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ref: -2015 tags: olshausen redwood autoencoder VAE MNIST faces variation date: 11-27-2020 03:04 gmt revision:0 [head]

Discovering hidden factors of variation in deep networks

  • Well, they are not really that deep ...
  • Use a VAE to encode both a supervised signal (class labels) as well as unsupervised latents.
  • Penalize a combination of the MSE of reconstruction, logits of the classification error, and a special cross-covariance term to decorrelate the supervised and unsupervised latent vectors.
  • Cross-covariance penalty:
  • Tested on
    • MNIST -- discovered style / rotation of the characters
    • Toronto faces database -- seven expressions, many individuals; extracted eigen-emotions sorta.
    • Multi-PIE --many faces, many viewpoints ; was able to vary camera pose and illumination with the unsupervised latents.

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ref: -2020 tags: replay hippocampus variational autoencoder date: 10-11-2020 04:09 gmt revision:1 [0] [head]

Brain-inspired replay for continual learning with artificial neural networks

  • Gudo M van de Ven, Hava Siegelmann, Andreas Tolias
  • In the real world, samples are not replayed in shuffled order -- they occur in a sequence, typically few times. Hence, for training an ANN (or NN?), you need to 'replay' samples.
    • Perhaps, to get at hidden structure not obvious on first pass through the sequence.
    • In the brain, reactivation / replay likely to stabilize memories.
      • Strong evidence that this occurs through sharp-wave ripples (or the underlying activity associated with this).
  • Replay is also used to combat a common problem in training ANNs - catastrophic forgetting.
    • Generally you just re-sample from your database (easy), though in real-time applications, this is not possible.
      • It might also take a lot of memory (though that is cheap these days) or violate privacy (though again who cares about that)

  • They study two different classification problems:
    • Task incremental learning (Task-IL)
      • Agent has to serially learn distinct tasks
      • OK for Atari, doesn't make sense for classification
    • Class incremental learning (Class-IL)
      • Agent has to learn one task incrementally, one/few classes at a time.
      • Like learning a 2 digits at a time in MNIST
        • But is tested on all digits shown so far.
  • Solved via Generative Replay (GR, ~2017)
  • Use a recursive formulation: 'old' generative model is used to generate samples, which are then classified and fed, interleaved with the new samples, to the new network being trained.
    • 'Old' samples can be infrequent -- it's easier to reinforce an existing memory rather than create a new one.
    • Generative model is a VAE.
  • Compared with some existing solutions to catastrophic forgetting:
    • Methods to protect parameters in the network important for previous tasks
      • Elastic weight consolidation (EWC)
      • Synaptic intelligence (SI)
        • Both methods maintain estimates of how influential parameters were for previous tasks, and penalize changes accordingly.
        • "metaplasticity"
        • Synaptic intelligence: measure the loss change relative to the individual weights.
        • δL=δLδθδθδtδt \delta L = \int \frac{\delta L}{\delta \theta} \frac{\delta \theta}{\delta t} \delta t ; converted into discrete time / SGD: L=Σ kω k=ΣδLδθδθδtδt L = \Sigma_k \omega_k = \Sigma \int \frac{\delta L}{\delta \theta} \frac{\delta \theta}{\delta t} \delta t
        • ω k\omega_k are then the weightings for how much parameter change contributed to the training improvement.
        • Use this as a per-parameter regularization strength, scaled by one over the square of 'how far it moved'.
        • This is added to the loss, so that the network is penalized for moving important weights.
    • Context-dependent gating (XdG)
      • To reduce interference between tasks, a random subset of neurons is gated off (inhibition), depending on the task.
    • Learning without forgetting (LwF)
      • Method replays current task input after labeling them (incorrectly?) using the model trained on the previous tasks.
  • Generative replay works on Class-IL!
  • And is robust -- not to many samples or hidden units needed (for MNIST)

  • Yet the generative replay system does not scale to CIFAR or permuted MNIST.
  • E.g. if you take the MNIST pixels, permute them based on a 'task', and ask a network to still learn the character identities , it can't do it ... though synaptic intelligence can.
  • Their solution is to make 'brain-inspired' modifications to the network:
    • RtF, Replay-though-feedback: the classifier and generator network are fused. Latent vector is the hippocampus. Cortex is the VAE / classifier.
    • Con, Conditional replay: normal prior for the VAE is replaced with multivariate class-conditional Gaussian.
      • Not sure how they sample from this, check the methods.
    • Gat, Gating based on internal context.
      • Gating is only applied to the feedback layers, since for classification ... you don't a priori know the class!
    • Int, Internal replay. This is maybe the most interesting: rather than generating pixels, feedback generates hidden layer activations.
      • First layer of a network is convolutional, dependent on visual feature statistics, and should not change much.
        • Indeed, for CIFAR, they use pre-trained layers.
      • Internal replay proved to be very important!
    • Dist, Soft target labeling of the generated targets; cross-entropy loss when training the classifier on generated samples. Aka distillation.
  • Results suggest that regularization / metaplasticity (keeping memories in parameter space) and replay (keeping memories in function space) are complementary strategies,
    • And that the brain uses both to create and protect memories.

  • When I first read this paper, it came across as a great story -- well thought out, well explained, a good level of detail, and sufficiently supported by data / lesioning experiments.
  • However, looking at the first authors pub record, it seems that he's been at this for >2-3 years ... things take time to do & publish.
  • Folding in of the VAE is satisfying -- taking one function approximator and use it to provide memory for another function approximator.
  • Also satisfying are the neurological inspirations -- and that full feedback to the pixel level was not required!
    • Maybe the hippocampus does work like this, providing high-level feature vectors to the cortex.
    • And it's likely that the cortex has some features of a VAE, e.g. able to perceive and imagine through the same nodes, just run in different directions.
      • The fact that both concepts led to an engineering solution is icing on the cake!

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ref: -2017 tags: google deepmind compositional variational autoencoder date: 04-08-2020 01:16 gmt revision:7 [6] [5] [4] [3] [2] [1] [head]

SCAN: learning hierarchical compositional concepts

  • From DeepMind, first version Jul 2017 / v3 June 2018.
  • Starts broad and strong:
    • "The seemingly infinite diversity of the natural world from a relatively small set of coherent rules"
      • Relative to what? What's the order of magnitude here? In personal experience, each domain involves a large pile of relevant details..
    • "We conjecture that these rules dive rise to regularities that can be discovered through primarily unsupervised experiences and represented as abstract concepts"
    • "If such representations are compositional and hierarchical, they can be recombined into an exponentially large set of new concepts."
    • "Compositionality is at the core of such human abilities as creativity, imagination, and language-based communication.
    • This addresses the limitations of deep learning, which are overly data hungry (low sample efficiency), tend to overfit the data, and require human supervision.
  • Approach:
    • Factorize the visual world with a Β\Beta -VAE to learn a set of representational primitives through unsupervised exposure to visual data.
    • Expose SCAN (or rather, a module of it) to a small number of symbol-image pairs, from which the algorithm identifies the set if visual primitives (features from beta-VAE) that the examples have in common.
      • E.g. this is purely associative learning, with a finite one-layer association matrix.
    • Test on both image 2 symbols and symbols to image directions. For the latter, allow irrelevant attributes to be filled in from the priors (this is important later in the paper..)
    • Add in a third module, which allows learning of compositions of the features, ala set notation: AND ( \cup ), IN-COMMON ( \cap ) & IGNORE ( \setminus or '-'). This is via a low-parameter convolutional model.
  • Notation:
    • q ϕ(z x|x)q_{\phi}(z_x|x) is the encoder model. ϕ\phi are the encoder parameters, xx is the visual input, z xz_x are the latent parameters inferred from the scene.
    • p theta(x|z x)p_{theta}(x|z_x) is the decoder model. xp θ(x|z x)x \propto p_{\theta}(x|z_x) , θ\theta are the decoder parameters. xx is now the reconstructed scene.
  • From this, the loss function of the beta-VAE is:
    • 𝕃(θ,ϕ;x,z x,β)=𝔼 q ϕ(z x|x)[logp θ(x|z x)]βD KL(q ϕ(z x|x)||p(z x)) \mathbb{L}(\theta, \phi; x, z_x, \beta) = \mathbb{E}_{q_{\phi}(z_x|x)} [log p_{\theta}(x|z_x)] - \beta D_{KL} (q_{\phi}(z_x|x)|| p(z_x)) where Β>1\Beta \gt 1
      • That is, maximize the auto-encoder fit (the expectation of the decoder, over the encoder output -- aka the pixel log-likelihood) minus the KL divergence between the encoder distribution and p(z x)p(z_x)
        • p(z)𝒩(0,I)p(z) \propto \mathcal{N}(0, I) -- diagonal normal matrix.
        • β\beta comes from the Lagrangian solution to the constrained optimization problem:
        • max ϕ,θ𝔼 xD[𝔼 q ϕ(z|x)[logp θ(x|z)]]\max_{\phi,\theta} \mathbb{E}_{x \sim D} [\mathbb{E}_{q_{\phi}(z|x)}[log p_{\theta}(x|z)]] subject to D KL(q ϕ(z|x)||p(z))<εD_{KL}(q_{\phi}(z|x)||p(z)) \lt \epsilon where D is the domain of images etc.
      • Claim that this loss function tips the scale too far away from accurate reconstruction with sufficient visual de-tangling (that is: if significant features correspond to small details in pixel space, they are likely to be ignored); instead they adopt the approach of the denoising auto-encoder ref, which uses the feature L2 norm instead of the pixel log-likelihood:
    • 𝕃(θ,ϕ;X,z x,β)=𝔼 q ϕ(z x|x)||J(x^)J(x)|| 2 2βD KL(q ϕ(z x|x)||p(z x)) \mathbb{L}(\theta, \phi; X, z_x, \beta) = -\mathbb{E}_{q_{\phi}(z_x|x)}||J(\hat{x}) - J(x)||_2^2 - \beta D_{KL} (q_{\phi}(z_x|x)|| p(z_x)) where J: WxHxC NJ : \mathbb{R}^{W x H x C} \rightarrow \mathbb{R}^N maps from images to high-level features.
      • This J(x)J(x) is from another neural network (transfer learning) which learns features beforehand.
      • It's a multilayer perceptron denoising autoencoder [Vincent 2010].
  • The SCAN architecture includes an additional element, another VAE which is trained simultaneously on the labeled inputs yy and the latent outputs from encoder z xz_x given xx .
  • In this way, they can present a description yy to the network, which is then recomposed into z yz_y , that then produces an image x^\hat{x} .
    • The whole network is trained by minimizing:
    • 𝕃 y(θ y,ϕ y;y,x,z y,β,λ)=1 st2 nd3 rd \mathbb{L}_y(\theta_y, \phi_y; y, x, z_y, \beta, \lambda) = 1^{st} - 2^{nd} - 3^{rd}
      • 1st term: 𝔼 q ϕ y(z y|y)[logp θ y(y|z y)] \mathbb{E}_{q_{\phi_y}(z_y|y)}[log p_{\theta_y} (y|z_y)] log-likelihood of the decoded symbols given encoded latents z yz_y
      • 2nd term: βD KL(q ϕ y(z y|y)||p(z y)) \beta D_{KL}(q_{\phi_y}(z_y|y) || p(z_y)) weighted KL divergence between encoded latents and diagonal normal prior.
      • 3rd term: λD KL(q ϕ x(z x|y)||q ϕ y(z y|y))\lambda D_{KL}(q_{\phi_x}(z_x|y) || q_{\phi_y}(z_y|y)) weighted KL divergence between latents from the images and latents from the description yy .
        • They note that the direction of the divergence matters; I suspect it took some experimentation to see what's right.
  • Final element! A convolutional recombination element, implemented as a tensor product between z y1z_{y1} and z y2z_{y2} that outputs a one-hot encoding of set-operation that's fed to a (hardcoded?) transformation matrix.
    • I don't think this is great shakes. Could have done this with a small function; no need for a neural network.
    • Trained with very similar loss function as SCAN or the beta-VAE.

  • Testing:
  • They seem to have used a very limited subset of "DeepMind Lab" -- all of the concept or class labels could have been implimented easily, e.g. single pixel detector for the wall color. Quite disappointing.
  • This is marginally more interesting -- the network learns to eliminate latent factors as it's exposed to examples (just like perhaps a Bayesian network.)
  • Similarly, the CelebA tests are meh ... not a clear improvement over the existing VAEs.

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ref: -2011 tags: Andrew Ng high level unsupervised autoencoders date: 03-15-2019 06:09 gmt revision:7 [6] [5] [4] [3] [2] [1] [head]

Building High-level Features Using Large Scale Unsupervised Learning

  • Quoc V. Le, Marc'Aurelio Ranzato, Rajat Monga, Matthieu Devin, Kai Chen, Greg S. Corrado, Jeff Dean, Andrew Y. Ng
  • Input data 10M random 200x200 frames from youtube. Each video contributes only one frame.
  • Used local receptive fields, to reduce the communication requirements. 1000 computers, 16 cores each, 3 days.
  • "Strongly influenced by" Olshausen & Field {1448} -- but this is limited to a shallow architecture.
  • Lee et al 2008 show that stacked RBMs can model simple functions of the cortex.
  • Lee et al 2009 show that convolutonal DBN trained on faces can learn a face detector.
  • Their architecture: sparse deep autoencoder with
    • Local receptive fields: each feature of the autoencoder can connect to only a small region of the lower layer (e.g. non-convolutional)
      • Purely linear layer.
      • More biologically plausible & allows the learning of more invariances other than translational invariances (Le et al 2010).
      • No weight sharing means the network is extra large == 1 billion weights.
        • Still, the human visual cortex is about a million times larger in neurons and synapses.
    • L2 pooling (Hyvarinen et al 2009) which allows the learning of invariant features.
      • E.g. this is the square root of the sum of the squares of its inputs. Square root nonlinearity.
    • Local contrast normalization -- subtractive and divisive (Jarrett et al 2009)
  • Encoding weights W 1W_1 and deconding weights W 2W_2 are adjusted to minimize the reconstruction error, penalized by 0.1 * the sparse pooling layer activation. Latter term encourages the network to find invariances.
  • minimize(W 1,W 2) minimize(W_1, W_2) i=1 m(||W 2W 1 Tx (i)x (i)|| 2 2+λ j=1 kε+H j(W 1 Tx (i)) 2) \sum_{i=1}^m {({ ||W_2 W_1^T x^{(i)} - x^{(i)} ||^2_2 + \lambda \sum_{j=1}^k{ \sqrt{\epsilon + H_j(W_1^T x^{(i)})^2}} })}
    • H jH_j are the weights to the j-th pooling element, λ=0.1\lambda = 0.1 ; m examples; k pooling units.
    • This is also known as reconstruction Topographic Independent Component Analysis.
    • Weights are updated through asynchronous SGD.
    • Minibatch size 100.
    • Note deeper autoencoders don't fare consistently better.