9.66 josh tenenbaum comp. cog.sci class + 9.s vikash<>josh #250
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I'm skeptical about "common sense". I think it's a catch-all term that is (over)used to invoke certainty or tradition where the speaker has none. I'm sure there's some underlying quantity that exists, but it's some kind of naive view of causality that applies only to simple situations. Real systems don't always suit common sense (example: https://metasd.com/2019/07/complexity-default-assumption/ ). |
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W2: Foundations of Inductive Learning, Bayesian Inference, Bayesian Concept Learningeight concepts on hypothesis, observation/example of concept, prior of hypothesis, likelihood of observations given hypothesis, posterior, size principle of likelihood (smaller hypothesis receives greater likelihood, more so as n increases), choice principle (natural over logic) of principle, hypothesis averaging for new observation (averaging prediction over all hypothesis weighted by posterior)
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This table clearly organizes the three levels proposed by Marr for reverse-engineering a cognitive system |
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applying marr's three levels for my project:
This table illustrates how the rational-resource-strategy approach is applied across the three levels:
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psetpset1
Toolkits:
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pset2
code in [[export.txt]] |
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with comparing rule-based and bayesian learning approaches cld
The paper discusses three main approaches to concept learning:
Rule-based learning (MIN algorithm) appears more similar to Bayesian learning:
Similarity-based learning (Weak Bayes) seems more aligned with evolutionary learning:
The full Bayesian model presented in the paper interestingly combines aspects of both rule-based and similarity-based approaches, potentially bridging the gap between Bayesian and evolutionary methods in a way similar to the "theory-based view" mentioned in the comparison.
This table highlights the key differences between the two grouped concepts, showing how rule-based/Bayesian approaches differ from similarity-based/evolutionary approaches in various aspects of learning and decision-making. It's important to note that these groupings are not absolute, and there can be overlap or combinations of these approaches, as demonstrated by the full Bayesian model in the concept learning paper and the "theory-based view" mentioned in the evolutionary vs Bayesian learning comparison. building on the 🧠bayes vs 🤜🧬evol developed in #242 and more on 🤜🧬evol in #100 |
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using 🦇bat_inspection cld todo2: connect [inspection paradox] with [gott's rule]. |
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Week 6: Graphical Models and Probabilistic Programmingbest lecture so far as i unpacked my attraction to probabilistic program as using how josh persuades prob.prog is better (finer) than graphical models, i can share suggestions on value lab's graphical representation of belief on node and arc of value hypothesis here. lec slide lecture transcript 🗣️. personal highlight is Angie-Josh QnA!
size principle: Smaller hypotheses receive greater likelihood, exponentially more so as example n increases question for today was
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mccoy: ced:
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W8
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W9. Probabilistic language of thought (meaning function) and MCMC as intuitive learning mechanismmeaning function allows purposeful knowledge projection to hyperplane that matters and implementable (i.e. have capability express any points in hyperplane with resources). todo: make collage of MCMC (TAC, three proposal comparison (indistinguishable after crossing) slides) using optimal fit through sequential monte carlo cld, i drew analogies between the proposal in the inference algorithm and how it might apply in the equity valuation negotiation situation in the context of #249. table shows how each inference technique maps to specific aspects of the equity valuation negotiation process, with particular attention to the objective function x*(i,c) and the various states and constraints specified in the problem setup.
The remaining techniques, while useful, play supporting roles in the negotiation process:
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W10 
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W11 |
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W12 hierarchical bayes
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I'm preparing a mail to josh after reading andrew's "Why forecast an election that’s too close to call? Predictive models don’t make the news, but they have a crucial role in democracy.", regarding josh's comment that if the p is closer to .5 (close call), sampling is a waste (just decide) from one and done paper. my argument is, the absence of modeler in one and done model. Modeling capability stock (which I believe is the key spirit of Bayesian workflow (centering modeler (process) instead of model (product)) andrew's "This predictability affects how politicians and journalists think about elections, the economy and the balance between parties" seem very related with josh's action understanding
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summary of the thirteen special topics to follow below
📐shallow to deep: structured ignorance priors enable robust inference by starting deliberately broad and refining incrementally as evidence accumulates. this approach maintains flexibility against unexpected cases while leveraging structure when appropriate, yielding systems that scale better than those with premature specificity. 👁️see flowing mass: probabilistic programming visualization reveals how probability distributes across hypothesis space rather than fixating on point estimates. this perceptual skill transforms inference from opaque guesswork to transparent reasoning, allowing rational uncertainty quantification that drives adaptive computation and robust decision-making. 🪒auto occam's razor: hierarchical model encodes uncertain beliefs and sampling navigates that uncertainty representation. together, they form consistent algorithm for probabilistic inference which behaves rationally compared to those violating consistency hence making predictably irrational decisions. 🧩compose to simplify: higher-order probabilistic operations automate mathematical reasoning by transforming sampling-based programs into expectation-operator form. this systematic approach allows gradient estimators and density evaluations to emerge from primitive transformations, replacing pages of derivations with composable building blocks that maintain unbiasedness guarantees while enabling exploration of variance-performance tradeoffs across inference algorithms. |
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1. scaling behavior of intelligence vs machine learningrational ai principle📐shallow to deep: structured ignorance priors enable robust inference by starting deliberately broad and refining incrementally as evidence accumulates. this approach maintains flexibility against unexpected cases while leveraging structure when appropriate, yielding systems that scale better than those with premature specificity. applying principle 1
📐shallow to deep: structured ignorance priors enable robust inference by starting deliberately broad and refining incrementally as evidence accumulates. this approach maintains flexibility against unexpected cases while leveraging structure when appropriate, yielding systems that scale better than those with premature specificity. |
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more on 📐shallow to deep
applying 📐shallow to deep principle to entrepreneurship: "At the heart of Vikash Mansinghka's seminars lies the novel concept of "structured ignorance" in probabilistic inference - a methodical approach to embracing and encoding uncertainty in decision-making models. Rather than making narrow, overconfident assumptions, this approach advocates for beginning with broad "ignorance priors" that acknowledge the vast range of possibilities in an open-world system. This foundational principle suggests that by explicitly structuring what we don't know, we can create more robust and adaptable models that better reflect reality. The document introduces a progressive refinement methodology that moves from "shallow" to "deep" probabilistic programs. Starting with simple models that capture broad uncertainties, the approach gradually adds layers of detail and structure as more evidence becomes available. This hierarchical approach to uncertainty allows for a systematic reduction of ignorance while maintaining flexibility at each level. Like zooming into a blurry picture, the process reveals finer details only when warranted by data and evidence, preventing premature commitment to potentially wrong assumptions. These concepts find particular resonance in entrepreneurship, where decision-makers must navigate complex uncertainties while building new ventures. The framework suggests practical strategies: starting with deliberately broad assumptions, layering learning from coarse to fine details, updating beliefs iteratively with new evidence, and maintaining flexibility for unexpected developments. By treating business models as living probabilistic programs that can be refined through data and experience, entrepreneurs can make more informed decisions while remaining adaptable to change. This Bayesian approach to entrepreneurship transforms uncertainty handling from a vague art into a structured, computational process that can be systematically improved over time." ⭐️rational inference
⭐️programmable inference
didn't find the need to digest yet 
The fact that they're policy computing systems in a compositional way. So liquid model probabilistic programming, which is developed by, principally by Alex Lew is a probabilistic programming model for language models that give some interesting new capabilities. So here's one distinctive problem of generating poems that can be plausibly reversed. Let's say you could ask GPT4 to try to generate a first line of a poem that could possibly be reversed to form the ending line of the problem. You don't need to generate the whole poem just a phrase whose words can be reversed. It turns out that many strong models really struggle with this. So GPT4 might say, Dawn, silence, whispers, softly, evenings, Echo fades, reversing. It fades. Echo, evening, softly, whispers, silence, thoughts didn't really work, so this task was introduced in the sparks of AGI paper as an example of failures of planning in language models. But you can actually use a llama 2 family model, plus our language model problems to programming language to get solutions like cold and dark. Was it when winter last, which traverses to last winter when it was dark and cold? Or are we there yet? Yeah, there we are, or there was nothing but love in her eyes, eyes are in love, but nothing was there. the way we did this was by writing a language model, probabilistic program that combines forward generation process with a test that reverses what was for was generated forward and scores. It may be a pretty intuitive reasoning strategy for solving the problem. This is an instance of a much more general affordance that language model problems to programs, which is the ability to take complex task specifications and model at least some of the semantics of this task specifications. So we can't understand symbolically all the semantics of some code generation task, but we can't break it down into right x such that y, which we could model a sample from a distribution prompted by an LLM over exits, but actually re weighted by a likelihood score that assesses the probability of y given x. So this is an example, again, of going from shallower to deep interpretations here, though it's of the task. You just throw it all the language model, or you could try to parse the task a little bit into a compositional specification, which you could then solve with probabilistic inference. So again, it's this 🦦shallow to deep inference process. And over the course of this semester, we'll actually see some some recent results that actually do natural language probabilistic programming with language models, where you can use language model probabilistic programs to take instructions and parse them into language model probabilistic programs so that you can actually implement the process like whatever just described. And that turns out to have some interesting capabilities in practice, and it could be even competitive with four much cheaper than 01, with very, very small models. Now we'll spend a little time when we talk about language model probabilistic programming, situating it against sort of the recent flurry of interest in reasoning, quotes of various kinds, and the chain of thought and all that kind of stuff. scientific knowledge of more structure (build in more knowledge) |
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2. Perception and navigationrational ai principle2👁️see flowing mass: probabilistic programming visualization reveals how probability distributes across hypothesis space rather than fixating on point estimates. this perceptual skill transforms inference from opaque guesswork to transparent reasoning, allowing rational uncertainty quantification that drives adaptive computation and robust decision-making. applying principle1, 2
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3. Foundations of modeling and inferencerational ai principle3🪒auto occam's razor: hierarchical model encodes uncertain beliefs and sampling navigates that uncertainty representation. together, they form consistent algorithm for probabilistic inference which behaves rationally compared to those violating consistency hence making predictably irrational decisions. applying principle 1,2,3
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Table 1: Shallow summary
Table 2: Deep dichotomy
Integrated Paragraph SummaryThe foundations of modeling and inference rest on two complementary dimensions: how we represent uncertainty in model space and how we compute with that uncertainty. Table 1 explores the model space, highlighting how hierarchical Bayesian models naturally implement Occam's Razor through the marginal likelihood p(D|m), which integrates over all parameter values p(θ|m) to evaluate how well a model class explains data p(D|θ,m). This integration naturally penalizes overly complex models without requiring explicit regularization. Vikash didn't cover it but I especially liked the log2(1/p(D|m)) as "number of bits of surprise at observing data D under model m" interpretation as a recent study in my field showed decision makers should experiment with more “surprising” theories because in this case experiments are more informative and enable more learning (Camuffo et al., Theory-Driven Strategic Management Decisions). Table 2 then examines how we navigate this model space, contrasting optimization (which finds single solutions often in improbable regions) with sampling (which represents typical behavior under the model). Together, these approaches create a synergy: hierarchical models provide the structure for encoding appropriate uncertainty, while sampling provides the computational mechanism for navigating that uncertainty, maintaining rational behavior even as problem complexity grows. I dubbed this as "🪒auto occam's razor" hierarchical model encodes uncertain beliefs and sampling navigates that uncertainty representation. together, they form consistent algorithm for probabilistic inference which behaves rationally compared to those violating consistency hence making predictably irrational decisions. (rational ai principle3) |
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I applied four principles in automating paper writing project Pose Estimation with Sensors:Basic principle: A robot's position is determined by combining noisy sensor measurements with a motion model to estimate its most likely location. Particle Filtering vs. Simple Importance Sampling:Basic principle: Particle filtering sequentially updates and resamples candidate solutions at each step, while importance sampling tries to estimate the entire distribution at once. Benefits of Rejuvenation:Basic principle: Rejuvenation perturbs resampled particles to maintain diversity, preventing collapse to a single solution in high-dimensional problems. Integrated Path vs. Probabilistic Inference:Basic principle: Simple path integration accumulates errors while probabilistic inference maintains uncertainty and can correct itself with new information. Differential Visualization ImplementationHere's a simple implementation of differential visualization that shows how changes to inputs propagate through the paper generation process: // The simplest implementation of Differential Visualization for paper generation
function createDifferentialVisualization() {
// Track current state
let state = {
inputs: {
phenomena: "",
theory: "",
application: ""
},
activeInput: "phenomena",
paperSections: {
introduction: { content: "", impactScores: {} },
literature: { content: "", impactScores: {} },
methodology: { content: "", impactScores: {} },
results: { content: "", impactScores: {} },
conclusion: { content: "", impactScores: {} }
}
};
// Define impact relationships (how inputs affect sections)
// These would be learned or defined based on model analysis
const impactMatrix = {
phenomena: {
introduction: 0.8,
literature: 0.4,
methodology: 0.2,
results: 0.3,
conclusion: 0.2
},
theory: {
introduction: 0.3,
literature: 0.7,
methodology: 0.9,
results: 0.5,
conclusion: 0.3
},
application: {
introduction: 0.2,
literature: 0.1,
methodology: 0.4,
results: 0.7,
conclusion: 0.8
}
};
// Calculate differential impact when input changes
function updateDifferentialImpact(inputKey, oldText, newText) {
// Calculate change magnitude (simplified)
// In a real implementation, this would use embeddings comparison
const changeRatio = newText.length > 0 ?
1 - (oldText.length / newText.length) : 1;
// Update impact scores based on change magnitude
Object.keys(impactMatrix[inputKey]).forEach(section => {
const baseImpact = impactMatrix[inputKey][section];
state.paperSections[section].impactScores[inputKey] = baseImpact * changeRatio;
});
// Update visualization
updateHeatmap();
}
// Update the heatmap visualization
function updateHeatmap() {
// Compute total impact for each section
Object.keys(state.paperSections).forEach(section => {
const sectionImpacts = state.paperSections[section].impactScores;
const totalImpact = Object.values(sectionImpacts).reduce((sum, val) => sum + val, 0);
// Update the visual heatmap for this section (DOM operation in real implementation)
console.log(`Section "${section}" impact: ${totalImpact.toFixed(2)}`);
// In a real implementation, we would update DOM elements:
// document.getElementById(`${section}-heatmap`).style.backgroundColor =
// `rgba(255, 102, 0, ${totalImpact})`;
});
}
// Input change handler
function handleInputChange(inputKey, newValue) {
const oldValue = state.inputs[inputKey];
state.inputs[inputKey] = newValue;
state.activeInput = inputKey;
// Calculate and visualize impact
updateDifferentialImpact(inputKey, oldValue, newValue);
// In a real system, we'd regenerate affected sections
// regenerateAffectedSections();
}
// Public API
return {
updateInput: handleInputChange,
getState: () => state
};
}
// Usage example
const paperVisualizer = createDifferentialVisualization();
paperVisualizer.updateInput("phenomena", "Experimental choice differences between entrepreneurs");
paperVisualizer.updateInput("theory", "Hierarchical Bayesian model of decision making");Key Logic for Differential Visualization
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4. automating mathlew25_auto(math(integ, diff)).pdf |
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i prompted below to katie as we have shared interest on model synthesis & entrepreneurship and angie would like to get advice on building domain specific language for entrepreneurial operations from katie Q1. does it make sense if i say nail scale sail comic book is an attempt for defining semantically rich but syntactically restrictive entrepreneurial operations? full paper below where ten casestudies are compactly used to illustarte ten tools: Q2. if Q1 is yes, if you were to design a domain specific language for entrepreneurial operations (below structure), where'd you spend most time developing?
Q3. what do you think about vikash's separation between generative program and causality?
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My favorite seminar so far! Seminar Transcript Summary: Challenges in Interdisciplinary ResearchKey Topics Covered:
The seminar encouraged participants to be intentional about research communication, to understand field-specific evaluation standards, and to balance technical excellence with strong presentation and positioning. |
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3 Course Description
An introduction to computational theories of human cognition, and the computational frameworks that could support human-like artificial intelligence (AI). Our central questions are: What is the form and content of people's knowledge of the world across different domains, and what are the principles that guide people in learning new knowledge and reasoning to reach decisions based on sparse, noisy data? We survey recent approaches to cognitive science and AI built on these principles:
World knowledge can be described using probabilistic generative models; perceiving, learning, reasoning and other cognitive processes can be understood as Bayesian inferences over these generative models.
To capture the flexibility and productivity of human cognition, generative models can be defined over richly structured symbolic systems such as graphs, grammars, predicate logics, and most generally probabilistic programs.
Inference in hierarchical models can explain how knowledge at multiple levels of abstraction is acquired.
Learning with adaptive data structures allows models to grow in complexity or change form in response to the observed data.
Approximate inference schemes based on sampling (Monte Carlo) and deep neural networks allow rich models to scale up efficiently, and may also explain some of the algorithmic and neural underpinnings of human thought.
We will introduce a range of modeling tools, including core methods from contemporary AI and Bayesian machine learning, as well as new approaches based on probabilistic programming languages. We will show how these methods can be applied to many aspects of cognition, including perception, concept learning and categorization, language understanding and acquisition, common-sense reasoning, decision-making and planning, theory of mind and social cognition. Lectures will focus on the intuitions behind these models and their applications to cognitive phenomena, rather than detailed mathematics. Recitations will fill in mathematical background and give hands-on modeling guidance in several probabilistic programming environments, including WebPPL and Gen.
4 Prequisites
(1) Basic probability and statistical inference as you would acquire in 9.014, 9.40, 18.05, 18.600, 6.008, 6.036, 6.041, or 6.042, or an equivalent class. If you have not taken one of these classes, please talk to the instructor after the first day. (2) Previous experience with programming, especially in Matlab, Python, Scheme or Javascript, which form the basis of the probabilistic programming environments we use. Also helpful would be previous exposure to core problems and methods in artificial intelligence, machine learning, or cognitive science.
5 Requirements and Grading (to be updated)
Participation: Attendance at lectures is required. Recitations are optional. Students must attend at least 80% of lectures, and not miss more than 2 in a row. Students failing to meet the attendance requirement will be penalized by one full letter grade (for example, the grade will go from an A- to a B-). Attendance will be taken using a Google form with a Question of the Day during each class. The only exception to this attendance requirement is by specific exemption from the S^3 Deans or DAS (Disability and Access Services).
Problem Sets [60%]: There will be 3 problem sets, along with an optional 4th problem set. The release and due dates of the problem sets are still being finalized, and this section will be updated in the future.
Final Project [40%]: this is a project-based course. You will submit a project proposal and a paper-style write up for a final course project. Projects can be done individually or in groups of 2-3, but proportionately more work is expected for a group project.
Late Policy: A late penalty of 5% per day will be applied to late problem sets, up to 1 week past the deadline. We can't accept work later than 1 week after the deadline except in extraordinary circumstances because doing so would hinder our ability to discuss solutions with students in a timely manner.
Collaboration Policy: Students are allowed to talk and work with others on problem sets, but the work they write up and hand in must be their own. Students should also indicate the names of anyone that they worked with or collaborated with.
The Institute obliges us to remind you of its policy on integrity. It can be found at the website http://web.mit.edu/academicintegrity/. Please read it if you have not already done so.
Consistent with MIT policy, there is no curve or pre-set grade distribution for this class.
Please let us know on an individual basis if you have a learning disability or other special concern you would like us to be aware of.
6 Topics
Specific techniques and topics in cognitive modeling to be covered this year will include some or all of the following:
Foundations of inductive learning: philosophical challenges and theories of how learning is possible.
Introduction to Bayesian inference and Bayesian concept learning.
Modeling human cognition as rational statistical inference: Bayes meets Marr’s levels of analysis. Case studies in modeling surface perception and predicting the future
Graphical models and Bayesian networks. Modeling how people learn and reason about simple causal structures.
Probabilistic programming languages: Generalizations of graphical models that can capture the core of common- sense reasoning. Modeling social evaluation and attribution, visual scene understanding and common-sense physical reasoning.
Sampling-based methods for approximate probabilistic inference: Markov chain Monte Carlo (MCMC) - Gibbs sampling, Metropolis-Hastings; Sequential Monte Carlo (particle filtering). Modeling the dynamics of binocular rivalry, online sentence processing, change detection and multiple object tracking.
Learning as Bayesian inference: parameter estimation and model selection; the Bayesian Occam’s razor. Modeling visual learning and classical conditioning in animals.
Hierarchical Bayesian models: a framework for learning to learn, transfer learning, and multitask learning. Mod- eling how children learn the meanings of words, and learn the basis for rapid (’one-shot’) learning. Building a machine that learns words like children do.
Probabilistic models for unsupervised clustering: Modeling human categorization and category discovery; prototype and exemplar categories; categorizing objects by relations and causal properties.
Nonparametric Bayesian models - capturing the long tail of an infinitely complex world: Dirichlet processes, adaptor grammars, fragment grammars. Models for morphology in language.
Planning with Markov Decision Processes (MDPs): Modeling single- and multi-agent decision-making. Modeling human ’theory of mind’ as inverse planning.
Modeling human cognitive development - how we get to be so smart: infants’ probabilistic reasoning and curiosity; how children learn about causality and number; the growth of intuitive theories.
W1
Sep.06
q1. does common sense evolve with sensory system ? i haven't seen tameren for the last five years and this'd affect my answer for his question on it.
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