Mike understood that his work on Navigating Among Movable Obstacles (NAMO) more could lead to abstracted hierarchical plans in terms a list of objects moved at the highest level, and then a hierarchy of plans for move orders, contacts made, contact ordering, locations moved to, actual grasps and manipulation, and full body trajectories at the lowest level. In retrospect, we missed an opportunity to relate Mike's work on NAMO, which is a form of blocks world AI, to previous symbolic approaches to blocks worlds, such as Fahlman's BUILD and Sussman's HACKER. I am eager to make this connection now.
Mike set the goal of building a MacGyver robot. I am eager to help make his dream real.
We want to enable robots to debug their errors, and find robust strategies to do tasks. We want to have robots reason using models and in multiple domains, such as mechanical, electrical, chemical, thermal, material, and software. We want robots to be able to answer questions like "Why will this plan work?" and "What went wrong?" in a way that satisfies a human supervisor.
It's Time To Bring Back GOFAI (Good Old-Fashioned AI) and Other Forms of Symbolic AI.
In the description below, we use the example of intermittent electrical power glitches, initially detected by power monitoring software in a watchdog computer.
1) We want to enable robots to think in several ways about the same problem.
2) We want robots to learn from single examples of watching people or other robots do things (including watching large numbers of youtube videos).
3) We want to automatically program robots to do the same task using the strategies from "watching" humans and other robots do the task. The strategies will need to be adapted to the current robot. Watching another robot involves complete access to all the data and reasoning available from the teaching robot.
4) We want to enable robots to apply alternative strategies to existing tasks, and learn to use the best strategy.
5) We want to enable robots to do novel tasks.
6) We want robots to be able to communicate with humans about what they are doing, using words, diagrams, and real and synthesized video.
7) We want the robots to be able to accept help from humans in the form of coaching, advice, correction, and instruction. This information could be in the form of words, demonstrations, and physical guidance.
Knowledge representation
Qualitative reasoning about idealized models such as circuits, and more detailed models of matter, space, and time.
Reasoning and learning from single examples: case-based, explanation-based,
Concepts and forming new concepts.
Procedural representations.
Planning and problem solving. We note that much of planning research is generated by assuming only short horizon search is possible, and hacks are needed to avoid the failures due to having too short a search horizon, such as the Sussman Anomaly. Given a reasonable lookahead, brute force search makes these problems go away.
Gradient descent, including deep learning
Function approximation
Probability, Probabilistic networks
Optimization and reinforcement learning
For our purposes, intelligence includes:
What is in our head are models of states and the effects of actions.
We believe that sensing, reasoning, acting, and learning occur concurrently and at mulitple time scales. An alternative and old fashioned view is that a robot senses, reasons, and then acts, and learns in between the sense/plan/act events. Another alternative view of intelligence is policy-based AI or behavior-based AI, where what is represented are rules of how to act, given a situation (aka policies). There is no mental model of the effects of actions, and no reasoning or planning. Reinforcement learning that modifies policies in response to experience dominates.
For our purposes, learning is optimization. Learning is figuring out what works best, and remembering that.
In our view the AI paradigms are:
This is a somewhat sloppy distinction. 1) Numeric reasoning includes discrete optimization, and thus may have a component of symbolic reasoning. 2) One form of numeric reasoning is to perform policy optimization using mental simulation of policies.
We will temporarily put aside policy optimization techniques, and focus on harnessing symbolic reasoning to make numeric reasoning work better.
In many situations, numeric reasoning techniques can be used to solve symbolic problems that involve integers (times, amounts, directions, count nouns) or involve quantities (mass nouns and relationships such as distances) by using continuous numbers to represent the amount, and turning hard constraints into soft constraints [CIO]. The answer produced by continuous optimization is discretized. This may not be the optimal discrete answer, but it is nevertheless often useful.
In asking the question "How can symbolic reasoning help numerical reasoning?" we need to figure out how symbols arise. We are motivated by the question "What is the second best answer to an optimization problem?" If we reject second best answers that are turned into the best answer by gradient descent as trivial, we see that a non-trivial second best answer is a locally optimum solution to the optimization problem.
This type of second best answer to an optimization problem is useful because it may become the best answer in the real world due to modeling error, or when the optimization problem changes slightly.
[PICTURE OF MINIMA CHANGING ORDER WITH PERTURBATIONS TO A COST FUNCTION]
There is a question of scale. We are typically not interested in high spatial frequencies. One way to think about scale is to think about a multi-scale representation of the cost function being optimized, and track the the local optima that arise as the spatial resolution is increased.
[PICTURE OF MULTISCALE REPRESENTATION OF A PROBLEM]
There are several ways symbols can arise:
[PICTURE OF 3 ABOVE]
This view of a symbol is useful, because it supports rapid optimization. Convex optimization problems only have one optima, which is therefore a global optima. Global optimization in continuous convex functions can be done inexpensively using gradient descent (a form of greedy optimization). Non-convex problems can be represented by sums or combinations of local convex functions, where each local function has a single corresponding local optima. Symbols represent different local functions which can be independently and rapidly optimized using gradient descent or other forms of greedy optimization, if a point in their domain is known.
Different types of materials are the outcome of chemical dynamic processes that find local optima. Different types of geology and landscapes are the outcome of mechanical dynamic processes that find local optima. The natural world is full of clusters of matter and dynamic phenomenon such as tornados and other weather that represent local optima of various optimization processes, including thermal processes.
It is interesting to note that the inanimate world does not usually produce identical individuals with defined extent ("bags of water"), while the biological world does. Ever since the evolution of the cell and cellular reproduction, the biological world produces large numbers of copies of almost identical individuals of a species. For our purposes, a species is a local optima of evolution. We will ignore counterarguments that we are seeing slow transients of a dynamic process that is still in progress, as that merely supports the point that we are looking at local optima, but at a particular time scale.
Because we are surrounded by and are ourselves local optima, we believe symbols, classes, and concepts have useful meaning. If we were giant gaseous beings inhabiting cloud planets, stars, or empty space, or giant fungal mats, we might not be so interested in symbols, concepts, or classes, and only have mass nouns and not count nouns or plural forms of words.
We are in the intellectual traditions of control theory, and honor Wiener and Cybernetics. Perhaps we should call ourselves Neo-Cybernetics. Wiener also spawned policy-based AI and behavior-based AI, along with Pavlov. Thorndike, Watson, and Skinner. We note that policy-based and behavior-based approaches play a similar role in robotics as behaviorism plays in Psychology.
In terms of the sense, reason, act, learn cycle, we honor Kalman for answering the question of how to use sensing to handle uncertainty, Bellman for telling us how to reason, and Feldbaum for showing us how to explore and learn.
Other possible names for this intellectual point of view include Symbolic Robotics, MOFAI (Modern Old Fashioned AI), Neo-GOFAI, Neo-Symbolism, Neo-Qualitative Physics, Approximate AI, Optimization-Based AI (OBAI), and Optimal AI (OAI).
One area where continuous optimization has led to "symbols" is differential games, where Isaacs, Breakwell, and Bernhard developed "singular surfaces" which arise from boundaries between different strategies. Singular surfaces are described in the book Differential Games: Theory and Methods for Solving Game Problems with Singular Surfaces by J. Lewin.
Meaningful distinctions: animate vs. inanimate. threat?
Meaningful abstractions about system properties. Time constant/natural frequency, oscillatory or damped, how much delay.
Ken Forbus is Mr. Analogy.
Multi-objective relaxation.
NAMO, Jungon, Jessica, method of characteristics
T-shirt design:
Front: MOFAI!
Back: Neo-Symbolists
Unite!
Sports examples: High jumps, Fosbury Flops (Local opt generate symbols), Football plays (Symbols generate local opt)
Modes and resonances are symbols. Use this to describe deformable objects, environments, and dynamic phenomenon.
Symbolic physics?
Intro chemistry is mostly symbolic