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ref: -2019 tags: lillicrap google brain backpropagation through time temporal credit assignment date: 03-14-2019 20:24 gmt revision:2 [1] [0] [head]

PMID-22325196 Backpropagation through time and the brain

  • Timothy Lillicrap and Adam Santoro
  • Backpropagation through time: the 'canonical' expansion of backprop to assign credit in recurrent neural networks used in machine learning.
    • E.g. variable rol-outs, where the error is propagated many times through the recurrent weight matrix, W TW^T .
    • This leads to the exploding or vanishing gradient problem.
  • TCA = temporal credit assignment. What lead to this reward or error? How to affect memory to encourage or avoid this?
  • One approach is to simply truncate the error: truncated backpropagation through time (TBPTT). But this of course limits the horizon of learning.
  • The brain may do BPTT via replay in both the hippocampus and cortex Nat. Neuroscience 2007, thereby alleviating the need to retain long time histories of neuron activations (needed for derivative and credit assignment).
  • Less known method of TCA uses RTRL Real-time recurrent learning forward mode differentiation -- δh t/δθ\delta h_t / \delta \theta is computed and maintained online, often with synaptic weight updates being applied at each time step in which there is non-zero error. See A learning algorithm for continually running fully recurrent neural networks.
    • Big problem: A network with NN recurrent units requires O(N 3)O(N^3) storage and O(N 4)O(N^4) computation at each time-step.
    • Can be solved with Unbiased Online Recurrent optimization, which stores approximate but unbiased gradient estimates to reduce comp / storage.
  • Attention seems like a much better way of approaching the TCA problem: past events are stored externally, and the network learns a differentiable attention-alignment module for selecting these events.
    • Memory can be finite size, extending, or self-compressing.
    • Highlight the utility/necessity of content-addressable memory.
    • Attentional gating can eliminate the exploding / vanishing / corrupting gradient problems -- the gradient paths are skip-connections.
  • Biologically plausible: partial reactivation of CA3 memories induces re-activation of neocortical neurons responsible for initial encoding PMID-15685217 The organization of recent and remote memories. 2005

  • I remain reserved about the utility of thinking in terms of gradients when describing how the brain learns. Correlations, yes; causation, absolutely; credit assignment, for sure. Yet propagating gradients as a means for changing netwrok weights seems at best a part of the puzzle. So much of behavior and internal cognitive life involves explicit, conscious computation of cause and credit.
  • This leaves me much more sanguine about the use of external memory to guide behavior ... but differentiable attention? Hmm.

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ref: -2014 tags: Lillicrap Random feedback alignment weights synaptic learning backprop MNIST date: 02-14-2019 01:02 gmt revision:5 [4] [3] [2] [1] [0] [head]

PMID-27824044 Random synaptic feedback weights support error backpropagation for deep learning.

  • "Here we present a surprisingly simple algorithm for deep learning, which assigns blame by multiplying error signals by a random synaptic weights.
  • Backprop multiplies error signals e by the weight matrix W T W^T , the transpose of the forward synaptic weights.
  • But the feedback weights do not need to be exactly W T W^T ; any matrix B will suffice, so long as on average:
  • e TWBe>0 e^T W B e > 0
    • Meaning that the teaching signal Be B e lies within 90deg of the signal used by backprop, W Te W^T e
  • Feedback alignment actually seems to work better than backprop in some cases. This relies on starting the weights very small (can't be zero -- no output)

Our proof says that weights W0 and W
evolve to equilibrium manifolds, but simulations (Fig. 4) and analytic results (Supple-
mentary Proof 2) hint at something more specific: that when the weights begin near
0, feedback alignment encourages W to act like a local pseudoinverse of B around
the error manifold. This fact is important because if B were exactly W + (the Moore-
Penrose pseudoinverse of W ), then the network would be performing Gauss-Newton
optimization (Supplementary Proof 3). We call this update rule for the hidden units
pseudobackprop and denote it by ∆hPBP = W + e. Experiments with the linear net-
work show that the angle, ∆hFA ]∆hPBP quickly becomes smaller than ∆hFA ]∆hBP
(Fig. 4b, c; see Methods). In other words feedback alignment, despite its simplicity,
displays elements of second-order learning.

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ref: -0 tags: lillicrap segregated dendrites deep learning backprop date: 01-31-2019 19:24 gmt revision:2 [1] [0] [head]

PMID-29205151 Towards deep learning with segregated dendrites https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5716677/

  • Much emphasis on the problem of credit assignment in biological neural networks.
    • That is: given complex behavior, how do upstream neurons change to improve the task of downstream neurons?
    • Or: given downstream neurons, how do upstream neurons receive ‘credit’ for informing behavior?
      • I find this a very limiting framework, and is one of my chief beefs with the work.
      • Spatiotemporal Bayesian structure seems like a much better axis (axes) to cast function against.
      • Or, it could be segregation into ‘signal’ and ‘error’ or ‘figure/ground’ based on hierarchical spatio-temporal statistical properties that matters ...
      • ... with proper integration of non-stochastic spike timing + neoSTDP.
        • This still requires some solution of the credit-assignment problem, i know i know.
  • Outline a spiking neuron model with zero one or two hidden layers, and a segregated apical (feedback) and basal (feedforward) dendrites, as per a layer 5 pyramidal neuron.
  • The apical dendrites have plateau potentials, which are stimulated through (random) feedback weights from the output neurons.
  • Output neurons are forced to one-hot activation at maximum firing rate during training.
    • In order to assign credit, feedforward information must be integrated separately from any feedback signals used to calculate error for synaptic updates (the error is indicated here with δ). (B) Illustration of the segregated dendrites proposal. Rather than using a separate pathway to calculate error based on feedback, segregated dendritic compartments could receive feedback and calculate the error signals locally.
  • Uses the MNIST database, naturally.
  • Poisson spiking input neurons, 784, again natch.
  • Derive local loss function learning rules to make the plateau potential (from the feedback weights) match the feedforward potential
    • This encourages the hidden layer -> output layer to approximate the inverse of the random feedback weight network -- which it does! (At least, the jacobians are inverses of each other).
    • The matching is performed in two phases -- feedforward and feedback. This itself is not biologically implausible, just unlikely.
  • Achieved moderate performance on MNIST, ~ 4%, which improved with 2 hidden layers.
  • Very good, interesting scholarship on the relevant latest findings ‘’in vivo’’.
  • While the model seems workable though ad-hoc or just-so, the scholarship points to something better: use of multiple neuron subtypes to accomplish different elements (variables) in the random-feedback credit assignment algorithm.
    • These small models can be tuned to do this somewhat simple task through enough fiddling & manual (e.g. in the algorithmic space, not weight space) backpropagation of errors.
  • They suggest that the early phases of learning may entail learning the feedback weights -- fascinating.
  • ‘’Things are definitely moving forward’’.