From: AAAI Technical Report SS-01-05. Compilation copyright © 2001, AAAI (www.aaai.org). All rights reserved. Grounding the Unobservable in the Observable: The Role and Representation of Hidden State in Concept Formation and Refinement ClaytonT. Morrison Tim Oates Gary King Experimental KnowledgeSystems Lab Artificial Intelligence Lab Experimental KnowledgeSystems Lab Department of Computer Science Massachusetts Institute of Technology Department of Computer Science University of Massachusetts, Amherst 545 Technology Square University of Massachusetts, Amherst Amherst, MA01003, USA Cambridge, MA02139 Amherst, MA01003, USA clayton @cs.umass.edu oates @ai.mit.edu [email protected] Introduction that explain as manyobservable phenomenaas compactly One of the great mysteries of humancognition is how we and accurately as possible. Predictiveness is central to this learn to discover meaningfuland useful categories and con- enterprise. If theory A makeseither more accurate predic- cepts about the world based on the data flowing from our tions or a larger set of verifiable predictions than theory B, then theory A is preferred. To explain observed phenomena, sensors. Whydo very young children acquire concepts like support and animate (Leslie 1988) rather than between three scientists often posit the existence of unobservableentities and six feet wide or blue with red and green dots? Onean- (Harr6 1970; 1986). No one has ever seen gravity or black swer to this question is that categories are created, refined holes, but they explain such a wide range of observable phe- and maintainedto support accurate prediction. Knowingthat nomenaso accurately that their existence goes virtually un- an entity is animate is generally muchmore useful for the challenged. Scientific progress wouldcome to a standstill if purpose of predicting howit will behave than knowingthat not for the ability to posit and collect evidencefor the ex- it is blue with red and green dots. istence of causally efficacious entities that do not manifest themselves directly in our percepts in the same way that, The idea of using predictability, or a lack thereof, as the say, the color blue does. driving force behind the creation and refinement of knowl- To bring the discussion back to concept acquisition in edge structures has been applied in a variety of contexts. children, consider the following example. Humansclearly Drescher (1991) and Shen (1993) used uncertainty in cannot perceive the mass of an object in the sameway that tion outcomesto trigger refinement of action models, and they can perceive its color. Thoughit mayseem as if we per- McCallum(1995) and Whitehead and Ballard (1991) ceive mass directly fromvisual observationthis is an illusion uncertainty in predicted reward in a reinforcement learning groundedin a vast corpus of knowledgeabout objects gath- setting to refine action policies. ered over a lifetime of physical interaction with the world. Virtually all of the workin this vein is based on two key Without this grounding we would be, like an infant, unable assumptions. First, an assumptionis madethat the world is to makejudgements about the masses of objects based solely in priciple deterministic; that given enoughknowledge, out- on their visual appearance. Indeed, it is equivocal whether comescan be predicted with certainty. Giventhis, an agent’s we wouldeven have a concept of mass at all. failure to predict implies that it is either missinginformation or incorrectly representing the informationthat it has. Sec- Representingthe Unobservable ond, it is assumedthat knowledgestructures sufficient for the task can be created by combiningraw perceptual infor- Howmight a child that cannot perceive mass directly ever mation in various ways. That is, everything the agent needs hope to gain a concept of mass?Our answeris that the child to makeaccurate predictions is available in its percepts, and posits the existence of a property that explains howobjects the problemfacing the agent is to find the right combina- behaveand that they later learn that this property is named tion of elements of its perceptual data for this task. (See "mass". Objects with different massesyield different propri- (Drescher 1991) for an early and notable exception.) oceptive sensations whenyou lift them and different haptic Our position is that the first of these assumptionsrepre- sensations whenyou drop them on your foot, they require sents an exceedingly useful mechanismfor driving unsuper- different amounts of force to get them movingat a given vised concept acquisition, whereas blind adherence to the speed and they decelerate at different rates whenthat force second makesit difficult or impossible to discover someof is removed.Positing a hiddenfeature of objects that explains the most fundamental concepts. To better understand this and is correlated with any of these observations suffices to position, consider the child-as-scientist metaphor(Gopnik predict (to somedegree of accuracy) all of the others. That 1997). Generally speaking, scientists aim towards an under- is, this hidden quantity makesa wider array of moreaccu- standing of the way the world works by developing theories rate predictions than any directly observablefeature such as color or size. CopyrightO 2001, AmericanAssociation for Artificial Intelli- So far we have mentionedone of the fundamentaltriggers gence(www.aaai.org). All rights reserved. for positing new unobservable representational elements: 45 failure to predict. But an account of howthe neonate human carrying out an experiment). Irrespective of where along or machine might support the acquisition of knowledgeof the continuum from atomic/concrete to compound/abstract these hiddenstates requires a representational infrastructure these actions are specified, they all share in commonthe key that can property of affecting, in someway, what future input the ¯ accommodaterecognition of failure to predict, and agent will receive from the world. In this view, there is no such thing as a system that is purely disembodiedor pas- ¯ accommodaterepresentations whose content is funda- sive with respect to the environmentit is learning about: the mentally reviseable and extendable. world affects the agent and the agent affects the world (see The first property highlights that these representations must (Bickhard 1993)). Furthermore, note that even "passive" provide someway for the agent to recognize that something tions that don’t directly causally impinge on states of the has gonewrong: its current representational repertoire fails world, such as passively observing a scene, still involve an to be useful in predicting someaspect of the environment. "action" that affects the subsequentinput - e.g., passive ob- Thesecond property is a little morecomplicated. First, it servation specifically involves sitting still and not altering highlights that, in its intial, naked form, the proposednew states of the environmentwhile there is a passageof time. representational element serves simply as a "place-marker" associated with the context of the failure to anticipate some Constructing a NewPredicate aspect of the world. At this point, the agent does not even Withinthis representational framework,it is nowpossible to knowwhether the new element represents a hidden state, create (discover) newpredicates that maycorrespond to un- someunobservable property, or someunseen process. Next, observable states or properties of the world. Thesenew pred- given the newelement, the agent must nowsearch for condi- icates are then useful for deterministically predicting previ- tions under whichit can reliably predict its state value. Once ously unpredictable behavior of the world. Following the these conditions are discovered, the state value of this repre- base representational form of the schema, and using a "just sentational element can then be used to makepredictions of so" story involving the dicovery of a mass-like concept, such the the previously unpredictable aspects of the world. These creation and discovery works as follows: conditions are themselvesstates of the worldthat are directly Initially, the agent does not knowhow to predict the out- observable or can be accurately anticipated by the agent. comesof actions or interactions involving objects and such They are associated with the newly constructed represen- diverse outcomesas proprioreceptive feedback whenlifting tational element, serving as conditions for determiningits an object, haptic feedback whenthe object is dropped on state value. In this way, the content (the meaning)of the one’s foot, the force required to achieve somevelocity in proposed new representation of an unobservable aspect of movingthe object, and the rate of deceleration of the object the world is fundamentallyrevisable and extendable. whenone stops pushing. Instead, the different outcomesof Interestingly, a commontheme is shared amongseveral these events are simply experienced as they happen. Fig- computationalmodels of representation learning along these ure 2 depicts a pair of schemasrepresenting two different lines (e.g., (Drescher 1991; Kwok1995)). Namely,the experiencesof lifting objects that are otherwiseperceptually data structure for a representational unit in these discov- identical (also in conditionsthat are essentially identical). ery systemsis a triple involving preconditions, someaction, and postconditions; following Drescher’s (1991) terminol- ogy, we will refer to this data structure as a schema(see Figure 1). Lift Object I Action Lift ,.@Object