Write-Only Memory

By Jessica Lake

I have been thinking about semantic knowledge.

Dangerous, I know.

For most of my life I thought of memory the obvious way. Something happens. You remember it. Presumably somewhere between happening and remembering, the brain stores something.

A recording of sorts.

I am no longer convinced that is a particularly useful way to think about semantic knowledge.

I wonder if semantic knowledge stores something very different.

Notch filters.

Let me explain.

You carve a notch into the edge of a bench as a precise marker. A notch filter carves a sharp, narrow groove out of the radio frequency spectrum. It blocks out a precise sliver of noise.

I am going to take some liberties with the concept. My notch filter is a bi-model transform.

Inclusively, it lets through the information within the notch.

Exclusively, it removes that information within the notch and lets everything else through.

That turns out to be potent. Reality contains an absurd amount of information.

Look at a tree.

How much information is equired to describe it completely?

Every leaf. Every vein in every leaf. Every molecule. Every photon reflected from its surface. Every movement caused by every puff of wind.

Forget about it.

No finite mind could contain reality. Fortunately, it doesn’t have to. I don’t need the tree. 7I need just enough of the “tree.”

That distinction is important.

By the way, there is already a problem way before semantic knowledge gets involved.

Out brains never observe reality directly.

Instead we have instruments.

  • Eyes.

  • Ears.

  • Skin.

  • Nose.

And when those aren’t good enough, we builds better ones.

  • Telescopes.

  • Radio telescopes.

  • Microscopes.

  • Electron microscopes.

Every instrument has its limitations. It measures some things and not others. It has a range, resolution, sensitivity, sampling rate, noise rejection, and latency.

  • Instrument - the tool sensitive to an focus of interest

  • metric - a calibration of the focus

  • unit - the expressed quantity/quality of focus

  • measure - an individual sample of the focus

My eyes do not magically see a chair.

They receive an avalanche of information.

“Chair” is preconceived interpretation of a portion of that information. That is a rather large distinction. This is a screwy metaphor so suspend disbelief. Suppose reality is an enormous spectrum of information. White noise, for the sake of argument. Somewhere hidden in that spectrum is a notch that is sufficiently chair-like.

I don’t need to recreate the chair in my head and compare the two. What I need is a filter that can distinguish that information.

That is my notch filter.

A notch filter is a parameterized transform that selectively includes or excludes information matching a statistical invariant.

Inclusively, it says:

Show me what is chair-like.

Exclusively:

What is not chair-like.

So reality has already been tarnished before cognition gets its grubby little hands on it. I observe reality. I throw away most of it.

Perhaps I see a chair?

What do I need to know?

That depends entirely upon what I intend to do with the chair.

  • If I want to sit on it, I care about whether it will support me.

  • If I want to carry it, I care about its weight and where I can grab it.

  • If I want to recognize it, I need enough information to distinguish a chair from a not-chair.

  • If somebody throws it at me, my requirements change considerably.

Same chair. Different information matters. And perhaps even “same chair” is getting ahead of myself.

I have an observation.

What can I say about it?

That depends upon the information available and the resolution I require. Maybe I can establish only that it is an object. Maybe I have enough information to establish that it is furniture. Perhaps I can establish that it is a chair.

With more information, a high chair.

And with still more:

Johnny’s high chair.

The filter doesn’t tell me what the thing ultimately and absolutely is. It tells me what I can know.

That suggests something interesting. Perhaps there isn’t one complete internal representation of the chair. Perhaps there doesn’t need to be.

  • I can cut the information any way I want.

  • I can examine the image.

  • I can examine spatial relationships.

  • I can examine affordances.

What about affordances?

  • Can I sit on it?

  • Can I pick it up?

  • Does it support weight?

  • Does it have legs?

  • Does it belong to Johnny?

Different realms provide different kinds of information. Only the realm lingo changes.

This is where Constraint Convergence enters the picture. Within a particular realm I have atoms—the available pieces of information in the language of that realm. Against those atoms I can apply constraints. A sufficiently useful collection of constraints forms what I call a Nexus.

  • CHAIR can be a Nexus

  • HIGH CHAIR can be another.

  • JOHNNY’S HIGH CHAIR another.

They are not necessarily stops along some mandatory hierarchical path. They are declarations that can be established when the available information supports them. An object can have many such declarations simultaneously.

I call that its Heritage. The Heritage of Johnny’s high chair might include:

  • OBJECT.

  • FURNITURE.

  • CHAIR.

  • HIGH CHAIR.

  • JOHNNY’S HIGH CHAIR.

Not because cognition necessarily walked down a tree from OBJECT to JOHNNY’S HIGH CHAIR.

It may have arrived from anywhere. The visual realm may establish CHAIR. Affordances may help establish HIGH CHAIR. Context may establish JOHNNY’S HIGH CHAIR.

The Heritage is simply the collection of declarations that remain simultaneously true. This gives cognition enormous flexibility.

It doesn’t have to identify everything as specifically as possible. It has to identify it as specifically as necessary.

  • If I am walking through a dark room, OBSTACLE may be plenty.

  • If I am looking for somewhere to sit, CHAIR may be enough.

  • If I am sorting children’s furniture, HIGH CHAIR suddenly matters.

  • If Johnny’s mother asks where his old high chair went, I had better do better than FURNITURE.

  • Criticality determines resolution. I stop when I know enough.

Now the notch filter becomes particularly useful. A filter is receptive. That distinction matters.

Elsewhere I have described generators. A generator is expressive. It takes what I know and produces an expression from it.

The notch filter does the opposite kind of work. It receives information and determines what within that information satisfies its invariant.

I had previously imagined that recognition might require generating an internal expectation and comparing reality against it.

But why?

STOP

Blah. Blah. Blah. Many of you out there are scratching your heads. But I see pictures. You have eliminated pictures. And you're right. You got me. Fair and square.

Blight spot. I have Aphantasia. Hence no pictures. Sorry for you chaps our there.

RESUME

Why generate an image of a chair merely to discover whether the thing in front of me differs from the generated chair?

Why generate an expected room just to compare it with the room I am standing in?

Skip the step.

Apply the filters directly to the incoming information. Recognition does not require reconstruction. That is a much cleaner machine.

And it suggests something about learning.

Suppose I encounter an object that is almost, but not quite, accepted by my existing CHAIR filter.

Something about it is unfamiliar.

Constraint Convergence brings in additional information.

Affordances.

Spatial information.

Context.

Whatever is available.

Eventually I establish:

Yes.

That is a chair.

Now I have something extremely valuable. My existing filter did not quite accept it. Reality did.

The delta tells me something about my filter.

Perhaps my definition of CHAIR is too narrow.

So I adjust it. Not by storing another chair. By recalibrating the filter. The next time I encounter that variation, it falls comfortably within the notch.

The reverse works too.

Perhaps my CHAIR filter accepts something that further examination establishes is not a chair. Again, I have a delta. Tighten the filter. Learning becomes calibration.

This also changes the way I think about familiar environments.

I walk into a room I know. I don’t need a stored photograph of the room. I already possess filters representing what I know about it. Apply them to the incoming information. Most of the room may be entirely unsurprising.

Then something doesn’t fit.

That is interesting.

The discrepancy is information.

I don’t need to manufacture an internal room merely so I can subtract one image from another. The receptive machinery can expose the difference directly.

And now we return to memory.

Why store a representation of a chair at all?

Suppose, instead, I store the means of isolating chair-like information from an informational spectrum.

Apply a notch filter.

There is an important distinction here. A recording stores an example. A filter stores a statistical invariant distilled from examples.

I am deliberately leaving open the implementation of such a filter.

A black box.

I care about its transform. Give it an appropriate informational field. Give it appropriate parameters.

Let it filter.

That’s the contract.

So I have successive stages of filtering.

Reality is filtered by the physical limits of our instruments.

Observation is filtered by immediate utility—what matters for the job at hand.

Notch filters isolate useful invariants within what remains.

Constraint Convergence determines what the available information permits me to establish.

Criticality determines when I know enough.

  • Reality.

  • Observation.

  • Useful information.

  • Notch filter.

  • Constraint Convergence.

  • Sufficient answer.

Each stage discards what doesn’t matter.

That sounds like loss until you realize that discarding what doesn’t matter is the entire point.

“I thought you said you knew everything,” William said peevishly. His had been a life of repeated disappointment.

“I said no such thing. What I said is I know everything important.”

I learned something like this principle more than fifty years ago through mathematics. I don’t remember much of the lesson. That’s rather the point.

What survived wasn’t Fourier. What survived was the art of approximation. Give me a finite series of measurements and Fourier analysis can describe them as a combination of periodic components. But the result is only as trustworthy as the observations that went into it. The range and resolution of the samples bound what I am entitled to infer.

Within its calibrated range, it is a marvel.

Outside it?

Good luck.

Give a filter unfamiliar information and it may still produce an answer. That doesn’t mean reality agreed. Every notch filter has a realm of competence. Learning, then, is not necessarily the accumulation of an ever-growing warehouse of examples.

Learning may mean calibrating the filters—tightening their tolerances, broadening them when reality establishes something they failed to admit, narrowing them when they admit something they shouldn’t, or discarding an obsolete filter when new observations demonstrate that it can no longer separate useful information from noise.

And now I arrive at the reason this interests me personally. I have severely deficient autobiographical memory. I don’t retain my life as a collection of episodes I can revisit and re-embody.

What remains available to me are the regularities.

What was home like—on average?

I can tell you.

What were summers like—accumulatively?

I can tell you.

Ask me for that one specific summer day?

I draw a blank.

Summer is summer.

The episodes are gone; beyond my reach.

The particulars have vanished. What remains available is the filter profile. The regularity.

Recently, I reached back to college more than fifty years ago. I couldn’t name the lecture hall. I couldn’t replay the professor’s voice. That specific noise has vanished.

Yet the operational machinery was sitting there, ready to engage.

Approximation.

I had not preserved the recording. I had preserved the transform. That distinction fascinates me. Perhaps my semantic memory is unusually aggressive about this form of reduction. Perhaps it isn’t. I have no idea.

But it gives me a way of asking a larger question.

What if semantic memory is not an enormous inventory of things we have recorded?

What if its clarity comes from maintaining sharp, parameter-driven notch filters?

Minimal receptive mechanisms whose boundaries encapsulate what cognition has learned to distinguish.

That would explain something else I have been musing about.

Expertise.

An expert encounters thousands upon thousands of examples. The prize is not the catalog of cases. It is the tuned filter distilled from them.

“Though the leaves are many, the root is one.” —W. B. Yeats.

We feed raw instances into cognition. Eventually, the specific contexts may drop away. What survives is the invariant. And perhaps this is why the mechanism can be so flexible. I don’t need one prescribed method for recognizing a thing.

One person may rely heavily on visual information. Another may rely on spatial relationships. Another may notice affordances immediately. The same person may use entirely different realms depending upon the problem.

Maybe every brain cuts the information differently.

I don’t know.

It doesn’t particularly matter to the architecture. The machinery does not prescribe the route. It provides the operations.

That brings me back to memory. Maybe learning constructs and calibrates notch filters. Maybe semantic memory preserves them. Maybe cognition applies them receptively to the information arriving from reality.

Constraint Convergence can then use what those filters establish to resolve an identity only as far as the current problem requires.

  • No complete internal reconstruction is necessary.

  • No warehouse of perfect chairs.

  • No photograph of every room.

  • No exhaustive representation of reality.

Just enough machinery to distinguish what matters. I don’t know whether semantic memory actually works this way. I certainly haven’t demonstrated that it does. And I am deliberately leaving considerable freedom in how these mechanisms might be arranged.

In fact, I suspect there is an algebra hiding in here.

  • Realms.

  • Atoms.

  • Constraints.

  • Nexuses.

  • Filters.

  • Heritage.

  • Convergence.

  • Criticality.

A small collection of operations that can be composed in an enormous number of ways. Perhaps that flexibility is the point.

Instead of asking:

How could a finite mind possibly store everything it encounters?

I can ask:

How sharp a filter must it retain to recognize what matters and discard the rest?

Those are very different questions.

And perhaps that is the secret.

Semantic memory may not be remarkable because of how much it stores.

It may be remarkable because of how precisely it cuts.