Transformation Equivariant Boltzmann Machines

By Jyri J. Kivinen, Christopher K. I. Williams. 2011

96 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

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Citations in the corpus

Disentangling by Factorising (2018, background): “Invariance and equivariance are frequently considered to be desirable properties of representations in the literature (Goodfellow et al., 2009; Kivinen & Williams, 2011; Lenc & Vedaldi, 2015).”
Group Equivariant Convolutional Networks (2016, methodology): “This includes work on transforming autoencoders (Hinton et al., 2011), equivariant Boltzmann machines (Kivinen & Williams, 2011; Sohn & Lee, 2012), equivariant descriptors (Schmidt & Roth, 2012), and equivariant ﬁltering (Skibbe, 2013).”
RotDCF: Decomposition of Convolutional Filters for Rotation-Equivariant Deep Networks (2018, background): “Rotation-invariant descriptors were studied in [31] with product models, and in [16, 19, 32] by estimating the speciﬁc image transformation.”
Exploiting Cyclic Symmetry in Convolutional Neural Networks (2016, background): “Kivinen & Williams (2011), Sohn & Lee (2012) and Schmidt & Roth (2012) propose modiﬁed restricted Boltzmann machines (RBMs) with tied weights to achieve rotation equivariance.”
Learning Invariant Representations with Local Transformations (2012, methodology): “In contemporary work of ours, Kivinen and Williams (2011) proposed the transformation equivariant Boltzmann machine, which shares a similar mathematical formulation to our models in that both try to infer the best matching ﬁl-ters by transforming them using linear transformation matrices.”
Locally Scale-Invariant Convolutional Neural Networks (2014, background): “[6] and [7] introduced transformation-invariant Restricted Boltzmann Machines (RBMs) where linear transformations of a filter are applied to each input to infer its highest activation.”
Rotation Equivariant Vector Field Networks (2016, methodology): “[15] propose such a scheme with Restricted Boltzmann Machines (RBM), while Marcos et al.”
Oriented Response Networks (2017, background): “In [21, 36], the Convolutional Restricted Boltzmann Machine (C-RBM) induces transformation-aware filters, i.”
Learning rotation invariant convolutional filters for texture classification (2016, background): “In [15], [16], [17], the authors propose to learn unsupervised rotation equivariant features by tying the weights of a Convolutional Restricted Boltzmann Machine (C-RBM).”
Learning image representations equivariant to ego-motion (2015, background): “While prior work [12, 24] focuses on equivariance where g is a 2D image warp, we explore the case where g ∈ P is an ego-motion pattern (cf.”
Neuronal Synchrony in Complex-Valued Deep Networks (2013, background): “2), if desired, and to allow the units to switch off (rather than being constrained to the unit circle), e.g. with a ‘spike and slab’ formulation (Courville et al., 2011; Kivinen & Williams, 2011).”
A Framework for the Quantitative Evaluation of Disentangled Representations (2018, background): “Properties such as invariance and equivariance have been proposed as desiderata for representations or codes (Goodfellow et al., 2009; Kivinen & Williams, 2011; Cohen & Welling, 2014b; Lenc & Vedaldi, 2015; Jayaraman & Grauman, 2015).”
Dreaming More Data: Class-dependent Distributions over Diffeomorphisms for Learned Data Augmentation (2015, methodology): “General linear invariances are also used for restricted Boltz-mann machines [29, 44], but again the linearity implies that the invariance is only inﬁnitesimal.”
Learning Image Representations Tied to Ego-Motion (2015, background): “o studied in [17], ensures that the structure of the mapping has a simple form, and is convenient for learning since M g can be encoded as a fully connected layer in a neural network. While priorwork [14, 26] focuses on equivariancewhere gis a 2Dimagewarp, we explorethecase whereg ∈ P is an ego-moti”
Learning Image Representations Tied to Egomotion from Unlabeled Video (2017, background): “While prior work (Kivinen and Williams 2011; Schmidt and Roth 2012) focuses on equivariance where g is a 2D image warp, we explore the case where g ∈ P is an egomotion pattern (cf.”