[Comp-neuro] Re: Attractors, variability and noise

Mario Negrello mnegrello at gmail.com
Tue Aug 12 16:27:49 CEST 2008


Ross, List,

>
> I'll make some responses to your post, although they speak rather  
> indirectly
> to issues of variability and noise.  Also, although I am working with
> connectionist systems my perspective is one of artificial intelligence
> engineering - I am trying to achieve functional performance without  
> any
> specific concern for biological plausibility.  (Having said that, the
> mechanisms I am investigating are not obviously incompatible with  
> neural
> implementation.)

This degree of correspondance is my main interest right now. I'd like  
to know to what extent analytic arguments about NNs of different sorts  
are more than mere analogies. Functional performance is at the core of  
the issue, as function has the troubles of being defined subjectively.
>
>> What do you think of recurrent neural networks (RNNs), with their  
>> wealth
> of attractors, as a model for variability/noise?
>
> In general, I have no idea.  [...] Arathorn claims that this  
> parallels some aspects of cortical
> architecture.  I wouldn't know about that.  The point is that this  
> allows a
> level of variability that is greater than most people would assume  
> when
> thinking about RNNs.  The point is that there are multiplicative
> interactions and there are internal degrees of freedom (the  
> selection of the
> transforms) - so that effectively the system has attractors that  
> evolve over
> the same time scale as the settling of the RNN.

I am somewhat familiar with arathorn's work, but his claims of  
plausibility (as you point out) may be more particular than general.  
In any case, to understand networks with high level of variability is  
a must for us.

You say attractors evolve as they are being visited. I wonder to what  
extent that is the case, for instance, in mammalian motor systems,  
where there are obvious advangates of having a somewhat stable system.  
One can think of other examples, consider invertebrates with many  
fewer neurons and networks that are somewhat stabler. What systems are  
emblematic of the role of multiplicative interactions?

> Let me return to an argument from cognitive function.  We can  
> recognise
> novel situations almost as rapidly as familiar ones.  All the time  
> we are
> exposed to and deal with novel situations (e.g. my hovercraft is  
> full of
> eels).  If we assume (as I do) that RNNs are a natural basis for  
> neural
> computation, then you think in terms of attractors.  Familiar  
> situations are
> recognised rapidly by the process of settling into an attractor.   
> But even
> novel situations are recognised so rapidly that it suggests they too  
> are
> recognised by the same process.  However, it is implausible to  
> believe that
> the brain comes pre-stocked with an attractor for every situation  
> which
> might ever arise (this is the dynamic systems equivalent of the  
> "grandmother
> cell" argument).  I believe the solution to this is to have dynamic
> attractors, i.e. attractors that are created on the fly to meet the  
> need of
> the moment.  Where there are multiplicative interactions one RNN can
> modulate the dynamics of another RNN leading to new attractors.

Intersting point about dynamic attractors. You talk about the creation  
of new attractors for recognition. But is it not the case that a fixed  
network structure already has an implicit attractor structure?  
Different initial conditions can take the network to attractors that  
have not yet been visited, but putatively already existed. This  
assumes fixed network structures, somewhat. The extent to which  
plasticity will impact on the visited attractors, is the extent to  
which we can talk about newly created attractors. Even so, plasticity  
may happen parallely. The brain may be in constant change, but the  
changes maybe modularized, hence, some attractor structures can  
remained unchanged while others do change. Would you agree with this?

But the brain structure changes less and less with age. So, one can  
think new thoughts, but these are compositional. Using the attractor  
structure already available, but in new combinations.

Could you comment on the following question: To what extent  
multiplicative interactions maintain attractor structures unaltered?

>
> The notion is to have the attractor corresponding to the entire  
> input arise
> as a function of the attactors corresponding to components of the  
> input.
> This relates to the notion of systematicity, which holds that a  
> system able
> to represent some situations (e.g. John loves Mary) will  
> *necessarily* be
> able to represent other related situations (e.g. Mary loves John).   
> This
> arises as a consequence of representations being composites of  
> components
> (which can be interchanged).

So, that's the idea with compositionality of attractors. It is amusing  
that we connectionists are driven back to explain stuff that old AI  
had to assume. Looking for mechanisms compositionality in neural  
networks leads to interesting conclusions about the 'meaning' of  
attractors.

In neural networks both orders, J loves M, and M loves J, may have  
different implications. Say, they evoke different emotions from the  
perspective of the thinker of the thoughts. E.g., J loves M implies  
Jealousy and M loves J implies disappointment.

In a sense, one can think of RNNs lodging not only the attractors that  
enable compositional thougths, but also having attractor structures  
that induce some further implications. For that, in principle, one  
wouldn't need to generate new attractors, in the sense that the net  
struct is fixed in a certain time scale. Or one could think that some  
changes in the network will have the same 'meaning'. That is, they  
will produce similar dispositions, or evoke similar categories of  
outputs. In that case, there must be a many to one mapping from  
attractors to categories. This is to say that a lot of neural changes  
may be irrelevant for categorization. It goes back to the idea that  
variation which is not useful is noise. The querstion becomes: from  
the perspective of the organism, when are two attractors the same? In  
other words, when do two attractors have the same meaning?

The answer to that question seem to me to point out that it is not  
only noise that has to be defined in terms of the observer, but also  
'stability'.  Two attractors (or transients) that have the same stable  
meaning, will be equivalent. In order to verify stability, one will  
have to make subjective assumptions about the meaning of the  
attractors. If the attractors predispose the same responses, they are  
essentially the same. Correct?

> The only point I really want to make out of this is that when you are
> dealing with RNNs in cognitive systems you should allow for the  
> likelihood
> that the attractors are dynamic and novel unless you are probing with
> exceptionally impoverished stimuli (which is probably the norm in
> electrophysiology).

It's a good point. But even with empoverished stimuli, there can be a  
lot of variability in the neurophysiology (unless one probes very  
close to the lower level sensory sheets). Interestingly, and i think  
this is a major point,



PS. Some might have noticed that there was a posting coming from my  
address with splintered phrases. I sent it by mistake, apologies for  
that!


> -----Original Message-----
> From: Mario Negrello [mailto:mnegrello at gmail.com]
> Sent: Saturday, 2 August 2008 12:33 AM
> To: r.gayler at mbox.com.au
> Cc: comp-neuro at neuroinf.org
> Subject: Attractors, variability and noise
>
> Dear Ross, Jim, David and list,
>
> First off, thank you for amazing discussion. I hope there is still  
> some
> momentum in it.
> I take the opportunity to summarize and combine a couple of points,  
> and pose
> a question.
>
> David Tam, among others, remarked that
>> "So do neurons (or the brain) use noise in its computation?  If the
>> neurons care about those signals, it is not noise.  If they don't
>> care, yes, then it is noise."
>
> This is a good working definition for noise, as it takes the  
> 'receiver' into
> consideration. I'll phrase it in terms of variability, if i may  
> (it's for a
> purpose):
> - When the receiving system is indifferent to incoming variability,  
> then
> that variability is noise.
>
> Jim and others insisted that it is hard to tell noise and  
> variability apart,
> when the systems are complex.
>>> the more sophisticated a coding system, the harder it is likely to  
>>> be
>>> to distinguish signal from "noise".
>
> 1. As Ross points out, concerning abstract connectionist models, the
> response of a single neuron may look random, because we d.on't see the
> multidimensional pattern of activity, by recording one neuron.
> 2. And as david adds, neural computation is distinction, if there is  
> no
> distinction, no computation.
> 3. Moreover, Jim added that (3) neural computation is likely to be
> sequential.
>
> The points above fit nicely with the idea that brain networks are  
> analogous
> to recurrent neural networks, which have, instead of a lot of noise,  
> complex
> transients.
>
> The question: What do you think of recurrent neural networks (RNNs),  
> with
> their wealth of attractors, as a model for variability/noise?
> Large networks produce much repeatable variability in 'unpredictable'
> oscillatory patterns. But with knowledge of the network structure,  
> much can
> be known about the possible dynamical patterns that the system may  
> produce.
> And with respect to functional levels,  one can distinguish between
> meaningful and meaningless variability. (by functional levels, i  
> mean levels
> of the network we may attrbitute particular functions, say perceptual
> categorization or motor pattern formation).
>
> Regarding the items above:
> To (1), It is self-evident when one takes a large network of, say,  
> sigmoidal
> units, and looks at the activity of any one neuron. Though the path  
> of the
> transients in phase space is highly structured, the activity of the   
> single
> neuron is scarcely predictable without knowledge of the network  
> structure.
> But if one has knowledge about the structure, she also has info about
> possible activities patterns.
>
> Will these patterns resemble those of more complex biological  
> networks? My
> guess is yes, to the extent of the level of abstraction introduced.
>
> To (2), there is something that can be said in terms of distinction
> mechanisms, and transient activity. If one considers the transient  
> activity
> of a module/area as an open path in phase space (an orbit), then the
> activity of one neuron must be a projection of all the incoming  
> activity,
> onto the hyperplane defined by the projections weight matrix (attached
> diagram).
>



|============]M[=============|
|www.firingrates.blogspot.com|

Every machine is the spiritualization of an organism.

Theo van Doesburg (1883-1931)



More information about the Comp-neuro mailing list