Category: Information Theory

Theoretical Reorganization

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Sean Carroll of Caltech takes on the philosophy of science in his paper, Beyond Falsifiability: Normal Science in a Multiverse, as part of a larger conversation on modern theoretical physics and experimental methods. Carroll breaks down the problems of Popper’s falsification criterion and arrives at a more pedestrian Bayesian formulation for how to view science. Theories arise, theories get their priors amplified or deflated, that prior support changes due to—often for Carroll—coherence reasons with other theories and considerations and, in the best case, the posterior support improves with better experimental data.

Continuing with the previous posts’ work on expanding Bayes via AIT considerations, the non-continuous changes to a group of scientific theories that arrive with new theories or data require some better model than just adjusting priors. How exactly does coherence play a part in theory formation? If we treat each theory as a binary string that encodes a Turing machine, then the best theory, inductively, is the shortest machine that accepts the data. But we know that there is no machine that can compute that shortest machine, so there needs to be an algorithm that searches through the state space to try to locate the minimal machine. Meanwhile, the data may be varying and the machine may need to incorporate other machines that help improve the coverage of the original machine or are driven by other factors, as Carroll points out:

We use our taste, lessons from experience, and what we know about the rest of physics to help guide us in hopefully productive directions.

The search algorithm is clearly not just brute force in examining every micro variation in the consequences of changing bits in the machine. Instead, large reusable blocks of subroutines get reparameterized or reused with variation.… Read the rest

Free Will and Algorithmic Information Theory (Part II)

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Bad monkey

So we get some mild form of source determinism out of Algorithmic Information Complexity (AIC), but we haven’t addressed the form of free will that deals with moral culpability at all. That free will requires that we, as moral agents, are capable of making choices that have moral consequences. Another way of saying it is that given the same circumstances we could have done otherwise. After all, all we have is a series of if/then statements that must be implemented in wetware and they still respond to known stimuli in deterministic ways. Just responding in model-predictable ways to new stimuli doesn’t amount directly to making choices.

Let’s expand the problem a bit, however. Instead of a lock-and-key recognition of integer “foodstuffs” we have uncertain patterns of foodstuffs and fallible recognition systems. Suddenly we have a probability problem with P(food|n) [or even P(food|q(n)) where q is some perception function] governed by Bayesian statistics. Clearly we expect evolution to optimize towards better models, though we know that all kinds of historical and physical contingencies may derail perfect optimization. Still, if we did have perfect optimization, we know what that would look like for certain types of statistical patterns.

What is an optimal induction machine? AIC and variants have been used to define that machine. First, we have Solomonoff induction from around 1960. But we also have Jorma Rissanen’s Minimum Description Length (MDL) theory from 1978 that casts the problem more in terms of continuous distributions. Variants are available, too, from Minimum Message Length, to Akaike’s Information Criterion (AIC, confusingly again), Bayesian Information Criterion (BIC), and on to Structural Risk Minimization via Vapnik-Chervonenkis learning theory.

All of these theories involve some kind of trade-off between model parameters, the relative complexity of model parameters, and the success of the model on the trained exemplars.… Read the rest

Free Will and Algorithmic Information Theory

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I was recently looking for examples of applications of algorithmic information theory, also commonly called algorithmic information complexity (AIC). After all, for a theory to be sound is one thing, but when it is sound and valuable it moves to another level. So, first, let’s review the broad outline of AIC. AIC begins with the problem of randomness, specifically random strings of 0s and 1s. We can readily see that given any sort of encoding in any base, strings of characters can be reduced to a binary sequence. Likewise integers.

Now, AIC states that there are often many Turing machines that could generate a given string and, since we can represent those machines also as a bit sequence, there is at least one machine that has the shortest bit sequence while still producing the target string. In fact, if the shortest machine is as long or a bit longer (given some machine encoding requirements), then the string is said to be AIC random. In other words, no compression of the string is possible.

Moreover, we can generalize this generator machine idea to claim that given some set of strings that represent the data of a given phenomena (let’s say natural occurrences), the smallest generator machine that covers all the data is a “theoretical model” of the data and the underlying phenomena. An interesting outcome of this theory is that it can be shown that there is, in fact, no algorithm (or meta-machine) that can find the smallest generator for any given sequence. This is related to Turing Incompleteness.

In terms of applications, Gregory Chaitin, who is one of the originators of the core ideas of AIC, has proposed that the theory sheds light on questions of meta-mathematics and specifically that it demonstrates that mathematics is a quasi-empirical pursuit capable of producing new methods rather than being idealistically derived from analytic first-principles.… Read the rest

The Elusive in Art and Artificial Intelligence

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Per caption.
Deep Dream (deepdreamgenerator.com) of my elusive inner Van Gogh.

How exactly deep learning models do what they do is at least elusive. Take image recognition as a task. We know that there are decision-making criteria inferred by the hidden layers of the networks. In Convolutional Neural Networks (CNNs), we have further knowledge that locally-receptive fields (or their simulated equivalent) provide a collection of filters that emphasize image features in different ways, from edge detection to rotation-invariant reductions prior to being subjected to a learned categorizer. Yet, the dividing lines between a chair and a small loveseat, or between two faces, is hidden within some non-linear equation composed of these field representations with weights tuned by exemplar presentation.

This elusiveness was at least part of the reason that neural networks and, generally, machine learning-based approaches have had a complicated position in AI research; if you can’t explain how they work, or even fairly characterize their failure modes, maybe we should work harder to understand the support for those decision criteria rather than just build black boxes to execute them?

So when groups use deep learning to produce visual artworks like the recently auctioned work sold by Christie’s for USD 432K, we can be reassured that the murky issue of aesthetics in art appreciation is at least paired with elusiveness in the production machine.

Or is it?

Let’s take Wittgenstein’s ideas about aesthetics as a perhaps slightly murky point of comparison. In Wittgenstein, we are almost always looking at what are effectively games played between and among people. In language, the rules are shared in a culture, a community, and even between individuals. These are semantic limits, dialogue considerations, standardized usages, linguistic pragmatics, expectations, allusions, and much more.… Read the rest

Indifference and the Cosmos

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I am a political independent, though that does not mean that I vote willy-nilly. I have, in fact, been reliably center left for most of my adult life, save one youthfully rebellious moment when I voted Libertarian, more as a statement than a commitment to the principles of libertarianism per se. I regret that vote now, given additional exposure to the party and the kinds of people it attracts. To me, the extremes of the American political system build around radical positions, and the increasingly noxious conspiracy theories and unhinged rhetoric is nothing like the cautious, problem-solving utopia that might make me politically happy, or at least wince less.

Some might claim I am indifferent. I would not argue with that. In the face of revolution, I would require a likely impossible proof of a better outcome before committing. How can we possibly see into such a permeable and contingent future, or weigh the goods and harms in the face of the unknown? This idea of indifference, as a tempering of our epistemic insights, serves as a basis for an essential idea in probabilistic reasoning where it even has the name, the principle of indifference, or, variously, and in contradistinction with Leibniz’s principle of sufficient reason, the principle of insufficient reason.

So how does indifference work in probabilistic reasoning? Consider a Bayesian formulation: we inductively guess based on a combination of a priori probabilities combined with a posteriori evidences. What is the likelihood of the next word in an English sentence being “is”? Indifference suggests that we treat each word as likely as any other, but we know straight away that “is” occurs much more often than “Manichaeistic” in English texts because we can count words.… Read the rest

Incompressibility and the Mathematics of Ethical Magnetism

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One of the most intriguing aspects of the current U.S. border crisis is the way that human rights and American decency get articulated in the public sphere of discourse. An initial pull is raw emotion and empathy, then there are counterweights where the long-term consequences of existing policies are weighed against the exigent effects of the policy, and then there are crackpot theories of “crisis actors” and whatnot as bizarro-world distractions. But, if we accept the general thesis of our enlightenment values carrying us ever forward into increasing rights for all, reduced violence and war, and the closing of the curtain on the long human history of despair, poverty, and hunger, we must also ask more generally how this comes to be. Steven Pinker certainly has rounded up some social theories, but what kind of meta-ethics might be at work that seems to push human civilization towards these positive outcomes?

Per the last post, I take the position that we can potentially formulate meaningful sentences about what “ought” to be done, and that those meaningful sentences are, in fact, meaningful precisely because they are grounded in the semantics we derive from real world interactions. How does this work? Well, we can invoke the so-called Cornell Realists argument that the semantics of a word like “ought” is not as flexible as Moore’s Open Question argument suggests. Indeed, if we instead look at the natural world and the theories that we have built up about it (generally “scientific theories” but, also, perhaps “folk scientific ideas” or “developing scientific theories”), certain concepts take on the character of being so-called “joints of reality.” That is, they are less changeable than other concepts and become referential magnets that have an elite status among the concepts we use for the world.… Read the rest

Running, Ancient Roman Science, Arizona Dive Bars, and Lightning Machine Learning

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I just returned from running in Chiricahua National Monument, Sedona, Painted Desert, and Petrified Forest National Park, taking advantage of the late spring before the heat becomes too intense. Even so, though I got to Massai Point in Chiricahua through 90+ degree canyons and had around a liter of water left, I still had to slow down and walk out after running short of liquid nourishment two-thirds down. There is an eerie, uncertain nausea that hits when hydration runs low under high stress. Cliffs and steep ravines take on a wolfish quality. The mind works to control feet against stumbling and the lips get serrated edges of parched skin that bite off without relieving the dryness.

I would remember that days later as I prepped to overnight with a wilderness permit in Petrified Forest only to discover that my Osprey Exos pack frame had somehow been bent, likely due to excessive manhandling by airport checked baggage weeks earlier. I considered my options and drove eighty miles to Flagstaff to replace the pack, then back again.

I arrived in time to join Dr. Richard Carrier in an unexpected dive bar in Holbrook, Arizona as the sunlight turned to amber and a platoon of Navajo pool sharks descended on the place for billiards and beers. I had read that Dr. Carrier would be stopping there and it was convenient to my next excursion, so I picked up signed copies of his new book, The Scientist in the Early Roman Empire, as well as his classic, On the Historicity of Jesus, that remains part of the controversial samizdat of so-called “Jesus mythicism.”

If there is a distinguishing characteristic of OHJ it is the application of Bayesian Theory to the problems of historical method.… Read the rest

Zebras with Machine Guns

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I was just rereading some of the literature on Plantinga’s Evolutionary Argument Against Naturalism (EAAN) as a distraction from trying to write too much on ¡Reconquista!, since it looks like I am on a much faster trajectory to finishing the book than I had thought. EAAN is a curious little argument that some have dismissed as a resurgent example of scholastic theology. It has some newer trappings that we see in modern historical method, however, especially in the use Bayes’ Theorem to establish the warrant of beliefs by trying to cast those warrants as probabilities.

A critical part of Plantinga’s argument hinges on the notion that evolutionary processes optimize against behavior and not necessarily belief. Therefore, it is plausible that an individual could hold false beliefs that are nonetheless adaptive. For instance, Plantinga gives the example of a man who desires to be eaten by tigers but always feels hopeless when confronted by a given tiger because he doesn’t feel worthy of that particular tiger, so he runs away and looks for another one. This may seem like a strange conjunction of beliefs and actions that happen to result in the man surviving, but we know from modern psychology that people can form elaborate justifications for perceived events and wild metaphysics to coordinate those justifications.

If that is the case, for Plantinga, the evolutionary consequence is that we should not trust our belief in our reasoning faculties because they are effectively arbitrary. There are dozens of responses to this argument that dissect it from many different dimensions. I’ve previously showcased Branden Fitelson and Elliot Sober’s Plantinga’s Probability Arguments Against Evolutionary Naturalism from 1997, which I think is one of the most complete examinations of the structure of the argument.… Read the rest

Apprendre à traduire

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Google’s translate has always been a useful tool for awkward gists of short texts. The method used was based on building a phrase-based statistical translation model. To do this, you gather up “parallel” texts that are existing, human, translations. You then “align” them by trying to find the most likely corresponding phrases in each sentence or sets of sentences. Often, between languages, fewer or more sentences will be used to express the same ideas. Once you have that collection of phrasal translation candidates, you can guess the most likely translation of a new sentence by looking up the sequence of likely phrase groups that correspond to that sentence. IBM was the progenitor of this approach in the late 1980’s.

It’s simple and elegant, but it always was criticized for telling us very little about language. Other methods that use techniques like interlingual transfer and parsers showed a more linguist-friendly face. In these methods, the source language is parsed into a parse tree and then that parse tree is converted into a generic representation of the meaning of the sentence. Next a generator uses that representation to create a surface form rendering in the target language. The interlingua must be like the deep meaning of linguistic theories, though the computer science versions of it tended to look a lot like ontological representations with fixed meanings. Flexibility was never the strong suit of these approaches, but their flaws were much deeper than just that.

For one, nobody was able to build a robust parser for any particular language. Next, the ontology was never vast enough to accommodate the rich productivity of real human language. Generators, being the inverse of the parser, remained only toy projects in the computational linguistic community.… Read the rest

Boredom and Being a Decider

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tds_decider2_v6Seth Lloyd and I have rarely converged (read: absolutely never) on a realization, but his remarkable 2013 paper on free will and halting problems does, in fact, converge on a paper I wrote around 1986 for an undergraduate Philosophy of Language course. I was, at the time, very taken by Gödel, Escher, Bach: An Eternal Golden Braid, Douglas Hofstadter’s poetic excursion around the topic of recursion, vertical structure in ricercars, and various other topics that stormed about in his book. For me, when combined with other musings on halting problems, it led to a conclusion that the halting problem could be probabilistically solved by an observer who decides when the recursion is too repetitive or too deep. Thus, it prescribes an overlay algorithm that guesses about the odds of another algorithm when subjected to a time or resource constraint. Thus we have a boredom algorithm.

I thought this was rather brilliant at the time and I ended up having a one-on-one with my prof who scoffed at GEB as a “serious” philosophical work. I had thought it was all psychedelically transcendent and had no deep understanding of more serious philosophical work beyond the papers by Kripke, Quine, and Davidson that we had been tasked to read. So I plead undergraduateness. Nevertheless, he had invited me to a one-on-one and we clashed over the concept of teleology and directedness in evolutionary theory. How we got to that from the original decision trees of halting or non-halting algorithms I don’t recall.

But now we have an argument that essentially recapitulates that original form, though with the help of the Hartmanis-Stearns theorem to support it. Whatever the algorithm that runs in our heads, it needs to simulate possible outcomes and try to determine what the best course of action might be (or the worst course, or just some preference).… Read the rest