NumentaResearch

Results of Numenta Research

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References

• Jeff Hawkins and others - [memory for prediction, inference and behaviour] - This paper proposes how each region of neocortex might learn the sequences necessary for this theory
• 2010 Lecture by Jeff Hawkins - [[1]]
• 2010 Understanding the Bitworm NuPIC HTM Example Program - [[2]]

Hierarchical Memory Models

• *Spatial only*: Convolutional Neural Networks (Le Cun & Bengio) - 1995; HMAX (Riesenhuber & Poggio) - 1999
• *Temporal*: HHMM - hierarchical hidden Markov model (Fine et al.) - 1998
• *Spatial and Temporal*: HTM (Numenta) - 2005

Constraints

Requirements that a biological sequence memory must meet, which are different from linear computer memory.

• *Probabilistic prediction* - input and prediction are probability distributions
• *Simultaneous learning and recall* - simultaneously recalling and predicting
• *Auto-associative recall* - recognize sequences even if it is presented with a partial sequence from the middle of a previously learned sequence; naturally auto-associative
• *Variable-order memory* - ‘ABCDE’ and ‘YBCDZ’ - correctly predict the last element of the sequence based on an input that occurred many time steps earlier; the internal representation of an afferent pattern must change depending on the temporal context in which it occurs; the representation for the elements ‘B’, ‘C’ and ‘D’ must be somehow different when preceded by ‘A’ than by ‘Y’
• *Biological constraints* - any proposed mechanism should map to one or more prominent features of neocortical anatomy

Biological Implications

• *Sparsification of response* - general cell activity in the neocortex should become more sparse and selective when receiving input in naturally occurring sequences versus receiving spatial inputs in temporal isolation or random order; sparse encoding - efficient method of representation in neural tissue
• *Inhibitory requirements* - excitatory lateral input to one or a few cells inhibits all the other cells in the near proximity; this laterally induced inhibition must be stronger and faster than the feed-forward excitation
• *Distributed representations* - distributed representations in two ways:

* in almost all cases, multiple cells are simultaneously active, although the pattern of activation will always be sparse
* activations are distributed; every region of the hierarchy passes a distribution of potentially active sequences to its parent regions

• *Efficient computation* - use information from previous inputs when making predictions, and both the history of inputs and the forward predictions are distributions over many states; calculation using dynamic programming by Bellman (see George, D. 2008 How the brain might work: a hierarchical and temporal model for learning and recognition. PhD thesis, Stanford University. §4.6.2)
• *Cortical layers* - some cell layers are learning feed-forward sequences (layers 4 and 3) and other layers are learning feedback sequences (layers 2 and 6). Layer 5 is where they are combined to form a belief
• *Sequence timing* - remember the duration for each element in the sequence; can speed up or slow down a recalled sequence, but the absolute duration of the sequence elements is stored and can be recalled; needs a neural mechanism that can encode the durations of sequence elements; this neural mechanism should exist in all regions of the neocortex and should be tightly coupled with the sequence memory mechanism; duration limits need not be fixed, but could depend on the parameters of the model
• *Memory capacity* - if have 12 columns each with 50 cells, where each column represents one of the 12 musical tones inWestern music, then:

* it could learn a single sequence of 600 notes using exactly 50 of each of the 12 tones
* it could learn 100 sequences of six notes each
* capacity of HTM derives primarily from the hierarchy, not the sequence memory in each node; the hierarchy allows learned sequences to be used repeatedly in different combinations

Implementation Hints

cortex implementation:

• columns with neurons having the same inputs
• lateral excitatory and inhibitory connections to model sequence activation; in human brain neocortex lateral connections are 90%, with only 10% feed-forward ones
• if one cell in the column becomes active it uses inhibitory lateral connections to hide other cells in the same column - "shut up the other guys"

general:

• bayesian network
• dynamic programming by Bellman to re-use history
• FDR - Fixed-sparsity Distributed Representation

spatial details:

• RBFs are used to make quantization points
• continuous representaion is ultimate goal, still not implemented in HTM

temporal patterns:

• variable-order Markov chain
• sequences of different length
• no sequence begin/end marks
• able to match sequence by middle part
• state-splitting algorithm
• store duration for each sequence item

Regions

• Region 1: run Spatial Pooler ->
• Region 1: run Temporal Pooler (form sequence memory) ->
• Region 2: run Spatial Pooler -> ...