Supermodelling

If, as is widely reported, AI researchers (those scurvy dogs) began barking up the wrong tree a long time ago, I wonder when exactly that was and what scent led them astray. They started the chase promisingly… I think a lot of the foundational work of the Old Masters was really quite brilliant.

Case in point: The Physical Symbol System Hypothesis.

If you’re inclined to speculate that a computer could in principle be “intelligent” (I am so inclined; if that turns out to be wrong, then, well), it would be helpful to say some more about what is meant by a “computer”. If the speculation is phrased as “the UNIVAC I on the third floor could be intelligent,” that seems overly specific. So the natural thing would be to express it using one of the (equivalent) abstractions for “computation”, such as the Turing Machine, and just say that intelligence is computable and leave it at that.

In 1976, Allen Newell and Herb Simon (Newell’s doctoral advisor) chose a different way of putting it, a more detailed hypothesis that emphasized what they considered to be some actual fundamental issues of cognition. They called their abstract computer a physical symbol system. So:

The PSSH: A physical symbol system has the necessary and sufficient means for general intelligent action.

To simplify a bit, I’ll take “physical” as given and (as a nuts’n'bolts engineering-type guy) I’ll leave off the “necessary” part. Thus: a symbol system has the sufficient means for general intelligent action. So what’s a symbol system? Let’s start with some of their definitions:

• A symbol is a physical pattern that can occur as components of another type of entity called a symbol structure.
• A symbol structure is composed of a number of instances (or tokens) of symbols related in some physical way.
• In addition to symbol structures, a symbol system has a collection of processes that operate on symbol structures to produce other symbol structures. These processes account for the creation, modification, reproduction, and destruction of symbol structures.
• Through the application of those processes, then, a symbol system is a machine that produces through time an evolving collection of symbol structures.

Although that seems straightforward enough, people view the world through their own set of biases, which produce a number of (in my opinion) erroneous views of the PSSH and, by extension, rather odd characterizations of the AI enterprise. For example:

Viewpoint 1: 0 and 1 are symbols and machine instructions are processes that manipulate structures of bits, so it sort of follows that the PSSH is really only saying the same thing as “computers could be intelligent.”

Although this is a comforting way to respond to critics who attack the AI enterprise by enumerating the inadequacies of particular symbol systems, it ignores one of the central concepts of the PSSH: designation (which is not part of the basic definitions given above but is nontheless part of the PSSH). According to Newell, a symbol structure designates a thing if the system can use the symbol structure to affect the thing itself or behave in ways dependent on the thing. That is, some sort of “access” to the object is provided by the symbol structure, and this relationship between symbols and the universe is critical, although it is of course limited (the map is not the territory, after all…). This gives rise to the usual way of thinking about symbols as “standing for” things.

Viewpoint 2: Symbols are atomic tokens such as hotdog. Although much work in AI has proceeded from this kind of assumption, it leads to significant difficulties and conundrums. Specifically, if hotdog is just a label floating around, where does the designation to an actual hotdog come from? This is one trivial reflection of the famous symbol grounding problem, which is a very subtle but crucial challenge to the “Viewpoint 2″ way of looking at the PSSH. In reaction to this, some folks start thinking of some elements of an AI system (for starters, data related directly to sensor readings such as a camera image) as being subsymbolic, a suggestive word implying that symbols are constructed out of nonsymbolic entities. But there is no room for semantically loaded “nonsymbolic entities” in symbol systems. Furthermore, ugly issues arise from this “duality” — what makes some tokens symbols and some subsymbols? Where does the symbolness come from? Perhaps (the thinking goes) the very concept of symbol as used in the PSSH is wrongheaded if it leads to this kind of mystical dualism and complication.

Viewpoint 2b: Going even further, if symbols are clean labeled tokens, it is convenient for many purposes to provide semantics by assigning truth values or, more generally, probability values to symbol structures, and then choosing the processes of the symbol system to be truth-preserving transformations. This leads to symbolic logic and it dates back at least as far as Aristotle. Its productivity has made logic fundamental to many AI approaches, though sometimes you have to dig a bit to reveal how a particular system relies on this foundational way of carving up the world.

Note, though, that there is no inherent reason that symbols have to be simple. One more time: there is no inherent reason that symbols have to be simple. One more time: … oh, never mind.

Newell viewed the designation issue through the idea of a “representation law” — suppose that X is some sort of situation in the world, and T is some sort of transformation. For example, X = me holding a hotdog, and T = me eating the hotdog. The representation law says:

decode[encode(T)encode(X)] = T(X).

Here, encode is a translation from the “external” situation to an “internal” representation, and decode is a translation in the opposite direction. So the law basically says that there is an internal process representing ‘eating a hotdog’ (encode(T)), and an internal symbol structure representing the situation of me holding a hotdog (encode(X)). Applying the process to the structure should produce a symbol structure that corresponds to the external situation after the hotdog is eaten. For example, both in the real world and in the internal representation:

• I am no longer holding the hotdog
• I desire an alka-seltzer tablet

This corresponds exactly to the intuitive sense of what I expect from a model, so perhaps the representation law could be the foundation for a theory of modelling. Unfortunately, though, it is kind of frustrating because it sidesteps all of the important practical issues by defining them away. It implies that the causal relationship between the hotdog and the representation of the hotdog is unimportant — as long as the representation law holds, it doesn’t matter where the representation came from. So basically symbols are defined as the things that do what symbols should do. This facile embedding of designation in compartmentalized encode and decode procedures trivializes the process — for evidence, notice that AI researchers talk a LOT about T and X and the symbol structures themselves, but rarely about encode or decode. Still, having this representation law as a starting point is better than nothing!

Of course, these early steps (however profound and crucial), as embodied in their shortcut Viewpoint 2 form, are not The Answer; mistaking this path for the destination led to an overly-optimistic implicit view of denotation as primarily residing in the relationship between things and indivisible symbol tokens. The result: brittle structures too leaky to hold much meaning.

But what of it? Taking that torch and marching with it down the road is our job, and let’s get to it. My little trail: designation follows naturally from the principle that things themselves exist only as their descriptions, so the invention of modelling substrates and simplicity-biased induction methods on those substrates is the natural direction to take. Easy to say! But if we wean ourselves off of an exclusive reliance on truth-preservation as the justification for model transformations, what can replace it? Reductively deducible laws (e.g. F = ma), certainly, but those are rare. Can simplicity + empirical correctness fill the gap? I don’t know.

In 1992, just five years after the William James Lectures which were later published as the magnum opus Unified Theories of Cognition, Allen Newell passed away at age 65, one of a hundred billion tragic triumphs for the great enemy. SOAR is the ambitious and still-active software system embodying the ideas of Newell and his many academic descendents. Check it out, it’s cool.