Sparse Distributed Representations (SDRs)

TL;DR:

• An SDR is a Sparse Distributed Representation, described below
• SDRs are biologically plausible data structures
• SDRs have powerful properties
• SDRs have received a lot of attention recently
• There are a few really great new resources on the topic:
• Presentation by Subutai Ahmad of Numenta 
• Older introductory presentation by Jeff Hawkins
• Excellent summary of their characteristics in Ferrier’s draft paper (discussed in an earlier blog post) 

Background

An SDR is a binary vector, where only a small portion of the bits are ‘on’. There is growing evidence that SDRs are a feature of biological computation, for storing and conveying information. In a biological context, this represents a small number of active cells in a population of cells. SDR’s have been adopted by HTM (in CLA), and HTM's focus on this has set it apart from the bulk of mainstream machine learning research.

SDRs have very promising characteristics and are still relatively under utilised in the field of AI and machine learning. It’s an exciting area to be watching as AGI leaps forward.

The concept of SDRs are not new however. Kanerva first proposed a sparse distributed memory as a physiologically plausible model for human memory in his influential 1988 book Sparse Distributed Memory [Kanerva1988]. The properties of sparse distributed memory were nicely summarised by Denning in 1989 [Denning1989].

As early as 1997, Hinton and Ghahramani described a generative model, implementable with a neural network, that ‘discovered’ sparse distributed representations for image analysis [Hinton1997].

Then in 1998 SDRs were used in the context of robot control for navigation by both Rajesh et. al and Rao et. al [Rajesh1998, Rao1998] and then in 2004 for reinforcement learning by Ratitch [Ratitch2004].

Recently some great new resources have become available. There is a new video from Numenta of Subutai Ahmad presenting on the topic. A nice companion to that is an older introductory video of Jeff Hawkins presenting. The recent draft paper by Ferrier on a universal cortical algorithm (discussed in an earlier blog post) gives an excellent summary of their characteristics.

What’s all the fuss about? - SDR Characteristics

Given that so much great (and recent) material exists describing SDRs, I won’t go into very much detail. This post would not be complete though, without at least a cursory look at the ‘highlights’ of SDRs.

• Semantic
• each bit corresponds to something meaningful
• Efficient/Versatile
• storage: there is a huge number of potential encodings for a given vector size, as capacity increases exponentially with number of potentially active bits
• compositionality: because of sparsity SDRs are generally linearly separable and can therefore be combined to represent a set of several states
• comparisons: it is very efficient to measure similarity between vectors (you just need to count overlap of ‘on’ bits) and if a state is part of a set (due to compositionality)
• Robust
• subsampled or noisy vectors are still semantically similar and can be compared effectively

Conclusion

We believe that these elements make SDRs an excellent choice as the main data structure of any AGI implementation - they are used in our current approach. The highlights and links given above should be a good start to anyone that wants to learn more.

Toward a Universal Cortical Algorithm: Examining Hierarchical Temporal Memory in Light of Frontal Cortical Function

This post is about a fantastic new paper by Michael R. Ferrier, titled:

Toward a Universal Cortical Algorithm: Examining Hierarchical Temporal Memory in Light of Frontal Cortical Function

The paper was posted to the NUPIC mailing list and can be found via:

http://numenta.org/community-content.html

The paper itself is currently hosted at:

https://drive.google.com/file/d/0B0RWGGOoommKM0llNUF3V2JJYTg/view

It isn't clear if this is going to be formally published in a journal at some point. If this happens we'll update the link.

So, what do we like about this paper?

Purpose & Structure of the paper

The paper is mostly a literature review and is very well referenced. This is a great introductory work to the topic.

The paper aims to look at the evidence for the existence of a universal cortical algorithm - i.e. one that can explain the anatomical features and function of the entire cortex. It is unknown whether such an algorithm exists, but there is some evidence it might. Or, more likely, variants of the same algorithm are used throughout the cortex.

The paper is divided into 3 parts. First, it reviews some relevant & popular algorithms that generate hierarchical models. These include Deep Learning, various forms of Bayesian inference, Predictive Coding, Temporal Slowness and Multi-Stage Hubel Wiesel Architectures (MHWA). I'd never heard of MHWA before, though some of the examples (such as convolutional networks and HMAX) are familiar.  The different versions of HTM are also described.

It is particularly useful that the author puts the components of HTM in a well-referenced context. We can see that the HTM/CLA Spatial Pooler is a form of Competitive Learning and that the proposed new HTM/CLA Temporal Pooler is an example of the Temporal Slowness principle. The Sequence Memory component is trained by a variant of Hebbian learning.

These ties to existing literature are useful because they allow us to understand the properties and alternatives to these algorithms: Earlier research has thoroughly explored their capabilities and limitations.

Although not an algorithm per se, Sparse Distributed Representations are explained particularly well. The author contrasts 3 types of representation: Localist (single feature or label represents state), Sparse and Dense. He argues that Sparse representations are preferable to Localist because the former can be gradually learnt and are more robust to small variations.

Frontal Cortex

The second part of the paper reviews the biology of frontal cortex regions. These regions are not normally described in computational theories. Ferrier suggests this omission is because these regions are less well understood, so they offer less insight and support for theory.

However these cortical areas are of particular interest because they are responsible for representation of tasks, goals, strategy and reward; the origin of goal-directed behaviour and motor control.

Of particular interest to us is discussion of biological evidence for the hierarchical generation of motor behaviour and output to motors directly from cortex.

Thalamus and Basal Ganglia

The paper discusses the role of the Thalamus in gating messages between cortical regions, and discusses evidence that the purpose of the Striatum and Basal Ganglia could include deciding which messages are filtered in the Thalamus.  Filtering is suggested to perform the roles of attention and control (this all perfectly matches our understanding of the same).

There is a brief discussion of Reinforcement Learning (specifically, Temporal-Difference learning) as a computational analogue of Thalamic filter weighting. This has been exhaustively covered in the literature so wasn't a surprise.

Towards a Comprehensive Model of Cortical Function

The final part of the paper links the computational theories to the referenced biology. There are some interesting insights (such as that messages in the feedback pathway from layer 5 to layer 1 in hierarchically lower regions must be "expanding" time; personally I think these messages are being re-interpreted in expanded time form on receipt).

Our general expectation is that feedback messages representing predicted state are being selectively biased or filtered towards "predicting" that the agent achieves rewards; in this case the biased or filtered predictions are synonymous with goal-seeking strategies.

Overall the paper does a great job of linking the "ghetto" of HTM-like computational theories with the relevant techniques in machine learning and neurobiology.