How should we represent visual scenes?
Common-Sense Core,
Probabilistic Programs
Josh Tenenbaum
MIT Brain and Cognitive Sciences
CSAIL
Joint work with Noah Goodman, Chris Baker, Rebecca Saxe,
Tomer Ullman, Peter Battaglia, Jess Hamrick and others.
Core of common-sense reasoning
Human thought is structured around a basic
understanding of physical objects, intentional
agents, and their relations.
“Core knowledge” (Spelke, Carey, Leslie, Baillargeon, Gergely…)
Intuitive theories (Carey, Gopnik, Wellman, Gelman, Gentner, Forbus, McCloskey…)
Primitives of lexical semantics (Pinker, Jackendoff, Talmy, Pustejovsky)
Visual scene understanding (Everyone here…)
From scenes to stories…
The key questions:
(1) What is the form and content of human common-sense
theories of the physical world, intentional agents, and their
interaction?
(2) How are these theories used to parse visual experience
into representations that support reasoning, planning,
communication?
A developmental perspective
A 3 year old and her dad:
Dad: “What's this a picture of?”
Sarah: “A bear hugging a panda bear.”
...
Dad: “What is the second panda bear
doing?”
Sarah: “It's trying to hug the bear.”
Dad: “What about the third bear?”
Sarah: “It’s walking away.”
But this feels too hard to approach now, so what about
looking at younger children (e.g.12 months or younger)?
Intuitive physics and psychology
Southgate and Csibra, 2009
(13 month olds)
Heider and Simmel, 1944
Intuitive physics
(Gupta, Efros, Hebert)
(Whiting et al)
Intuitive psychology
Probabilistic generative models
• early 1990’s-early 2000’s
– Bayesian networks: model the causal processes that
give rise to observations; perform reasoning, prediction,
planning via probabilistic inference.
– The problem: not sufficiently flexible, expressive.
Scene understanding as an
inverse problem
The “inverse Pixar” problem:
World state (t)
graphics
Image (t)
Scene understanding as an
inverse problem
The “inverse Pixar” problem:
physics
… World state (t-1)
World state (t)
World state (t+1) …
graphics
Image (t-1)
Image (t)
Image (t+1)
Probabilistic programs
• Probabilistic models a la Laplace.
– The world is fundamentally deterministic (described by a program),
and perfectly predictable if we could observe all relevant variables.
– Observations are always incomplete or indirect, so we put probability
distributions on what we can’t observe.
• Compare with Bayesian networks.
– Thick nodes. Programs defined over unbounded sets of objects, their
properties, states and relations, rather than traditional finitedimensional random variables.
– Thick arrows. Programs capture fine-grained causal processes
unfolding over space and time, not simply directed statistical
dependencies.
– Recursive. Probabilistic programs can be arbitrarily manipulated
inside other programs. (e.g. perceptual inferences about entities that make
perceptual inferences, entities with goals and plans re: other agents’ goals and plans.)
• Compare with grammars or logic programs.
Probabilistic programs for “inverse
pixar” scene understanding
• World state: CAD++
• Graphics
– Approximate Rendering
• Simple surface primitives
• Rasterization rather than ray tracing (for each primitive, which
pixels does it affect?)
• Image features rather than pixels
– Probabilities:
• Image noise, image features
• Unseen objects (e.g., due to occlusion)
Probabilistic programs for “inverse
pixar” scene understanding
• World state: CAD++
• Graphics
• Physics
– Approximate Newton (physical simulation toolkit, e.g. ODE)
• Collision detection: zone of interaction
• Collision response: transient springs
• Dynamics simulation: only for objects in motion
– Probabilities:
• Latent properties (e.g., mass, friction)
• Latent forces
Modeling stability judgments
Modeling stability judgments
physics
… World state (t-1)
World state (t)
World state (t+1) …
graphics
Image (t-1)
Image (t)
Image (t+1)
Modeling stability judgments
physics
… World state (t-1)
World state (t)
World state (t+1) …
Prob. approx. rendering
Image (t-1)
Image (t)
Image (t+1)
Modeling stability judgments
physics
… World state (t-1)
World state (t)
World state (t+1) …
Prob. approx. rendering
Image (t-1)
Image (t)
Image (t+1)
Modeling stability judgments
Prob.
approx.
Newton
… World state (t-1)
World state (t)
World state (t+1) …
Prob. approx. rendering
Image (t-1)
Image (t)
Image (t+1)
Modeling stability judgments
Prob.
approx.
Newton
… World state (t-1)
World state (t)
World state (t+1) …
Prob. approx. rendering
Image (t-1)
Image (t)
Image (t+1)
s = perceptual uncertainty
Modeling stability judgments
(Hamrick,
Battaglia,
Tenenbaum,
Cogsci 2011)
Perception: Approximate posterior with block positions normally distributed
around ground truth, subject to global stability.
Reasoning : Draw multiple samples from perception.
Simulate forward with deterministic approx. Newton (ODE)
Decision: Expectations of various functions evaluated on simulation outputs.
Results
Mean human
stability
judgment
Model prediction
(expected proportion of tower that will fall)
Simpler alternatives?
The flexibility of common sense
(“infinite use of finite means”, “visual Turing test”)
•
•
•
•
Which way will the blocks fall?
How far will the blocks fall?
If this tower falls, will it knock that one over?
If you bump the table, will more red blocks or
yellow blocks fall over?
• If this block had (not) been present, would the
tower (still) have fallen over?
• Which of these blocks is heavier or lighter than
the others?
• …
Direction of fall
Direction and distance of fall
If you bump the table…
If you bump the table…
(Battaglia, & Tenenbaum, in prep)
Mean human
judgment
Model prediction
(expected proportion of red vs. yellow blocks that fall)
Experiment 1: Cause/ Prevention Judgments
(Gerstenberg, Tenenbaum,
Goodman, et al., in prep)
Modeling people’s cause/prevention judgments
• Physics Simulation Model
p(B|A) – p(B| not A)
p(B|A)
0 if ball misses
1 if ball goes in
p(B| not A): assume
sparse latent Gaussian
perturbations on B’s
velocity.
Simulation Model
Intuitive psychology
Beliefs (B)
Desires (D)
Actions (A)
Heider and Simmel, 1944
Intuitive psychology
Beliefs (B)
Desires (D)
Actions (A)
Beliefs (B)…
Pr(A|B,D)
Desires (D) …
Heider and Simmel, 1944
Intuitive psychology
Beliefs (B)
Desires (D)
Probabilistic
approximate
planning
Actions (A)
Probabilistic program
Heider and Simmel, 1944
Intuitive psychology
Beliefs (B)
Desires (D)
Probabilistic
approximate
planning
Actions (A)
Probabilistic program
Actions i
States j
In state j, choose
action i* =
arg max pij , j u j
i
j
“Inverse economics”
“Inverse optimal control”
“Inverse reinforcement learning”
“Inverse Bayesian decision theory”
(Lucas & Griffiths; Jern & Kemp;
Tauber & Steyvers; Rafferty & Griffiths;
Goodman & Baker; Goodman & Stuhlmuller;
Bergen, Evans & Tenenbaum …
Ng & Russell; Todorov; Rao;
Ziebart, Dey & Bagnell…)
Goal inference as inverse
probabilistic planning
constraints
rational planning
(MDP)
(Baker, Tenenbaum & Saxe, Cognition, 2009)
People
1
r = 0.98
Agent
0.5
0
0
0.5
Model
goals
1
actions
Theory of mind:
Joint inferences about beliefs
and preferences
Agent
state
Environment
rational
perception
(Baker, Saxe & Tenenbaum, CogSci 2011)
Beliefs
Food truck scenarios:
Preferences
rational
planning
Preferences
Initial Beliefs
Actions
Agent
Goal inference with
multiple agents
(Baker, Goodman & Tenenbaum,
CogSci 2008, in prep)
Southgate
& Csibra:
constraints
constraints
goals
rational planning
(MDP)
rational planning
(MDP)
Agent
Agent
goals
actions
actions
People
Model
constraints
Inferring social goals
goals
rational planning
(MDP)
Agent
Subject
ratings
actions
Model
prediction
Agent
rational planning
(MDP)
Subject
ratings
Hamlin, Kuhlmeier, Wynn & Bloom:
constraints
Model
prediction
(Baker, Goodman & Tenenbaum, Cog
Sci 2008; Ullman, Baker, Evans,
Macindoe & Tenenbaum, NIPS 2009)
goals
actions
Conclusions
From scenes to stories… What contents of stories are
routinely accessed through visual scenes? How can we
represent that content for reasoning, communication,
prediction and planning?
Focus on core knowledge present in preverbal infants:
intuitive physics, intuitive psychology.
Representations using probabilistic programs: thick nodes
(e.g. CAD++), thick arrows (physics, graphics, planning),
recursive (inference about inference, goals about goals).
Challenges for future work: (1) Integrating physics and
psychology. (2) Efficient inference. (3) Learning.