Unified Cognitive Science Neurobiology Psychology Computer Science Linguistics

Unified Cognitive Science • Neurobiology • Psychology • Computer Science • Linguistics • Philosophy • Social Sciences • Experience Take all the Findings and Constraints Seriously

What are schemas? • • • Regularities in our perceptual, motor and cognitive systems Structure our experiences and interactions with the world. May be grounded in a specific cognitive system, but are not situation-specific in their application (can apply to many domains of experience)

Basis of Image schemas • Perceptual systems • Motor routines • Social Cognition • Image Schema properties depend on • Neural circuits • Interactions with the world

Spatial schemas • TR/LM relation • Boundaries, bounded region • Topological relations • Orientational Axes • Proximal/Distal

Trajector/Landmark Schema • Roles: Trajector (TR) – object being located Landmark (LM) – reference object TR and LM may share a location (at)

TR/LM -- asymmetry • The cup is on the table • ? The table is under the cup. • The skateboard is next to the post. • ? The post is next to the skateboard.

Topological Relations • Separation

Topological Relations • Separation • Contact

Topological Relations • Separation • Contact • Coincidence: - Overlap - Inclusion

Orientation • Vertical axis -- up/down up above below down upright

Orientation Horizontal plane – Two axes:

Language and Frames of Reference • There seem to be three prototypical frames of reference in language (Levinson) • Intrinsic • Relative • Absolute

Intrinsic frame of reference left back front right

Relative frame of reference right? ? back front left? ?

Absolute frame of reference west south north east

Representing image schemas semantic schema Source-Path-Goal semantic schema Container roles: source interior path exterior goal portal trajector boundary Boundary Source Trajector Goal Interior Portal Path Exterior These are abstractions over sensorimotor experiences.

Language and Spatial Schemas • • People say that they look up to some people, but look down on others because those we deem worthy of respect are somehow “above” us, and those we deem unworthy are somehow “beneath” us. But why does respect run along a vertical axis (or any spatial axis, for that matter)? Much of our language is rich with such spatial talk. Concrete actions such as a push or a lift clearly imply a vertical or horizontal motion, but so too can more abstract concepts. Metaphors: Arguments can go “back and forth, ” and hopes can get “too high. ”

Regier Model Lecture Jerome A. Feldman March 4, 2008 With help from Matt Gedigian

Neural Theory of Language

Language Development in Children • 0 -3 mo: prefers sounds in native language • 3 -6 mo: imitation of vowel sounds only • 6 -8 mo: babbling in consonant-vowel segments • 8 -10 mo: word comprehension, starts to lose sensitivity to consonants outside native language • 12 -13 mo: word production (naming) • 16 -20 mo: word combinations, relational words (verbs, adj. ) • 24 -36 mo: grammaticization, inflectional morphology • 3 years – adulthood: vocab. growth, sentence-level grammar for discourse purposes

Trajector/Landmark Schema • Roles: Trajector (TR) – object being located Landmark (LM) – reference object TR and LM may share a location (at)

Language and Frames of Reference • There seem to be three prototypical frames of reference in language (Levinson) • Intrinsic • Relative • Absolute

English ‘on’ 1. The computer is on the desk 2. The picture is on the wall 3. The projector is on the ceiling UP TR LM DN TR/LM, verticality, contact, support TR LM TR/LM, contact, attaching force

Image schemas • Trajector / Landmark (asymmetric) • The bike is near the house • ? The house is near the bike TR LM • Boundary / Bounded Region bounded region • bounded region has a closed boundary • Topological Relations • Separation, Contact, Overlap, Inclusion, Surround • Orientation • Vertical (up/down), Horizontal • Absolute (E, S, W, N) boundary

Spatial schemas • TR/LM relation • Boundaries, bounded region • Topological relations • Orientational Axes • Proximal/Distal

Regier’s Model above below left right in out on off Learning System Input: TR LM above • Training input: configuration of TR/LM and the correct spatial relation term • Learned behavior: input TR/LM, output spatial relation

Issue #1: Implicit Negatives • • • Children usually do not get explicit negatives But we won’t know when to stop generalizing if we don’t have negative evidence Yet spatial relation terms aren’t entirely mutually exclusive The same scene can often be described with two or more spatial relation terms (e. g. above and outside) How can we make the learning problem realistic yet learnable?

Dealing with Implicit Negatives • • • Explicit positive for above Implicit negatives for below, left, right, etc in Regier: E = ½ ∑i, p (( ti, p – oi, p) * βi, p )2, where i is the node, p is the pattern, βi, p = 1 if explicit positive, βi, p < 1 if implicit negative

above – positive examples

above – negative examples

above – after training

above – test examples

Learning System dynamic relations (e. g. into) structured connectionist network (based on visual system)

Issue #2: Shift Invariance • • • Backprop cannot handle shift invariance (it cannot generalize from 0011, 0110 to 1100) But the cup is on the table whether you see it right in the center or from the corner of your eyes (i. e. in different areas of the retina map) What structure can we utilize to make the input shift-invariant?

Topological Relations • Separation • Contact • Coincidence: - Overlap - Inclusion - Encircle/surround

Limitations • Scale • Uniqueness/Plausibility • Grammar • Abstract Concepts • Inference • Representation

Demo of the Regier System • on the English above

Language and Thought Language • • Thought cognitive processes • • We know thought (our cognitive processes) constrains the way we learn and use language Does language also influence thought? Benjamin Whorf argues yes Psycholinguistics experiments have shown that linguistics categories influence thinking even in non-linguistics task

Image schemas • Trajector / Landmark (asymmetric) • The bike is near the house • ? The house is near the bike TR LM • Boundary / Bounded Region • a bounded region has a closed boundary • Topological Relations • Separation, Contact, Overlap, Inclusion, Surround • Orientation • Vertical (up/down), Horizontal (left/right, front/back) • Absolute (E, S, W, N) boundary bounded region

More image schemas • Proximal / Distal • distance from center (near/far) • Part / Whole • top of the hill, cover of the magazine • Container • interior, exterior, boundary, portal • Source-Path-Goal S • source, path, goal, trajector • Force-Dynamics • support, force TR P G

Regier’s Model above below left right in out on off Learning System Input: TR LM above • Training input: configuration of TR/LM and the correct spatial relation term • Learned behavior: input TR/LM, output spatial relation

Learning System dynamic relations (e. g. into) structured connectionist network (based on visual system) We’ll look at the details next lecture