The DOI matches its Crossref record; 14 of the 15 references it cites were found in a registry or an index.
Learning Invariance from Transformation Sequences
Abstract
The visual system can reliably identify objects even when the retinal image is transformed considerably by commonly occurring changes in the environment. A local learning rule is proposed, which allows a network to learn to generalize across such transformations. During the learning phase, the network is exposed to temporal sequences of patterns undergoing the transformation. An application of the algorithm is presented in which the network learns invariance to shift in retinal position. Such a principle may be involved in the development of the characteristic shift invariance property of complex cells in the primary visual cortex, and also in the development of more complicated invariance properties of neurons in higher visual areas.
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“This idea of continuity is used in a great number of artificial neural networks and related models (Wiskott and Sejnowski, 2002; Földiák, 2008; Mobahi et al., 2009).”
From Toward an integration of deep learning and neuroscience (2016) · cites this paper as Földiák, 2008
Citations
Cites
Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex
Hubel, D. H., & Wiesel, T. N. (1962) · The Journal of Physiology · doi:10.1113/jphysiol.1962.sp006837 · Cited by 13,680
Backpropagation Applied to Handwritten Zip Code Recognition
LeCun, Y., Boser, B., Denker, J. S., Henderson, D., Howard, R. E., Hubbard, W., & Jackel, L. D. (1989) · Neural Computation · doi:10.1162/neco.1989.1.4.541 · Cited by 11,891
Fukushima, K. (1980) · Biological Cybernetics · doi:10.1007/bf00344251 · Cited by 5,759
Toward a modern theory of adaptive networks: Expectation and prediction.
Sutton, R. S., & Barto, A. G. (1981) · Psychological Review · doi:10.1037/0033-295x.88.2.135 · Cited by 1,450
Feature Discovery by Competitive Learning*
Rumelhart, D. E., & Zipser, D. (1985) · Cognitive Science · doi:10.1207/s15516709cog0901_5 · Cited by 1,398
Visual neurones responsive to faces in the monkey temporal cortex
Perrett, D. I., Rolls, E. T., & Caan, W. (1982) · Experimental Brain Research · doi:10.1007/bf00239352 · Cited by 1,385
Forming sparse representations by local anti-Hebbian learning
Földiák, P. (1990) · Biological Cybernetics · doi:10.1007/bf02331346 · Cited by 541
Adaptation and decorrelation in the cortex
Barlow, H. B., & Földiák, P. (1989) · Addison-Wesley Longman Publishing Co., Inc. eBooks · Cited by 263
Learning translation invariant recognition in a massively parallel networks
Hinton, G. E. (1987) · Lecture notes in computer science · doi:10.1007/3-540-17943-7_117 · Cited by 179
A complex-cell receptive-field model
Spitzer, H., & Hochstein, S. (1985) · Journal of Neurophysiology · doi:10.1152/jn.1985.53.5.1266 · Cited by 144
Research works printed but not linked: 2
- Barlow H. B., 1989, Chap., 4, 54
- Sutton R. S., 1981, Psychol. RKV., 88, 135
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“Learning invariance in this manner is known as temporal trace learning (Földiák, 1991; see Rolls, 2012, for a review), and it is the focus of the study by Isik and colleagues.”
BackgroundModelling Singularity in Vision to Learn Rotation Invariance toward Recognition
Zou, Q., & Luo, S. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-24840-8_51
Learning invariant features in neocortex-inspired hierarchical networks
Andryszek, P. (n.d.) · Homo Politicus (Academy of Humanities and Economics in Lodz)
Stability Criteria for Unsupervised
Wallis, G. M. (2005)
Hurri, J., Väyrynen, J. J., & Hyvärinen, A. (2004) · Neural Computation and Psychology Workshop (NCPW) · doi:10.1142/9789812702784_0003
Brain mechanisms for invariant visual and learning recognition
Rolls, E. T. (1994)
Spatio-temporal convolutional networks explain neural representations of human actionsPreprint
Tacchetti, A., Işık, L., & Poggio, T. (2016) · arXiv (Cornell University)
A Computational Approach to the Neuropsychology of Visual Attention
Rolls, E. T. (2001) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780198524885.003.0011
Models of invariant object recognition
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The cortical neurodynamics of visual attention - a model
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Visual search: Attentional neurodynamics at work
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Workshop New Challenges in Neural Computation 2010
Hammer, B., & Villmann, T. (2010)
Models of learning in the visual system: dependence on retinal eccentricity
Al-Shaikhli, B. (2006) · Publikationsserver (Universitat Marburg) · doi:10.17192/z2006.0144
Biasing restricted Boltzmann machines using Gaussian filters to learn invariant visual features
Yogeswaran, A., & Payeur, P. (2016) · IEEE Symposium Series on Computational Intelligence (SSCI) · doi:10.1109/ssci.2016.7850122
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BackgroundMethodTask-dependent recurrent dynamics in visual cortexPreprint
Tajima, S., Koida, K., Tajima, C. I., Suzuki, H., Aihara, K., & Komatsu, H. (2017) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/120725
A computational model of spatial encoding in the hippocampus
Schönfeld, F. (2016) · Dokumentenrepositorium der RUB (Ruhr University Bochum)
Effects of a Diffusing Messenger: Learning Temporal Correlations
Krekelberg, B., & Taylor, J. G. (1997) · Springer eBooks · doi:10.1007/978-1-4757-9800-5_18
The Principles of Adaptation in Recognition and Behavior
Shimazaki, H. (2018) · The Brain & Neural Networks · doi:10.3902/jnns.25.86
Graphical Models of the Visual Cortex
Dean, T. (2010)
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Tanaka, T. (2018) · The Brain & Neural Networks · doi:10.3902/jnns.25.104
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Galtier, M. N., Faugeras, O. D., & Bressloff, P. C. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1102.0166
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Self-organized learning of 3 dimensions
Szepesvári, C., & Lörincz, A. (2002) · IEEE International Conference on Neural Networks/IEEE ... International Conference on Neural Networks · doi:10.1109/icnn.1994.374256
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Michelson, J., Palmer, J. H., Dasari, A., & Kunda, M. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1912.01553 · Cited by 1
“Thus, AI research on representing and learning transformation invariance [10], [11] is not directly relevant to the Fig.”
BackgroundTalyansky, S. D., & Brinkman, B. A. W. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.01.06.896324
Invariant Object Representation Based on Principle of Maximal Dependence CapturingPreprint
Raj, R., Dahlen, D., Duyck, K., & Yu, C. R. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/662130
“Whereas these models can account for novel viewpoints or forms (21, 25-31), they are not effective in mapping corrupted or occluded forms of objects to the same representation (Fig.”
BackgroundBahroun, Y., Sengupta, A. M., & Chklovskii, D. B. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2102.05503
“dimensionality reduction and sparse coding [8, 26].”
The Sparse Manifold Transform and Unsupervised Learning for Signal Representation
Chen, Y. (2020) · eScholarship (California Digital Library)
Does the Brain Infer Invariance Transformations From Graph Symmetries?
Linde, H. (2023) · IEEE Transactions on Cognitive and Developmental Systems · doi:10.1109/tcds.2023.3281406
Baker, C. I. (2014) · Faculty Opinions – Post-Publication Peer Review of the Biomedical Literature · doi:10.3410/f.718084051.793490187
A model of complex cell development by information separation
Date, A., & Kurata, K. (2007) · Systems and Computers in Japan · doi:10.1002/scj.20483
“(2) Then, the same result as in Földiák [7] can be obtained without trace learning.”
BackgroundMethodResultInfluentialRolls, E. T. (2001) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780198524885.003.0001
Prince, C. G. (2006) · Connection Science · doi:10.1080/09540090600783442
“Connectionist modelling techniques in these chapters include autoencoders (chapter 2), recurrent networks (chapters 2 and 5), Hebbian learning (chapters 3 and 7), Hopfield networks (chapter 7), an unsupervised learning algorithm (chapter 2: Foldiak 1991) and backpropagation (chapter 2).”
BackgroundFaculty Opinions recommendation of A developmental approach to machine learning?
Moore, D. (2020) · Faculty Opinions – Post-Publication Peer Review of the Biomedical Literature · doi:10.3410/f.732332264.793574321
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Fukushima, K. (2003) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.1999.831107
da Silva, E. C. (2022) · Digital Library of Theses and Dissertations (Universidade de São Paulo) · doi:10.11606/d.59.2022.tde-22112022-152337
Introduction to linear algebra for neural networks
(2001) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780198524885.005.0001
(2001) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780198524885.002.0004
(2001) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780198524885.005.0002
(2001) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780198524885.002.0003
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Okamura, J., Fukano, D., Murakami, K., & Gang, W. (2025) · IBRO Neuroscience Reports · doi:10.1016/j.ibneur.2025.07.010
“It was assumed that the view-invariant object recognition develops through experiencing different views of an object and learning association of the different views (F ¨ oldi ´ ak, 1991; Masquelier & Thorpe, 2007; Stryker, 1991; Wiskott & Sejnowski, 2002; Wyss et al., 2006).”
Brands, A. M., Ortiz, P., & Groen, I. I. A. (2025) · Conference on Cognitive Computational Neuroscience (CCN) · doi:10.32470/2ji25f0 · Cited by 1
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Banville, H. J. (2022) · theses.fr (ABES) · doi:10.70675/12e08edaz0021z43fbzb6adz07d315fc6ee2
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Aubret, A., & Triesch, J. (2026) · Developmental Science · doi:10.1111/desc.70240
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Yu, Z., Aubret, A., Raabe, M. C., Yang, J., Yu, C., & Triesch, J. (2026) · Developmental Science · doi:10.1111/desc.70231
“Toddlers abundantly manipulate (or walk around) objects while watching them, which gives them access to diverse views of a single object over a short period of time.”
Wood, J. N., & Wood, S. M. W. (2026) · Current Directions in Psychological Science · doi:10.1177/09637214261469163
Hierarchical feature binding in a spiking neural network model of the primate ventral visual pathway
Gardner, B., McCarthy, P. J., Chrol-Cannon, J., Goodman, D. F. M., Schultz, S. R., Iacono, G. L., & Stringer, S. M. (2026) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1014752
Inoue, P., Röhrbein, F., & Knoblauch, A. (2026) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2026.1943064
“…for association-based tolerance learning, consistent with models in which invariance can be learned from transformation sequences and with evidence that unsupervised natural experience can rapidly alter invariant object representations in visual cortex (Földiák, 1991; Li and DiCarlo, 2008).”
Biologically-Inspired Translation, Scale, and rotation invariant object recognition models
Woo, M. (2007) · RIT Scholar Works (Rochester Institute of Technology)
Dynamic Inputs and Attraction Force Analysis for Visual Invariance and Transformation Estimation
Maul, T., Baba, S., & Yusof, A. (2005) · Lecture notes in computer science · doi:10.1007/11539087_120
“Some examples from the literature are: the Neocognitron [6], neural traces and temporal sequences [7], slow feature analysis [8], and others.”
BackgroundDeep Predictive Learning: A Comprehensive Model of Three Visual Streams
O'Reilly, R. C., Wyatte, D. R., & Rohrlich, J. (2017) · arXiv · doi:10.48550/arxiv.1709.04654 · Cited by 26
“…on all layers, but only found benefits for these higher What pathway layers, which is consistent with the idea that these areas have more sustained representations to support the development of more invariant representations (Foldiak, 1991; O’Reilly & Johnson, 1994; Wiskott & Sejnowski, 2002).”
Background
Metadata
- Authors
- Földiák, P.
- Affiliations
- Physiological Laboratory, University of Cambridge, Downing Street, Cambridge CB2 3EG, U.K.
- Venue
- Neural Computation
- Publisher
- MIT Press - Journals
- Published
- 1991-06
- Volume
- 3
- Issue
- 2
- Pages
- 194-200
- ISSN
- 0899-7667 (ISSN-L)
- 1530-888X
- OpenAlex
- W2096388912
- Cited by
- 661
- References
- 15
- Citations by year
- 2026: 9 · 2025: 6 · 2024: 10 · 2023: 12 · 2022: 11 · 2021: 20 · 2020: 16 · 2019: 18 · 2018: 21 · 2017: 16 · 2016: 37 · 2015: 20 · 2014: 31 · 2013: 24 · 2012: 28
- FWCI
- 5.77
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Neural Computation (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Visual perception and processing mechanisms
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Image and Video Retrieval Techniques
- Keywords
- invariance learning, transformation sequences, translation invariance, local learning rules, visual object recognition, complex cells, primary visual cortex, visual system development
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