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ref: -0 tags: inductive logic programming deepmind formal propositions prolog date: 11-21-2020 04:07 gmt revision:0 [head]

Learning Explanatory Rules from Noisy Data

  • From a dense background of inductive logic programming (ILP): given a set of statements, and rules for transformation and substitution, generate clauses that satisfy a set of 'background knowledge'.
  • Programs like Metagol can do this using search and simplify logic built into Prolog.
    • Actually kinda surprising how very dense this program is -- only 330 lines!
  • This task can be transformed into a SAT problem via rules of logic, for which there are many fast solvers.
  • The trick here (instead) is that a neural network is used to turn 'on' or 'off' clauses that fit the background knowledge
    • BK is typically very small, a few examples, consistent with the small size of the learned networks.
  • These weight matrices are represented as the outer product of composed or combined clauses, which makes the weight matrix very large!
  • They then do gradient descent, while passing the cross-entropy errors through nonlinearities (including clauses themselves? I think this is how recursion is handled.) to update the weights.
    • Hence, SGD is used as a means of heuristic search.
  • Compare this to Metagol, which is brittle to any noise in the input; unsurprisingly, due to SGD, this is much more robust.
  • Way too many words and symbols in this paper for what it seems to be doing. Just seems to be obfuscating the work (which is perfectly good). Again: Metagol is only 330 lines!

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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: -0 tags: reinforcement learning distribution DQN Deepmind dopamine date: 03-30-2020 02:14 gmt revision:5 [4] [3] [2] [1] [0] [head]

PMID-31942076 A distributional code for value in dopamine based reinforcement learning

  • Synopsis is staggeringly simple: dopamine neurons encode / learn to encode a distribution of reward expectations, not just the mean (aka the expected value) of the reward at a given state-action pair.
  • This is almost obvious neurally -- of course dopamine neurons in the striatum represent different levels of reward expectation; there is population diversity in nearly everything in neuroscience. The new interpretation is that neurons have different slopes for their susceptibility to positive and negative rewards (or rather, reward predictions), which results in different inflection points where the neurons are neutral about a reward.
    • This constitutes more optimistic and pessimistic neurons.
  • There is already substantial evidence that such a distributional representation enhances performance in DQN (Deep q-networks) from circa 2017; the innovation here is that it has been extended to experiments from 2015 where mice learned to anticipate water rewards with varying volume, or varying probability of arrival.
  • The model predicts a diversity of asymmetry below and above the reversal point
  • Also predicts that the distribution of reward responses should be decoded by neural activity ... which it is ... but it is not surprising that a bespoke decoder can find this information in the neural firing rates. (Have not examined in depth the decoding methods)
  • Still, this is a clear and well-written, well-thought out paper; glad to see new parsimonious theories about dopamine out there.

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ref: -2019 tags: meta learning feature reuse deepmind date: 10-06-2019 04:14 gmt revision:1 [0] [head]

Rapid learning or feature reuse? Towards understanding the effectiveness of MAML

  • It's feature re-use!
  • Show this by freezing the weights of a 5-layer convolutional network when training on Mini-imagenet, either 5shot 1 way, or 5shot 5 way.
  • From this derive ANIL, where only the last network layer is updated in task-specific training.
  • Show that ANIL works for basic RL learning tasks.
  • This means that roughly the network does not benefit much from join encoding -- encoding both the task at hand and the feature set. Features can be learned independently from the task (at least these tasks), with little loss.