaou, M. A., Anandkumar, A., & Zafeiriou, S. P. (2021) · Proceedings of the IEEE · doi:10.1109/jproc.2021.3074329 · Cited by 187 · see citing works
Matsubara, T., & Morimoto, J. (2013) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2013.2250502 · Cited by 180 · see citing works
“, multiuser interface, using the style and content separation approach [21].”
BackgroundMethodInfluentialMiME: Multilevel Medical Embedding of Electronic Health Records for Predictive HealthcarePreprint
Choi, E., Xiao, C., Stewart, W. F., & Sun, J. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1810.09593 · Cited by 177 · see citing works
“(3) was inspired by recent developments in bilinear pooling technique [37, 21, 19, 24], which we discuss in more detail in Appendix A.”
BackgroundUnsupervised Learning of Image Transformations
Memisevic, R., & Hinton, G. E. (2007) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2007.383036 · Cited by 175 · see citing works
“There is some resemblance between our approach and the bilinear model of style and content proposed in [18], but the learning methods are quite different and our approach allows the transformations to be highly non-linear functions of the data.”
ResultHuang, D.-A., & Wang, Y.-C. F. (2013) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2013.310 · Cited by 174 · see citing works
“Besides considering CCA as the baseline approach, we consider the methods of Tang & Wang [17], PLS [16], bilinear model [18], SCDL [19], and joint dictionary learning Figure 7.”
BackgroundMethodCombining multiple sources of knowledge in deep CNNs for action recognition
Park, E., Han, X., Berg, T. L., & Berg, A. C. (2016) · IEEE Winter Conference on Applications of Computer Vision · doi:10.1109/wacv.2016.7477589 · Cited by 167 · see citing works
Expressive speech-driven facial animation
Cao, Y., Tien, W. C., Faloutsos, P., & Pighin, F. P. (2005) · ACM Transactions on Graphics · doi:10.1145/1095878.1095881 · Cited by 162 · see citing works
Dumoulin, V., Perez, E., Schucher, N., Strub, F., de Vries, H., Courville, A. C., & Bengio, Y. (2018) · Distill · doi:10.23915/distill.00011 · Cited by 166 · see citing works
Towards Robust Pattern Recognition: A Review
Zhang, X.-Y., Liu, C., & Suen, C. Y. (2020) · Proceedings of the IEEE · doi:10.1109/jproc.2020.2989782 · Cited by 161 · see citing works
“Content and style [276] are two important factors in pattern recognition.”
BackgroundAdaptive Semi-Supervised Feature Selection for Cross-Modal Retrieval
Yu, E., Sun, J., Li, J., et al. (2018) · IEEE Transactions on Multimedia · doi:10.1109/tmm.2018.2877127 · Cited by 157 · see citing works
“Unsupervised subspace learning methods merely leverage the pairwise information of unlabeled samples from different modalities to learn the common latent subspace [14], [18], [20], [21].”
BackgroundAhrens, M. B., Linden, J. F., & Sahani, M. (2008) · Journal of Neuroscience · doi:10.1523/jneurosci.3377-07.2008 · Cited by 151 · see citing works
“Other multilinear methods have been useful in various settings in the statistics and machine learning setting (e.g. Vasilescu and Terzopoulos, 2005; Tenenbaum and Freeman, 2000; Harshman and Lundy, 1994).”
Cluster Canonical Correlation Analysis
Rasiwasia, N., Mahajan, D. K., Mahadevan, V., & Aggarwal, G. (2014) · Cited by 152 · see citing works
Bilinear classifiers for visual recognition
Pirsiavash, H., Ramanan, D., & Fowlkes, C. C. (2009) · doi:10.13016/m2uvdv-qzxg · Cited by 141 · see citing works
Discovering Hidden Factors of Variation in Deep NetworksPreprint
Cheung, B., Livezey, J. A., Bansal, A. K., & Olshausen, B. A. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1412.6583 · Cited by 152 · see citing works
“Previous approaches to separating factors of variation in data, such as content vs. style [3] or form vs. motion [4, 5, 6, 7, 8, 9], have relied upon a bilinear model architecture in which the units representing different factors are combined multiplicatively.”
MethodGeneralized Semi-supervised and Structured Subspace Learning for Cross-Modal Retrieval
Zhang, L., Ma, B., Li, G., et al. (2017) · IEEE Transactions on Multimedia · doi:10.1109/tmm.2017.2723841 · Cited by 139 · see citing works
“The unsupervised cross-modal methods use paired training samples between two modalities to learn the common subspace, including Partial Least Squares (PLS) [21], Canonical Correlation Analysis (CCA) [19], Bilinear Model (BLM) [22], Kernel CCA (KCCA) [19], and Deep CCA (DCCA) [2].”
MethodWang, Z., Rui-qing, L., Wang, M., & Li, A. (2021) · Bioinformatics · doi:10.1093/bioinformatics/btab185 · Cited by 139 · see citing works
Cross-Modal Retrieval via Deep and Bidirectional Representation Learning
He, Y., Xiang, S., Kang, C., Wang, J., & Pan, C. (2016) · IEEE Transactions on Multimedia · doi:10.1109/tmm.2016.2558463 · Cited by 135 · see citing works
“There exist some classic algorithms for constructing a common space, such as canonical correlation analysis (CCA) [19], partial least squares (PLS) [20], bilinear models (BLM) [21] and generalized multiview analysis (GMA) [22].”
MethodHuman motion signatures: analysis, synthesis, recognition
Vasilescu, M. A. O. (2003) · doi:10.1109/icpr.2002.1047975 · Cited by 134 · see citing works
Content-based image retrieval with compact deep convolutional features
Alzu’bi, A., Amira, A., & Ramzan, N. (2017) · Neurocomputing · doi:10.1016/j.neucom.2017.03.072 · Cited by 133 · see citing works
“The proposed architecture is inspired by the bilinear models proposed by Tenenbaum and Freeman [15] to model the separation between the “content” and “style” factors of perceptual systems and by the promising results obtained using bilinear CNNs applied to fine-grained categorization [16].”
High Resolution Acquisition, Learning and Transfer of Dynamic 3‐D Facial Expressions
Wang, Y., Huang, X., Lee, C.-S., et al. (2004) · Computer Graphics Forum · doi:10.1111/j.1467-8659.2004.00800.x · Cited by 133 · see citing works
Natural facial expression recognition using differential-AAM and manifold learning
Cheon, Y., & Kim, D. (2008) · Pattern Recognition · doi:10.1016/j.patcog.2008.10.010 · Cited by 131 · see citing works
“Linear models such as principal component analysis (PCA) [2], bilinear [3], and tensor model [4] are simple and efficient [5].”
MethodMultilinear Multitask Learning
Romera‐Paredes, B., Aung, M. H., Bianchi‐Berthouze, N., & Pontil, M. (2013) · UCL Discovery (University College London) · Cited by 130 · see citing works
FineGAN: Unsupervised Hierarchical Disentanglement for Fine-Grained Object Generation and Discovery
Singh, K. K., Ojha, U., & Lee, Y. J. (2019) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2019.00665 · Cited by 132 · see citing works
“Disentangled representation learning has a vast literature (e.g., [3, 46, 22, 51, 9, 21, 11, 23]).”
BackgroundMultifactor Gaussian process models for style-content separation
Wang, J. M.-C., Fleet, D. J., & Hertzmann, A. (2007) · International Conference on Machine Learning · doi:10.1145/1273496.1273619 · Cited by 126 · see citing works
Wu, L. Y., Wang, Y., Li, X., & Gao, J. (2017) · Pattern Recognition · doi:10.1016/j.patcog.2017.10.004 · Cited by 126 · see citing works
“Bilinear models [50] can model two-factor variations and provide richer representations than linear models.”
BackgroundBilinear spatiotemporal basis models
Akhter, I., Simon, T., Khan, S., Matthews, I. A., & Sheikh, Y. A. (2012) · ACM Transactions on Graphics · doi:10.1145/2159516.2159523 · Cited by 121 · see citing works
Describing Visual Scenes using Transformed Dirichlet Processes
Torralba, A. B., Willsky, A. S., Sudderth, E. B., & Freeman, W. T. (2005) · neural information processing systems · Cited by 122 · see citing works
Self-citationSemantic Label Sharing for Learning with Many Categories
Fergus, R., Bernal, H. J., Weiss, Y., & Torralba, A. B. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-15549-9_55 · Cited by 118 · see citing works
“Other approaches transfer information across object categories by sharing a common set of parts [16, 17], by sharing transformations across different instances [18–20], or by sharing a set of prototypes [21].”
BackgroundTwo Distributed-State Models For Generating High-Dimensional Time Series
Taylor, G. W., Hinton, G. E., & Roweis, S. T. (2011) · doi:10.5555/1953048.2021035 · Cited by 114 · see citing works
“Therefore at first glance, the model appears similar to the bilinear factor model (Tenenbaum and Freeman, 2000).”
MethodHuman Carrying Status in Visual Surveillance
Tao, D., Li, X., Maybank, S. J., et al. (2006) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2006.138 · Cited by 114 · see citing works
Few-shot Font Generation with Localized Style Representations and Factorization
Park, S., Chun, S., Cha, J., Lee, B., & Shim, H. (2021) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v35i3.16340 · Cited by 117 · see citing works
Are Disentangled Representations Helpful for Abstract Visual Reasoning?Preprint
van Steenkiste, S., Locatello, F., Schmidhuber, J., & Bachem, O. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1905.12506 · Cited by 119 · see citing works
“Disentangling pose, style, or motion from content are classical vision tasks that has been studied with different degrees of supervision [72, 79, 80, 34, 19, 14, 21, 36].”
BackgroundMood swings: expressive speech animation
Chuang, E. S., & Bregler, C. (2005) · ACM Transactions on Graphics · doi:10.1145/1061347.1061355 · Cited by 113 · see citing works
- Authors
- Tenenbaum, J. B., & Freeman, W. T.
- Affiliations
- Massachusetts Institute of Technology (US)
- Mitsubishi Electric Research Laboratories (United States) (US)
- Venue
- Neural Computation
- Publisher
- MIT Press
- Published
- 2000-06-01
- Volume
- 12
- Issue
- 6
- Pages
- 1247-1283
- ISSN
- 0899-7667 (ISSN-L)
- 1530-888X
- OpenAlex
- W2170653751
- Semantic Scholar
- 7e85f7d59e37972ec52cbabfef0512588d87f125
- Cited by
- 840
- References
- 61
- Citations by year
- 2026: 2 · 2025: 17 · 2024: 20 · 2023: 31 · 2022: 38 · 2021: 61 · 2020: 58 · 2019: 70 · 2018: 49 · 2017: 39 · 2016: 56 · 2015: 34 · 2014: 27 · 2013: 39 · 2012: 30
- FWCI
- 13.29
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Neural Computation (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Face and Expression Recognition
- Physical Sciences › Computer Science › Artificial Intelligence › Speech Recognition and Synthesis
- Keywords
- bilinear model, factor models, perceptual learning, speaker accent, singular value decomposition, expectation-maximization algorithm, factor interactions
- MeSH terms
- Algorithms, Face, Humans, Learning, Pattern Recognition, Visual, Speech Perception, Linear Models, Neural Networks, Computer
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
