Fixing Artificial Intelligence with Natural Intelligence

Joshua (jovo) Vogelstein, PhD

BME@JHU

Experiential Learning: 2 experiments

Experiential Learning

• 5 heads?
• 6 heads or tails?
• 7 heads or tails?
• 8 heads or tails?
• Longest sequence?

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Can LLMs even generate random coin flips?

Executive Summary

• What is learning
• How did we get it
• How do we model it
• What is wrong with our model
• How do we fix it
• Now what do we do

What’s the deal with biological learning?

• Learning: the ability to use the past to improve future performance.
• It evolved because the past is related to the future (though distinct from it).

How do we model learning?

• In AI, what we call “learning”, is a model of a natural phenomenon
• Multiple formal definitions
• PAC learning
• Online learning
• Reinforcement learning
• George Box: “All models are wrong, some are useful.”

The leading AI model of learning

The leading AI model of learning

Probably Approximately Correct (PAC)

• Nearly 100 years old
• Workhorse of modern AI revolution (useful)
• Assumptions are wrong:
• Data are IID: identical and independently distributed
• Goal is fixed.

Simplest. Model. Ever. (coin flips)

Next. Simplest. Model. Ever. (Alternating coin flips)

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Why you might care…

Why else you might care…

• Intelligence makes us us.
• We call ourselves homo sapiens!

Published: 2013

Data model

• Input: x (e.g., images, questionnaire answers, etc.)
• Output: y (e.g., disease status)
• Comes in pairs, (x,y)
• Each pair is IID
• D: a “data corpus” of n pairs of IID data

Hypotheses

• h: eats input, spits out output
• h(x) → y
• H: the set of all possible h’s
• Deep nets
• Random forests
• Linear functions
• etc.

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Learner

• Eats a data corpus, spits out a hypothesis
• L(D) → h
• We choose a learner that we hope learns a good hypothesis

A “good” hypothesis

• Minimize empirical loss between predictions and truth
• Loss could be sum of squared errors
• minimize sum( (h(x_i) - y_i)²)
• But what about overfitting and stuff?
• Instead, find hypothesis that minimizes expected loss in the future
• Risk = expected future loss

Fundamental theorem of pattern recognition

A learner exists with the following property: with enough data, it will select a hypothesis that is probably approximately correct.

In other words, with enough data, the learner will select a hypothesis whose expected loss is arbitrarily close to the best one could do, with arbitrarily high probability.

Example learners with this property

Example learners without this property

• Histograms
• Support Vector Machines
• Random Forests
• Empirical risk minimization

• Linear regression
• Deep networks

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Notice any issues?

No time.

Our proposed solution:

Prospective Learning

Data model

• Input: x (e.g., images, questionnaire answers, etc.)
• Output: y (e.g., disease status)
• Comes in pairs, (x,y)
• Each pair is IID
• Each pair neither identical nor independently distributed
• D: a “data corpus” of n pairs of IID data

Hypothesis class

• Eats input & time, spits out output
• h(x,t) → y(t)
• H: the set of all possible h’s
• Deep nets with time
• Random forests with time
• Linear functions with time
• etc. with time

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Learner

• Eats a data corpus, spits out a hypothesis sequence
• L(D) → h(. , t)
• We choose a learner that we hope learns a good hypothesis sequence

A “good” hypothesis

• Minimize empirical loss between predictions and truth in the future
• Loss could be sum of squared errors over the future
• minimize sum( (h(x,t) - y(t))²)
• But what about overfitting and stuff?
• Instead, find hypothesis that minimizes expected loss in the future
• Risk = expected future loss

Fundamental theorem of pattern recognition

prospective learning

A learner exists with the following property: with enough data, it will select a hypothesis that is probably approximately correct forever in the future.

In other words, with enough data, the learner will select a hypothesis whose expected loss is arbitrarily close to the best one could do, with arbitrarily high probability.

Example 1: reversal learning

Example 2: non-Markov learning

Can GenAI Prospect (LLMs)?

No.

Discussion

• We just added time to the foundation of ML/AI
• Theory says simple algorithms should work
• Simple (prospective) algorithms solve simple (prospective) problems
• Fancy (retrospective) algorithms utterly/embarrassingly fail

What’s next?

• Model some humans?
• See whether simple algorithms work on real-world problems
• Make better algorithms

Publications

1. De Silva et al. The Value of Out-of-Distribution Data, ICML, 2023.
2. De Silva et al. Prospective Learning: Principled Extrapolation to the Future, CoLLAs, 2023.
3. De Silva et al. Prospective Learning: Principled Extrapolation to the Future, preprint available upon request.

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Thanks

NSF Simons MoDL,�ONR N00014-22-1-2255, �NSF CCF 2212519

More thanks.

Questions?

Kinds of biological learning

• reinforcement learning
• behavioral learning
• imitation learning
• associational learning
• sensorimotor learning

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Time encoding

Example A.2:

number learning

Task 1: 1-5�Task 2: 4-7�Task 3: 6-9�Task 4: 8-10

Example A.3:

image learning

Example B.2:

number learning

Task 1: 1-5�Task 2: 4-7�Task 3: 6-9�Task 4: 8-10

Example B.3:

image learning