Category: Cognitive Science

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

Desire and Other Matters

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“What matters?” is a surprisingly interesting question. I think about it constantly since it weighs-in whenever plotting future choices, though often I seem to be more autopilot than consequentialist in these conceptions. It is an essential first consideration when trying to value one option versus another. I can narrow the question a bit to “what ideas matter?” This immediately externalizes the broad reality of actions that meaningfully improve lives, like helping others, but still leaves a solid core of concepts that are valued more abstractly. Does the traditional Western liberal tradition really matter? Do social theories? Are less intellectually-embellished virtues like consistency and trust more relevant and applicable than notions like, well, consequentialism?

Maybe it amounts to how to value certain intellectual systems against others?

Some are obviously more true than others. So “dowsing belief systems” are less effective in a certain sense than “planetary science belief systems.” Yet there are a broader range of issues at work.

But there are some areas of the liberal arts that have a vexing relationship with the modern mind. Take linguistics. The field ranges from catalogers of disappearing languages to theorists concerned with how to structure syntactic trees. Among the latter are the linguists who have followed Noam Chomsky’s paradigm that explains language using a hierarchy of formal syntactic systems, all of which feature recursion as a central feature. What is interesting is that there have been very few impacts of this theory. It is very simple at its surface: languages are all alike and involve phrasal groups that embed in deep hierarchies. The specific ways in which the phrases and their relative embeddings take place may differ among languages, but they are alike in this abstract way.… Read the rest

Motivation, Boredom, and Problem Solving

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shatteredIn the New York Times Stone column, James Blachowicz of Loyola challenges the assumption that the scientific method is uniquely distinguishable from other ways of thinking and problem solving we regularly employ. In his example, he lays out how writing poetry involves some kind of alignment of words that conform to the requirements of the poem. Whether actively aware of the process or not, the poet is solving constraint satisfaction problems concerning formal requirements like meter and structure, linguistic problems like parts-of-speech and grammar, semantic problems concerning meaning, and pragmatic problems like referential extension and symbolism. Scientists do the same kinds of things in fitting a theory to data. And, in Blachowicz’s analysis, there is no special distinction between scientific method and other creative methods like the composition of poetry.

We can easily see how this extends to ideas like musical composition and, indeed, extends with even more constraints that range from formal through to possibly the neuropsychology of sound. I say “possibly” because there remains uncertainty on how much nurture versus nature is involved in the brain’s reaction to sounds and music.

In terms of a computational model of this creative process, if we presume that there is an objective function that governs possible fits to the given problem constraints, then we can clearly optimize towards a maximum fit. For many of the constraints there are, however, discrete parameterizations (which part of speech? which word?) that are not like curve fitting to scientific data. In fairness, discrete parameters occur there, too, especially in meta-analyses of broad theoretical possibilities (Quantum loop gravity vs. string theory? What will we tell the children?) The discrete parameterizations blow up the search space with their combinatorics, demonstrating on the one hand why we are so damned amazing, and on the other hand why a controlled randomization method like evolutionary epistemology’s blind search and selective retention gives us potential traction in the face of this curse of dimensionality.… Read the rest

Local Minima and Coatimundi

Mark Davis1 Comment

CoatimundiEven given the basic conundrum of how deep learning neural networks might cope with temporal presentations or linear sequences, there is another oddity to deep learning that only seems obvious in hindsight. One of the main enhancements to traditional artificial neural networks is a phase of supervised pre-training that forces each layer to try to create a generative model of the input pattern. The deep learning networks then learn a discriminant model after the initial pre-training is done, focusing on the error relative to classification versus simply recognizing the phrase or image per se.

Why this makes a difference has been the subject of some investigation. In general, there is an interplay between the smoothness of the error function and the ability of the optimization algorithms to cope with local minima. Visualize it this way: for any machine learning problem that needs to be solved, there are answers and better answers. Take visual classification. If the system (or you) gets shown an image of a coatimundi and a label that says coatimundi (heh, I’m running in New Mexico right now…), learning that image-label association involves adjusting weights assigned to different pixels in the presentation image down through multiple layers of the network that provide increasing abstractions about the features that define a coatimundi. And, importantly, that define a coatimundi versus all the other animals and non-animals.,

These weight choices define an error function that is the optimization target for the network as a whole, and this error function can have many local minima. That is, by enhancing the weights supporting a coati versus a dog or a raccoon, the algorithm inadvertently leans towards a non-optimal assignment for all of them by focusing instead on a balance between them that is predestined by the previous dog and raccoon classifications (or, in general, the order of presentation).… Read the rest

New Behaviorism and New Cognitivism

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lstm_memorycellDeep Learning now dominates discussions of intelligent systems in Silicon Valley. Jeff Dean’s discussion of its role in the Alphabet product lines and initiatives shows the dominance of the methodology. Pushing the limits of what Artificial Neural Networks have been able to do has been driven by certain algorithmic enhancements and the ability to process weight training algorithms at much higher speeds and over much larger data sets. Google even developed specialized hardware to assist.

Broadly, though, we see mostly pattern recognition problems like image classification and automatic speech recognition being impacted by these advances. Natural language parsing has also recently had some improvements from Fernando Pereira’s team. The incremental improvements using these methods should not be minimized but, at the same time, the methods don’t emulate key aspects of what we observe in human cognition. For instance, the networks train incrementally and lack the kinds of rapid transitions that we observe in human learning and thinking.

In a strong sense, the models that Deep Learning uses can be considered Behaviorist in that they rely almost exclusively on feature presentation with a reward signal. The internal details of how modularity or specialization arise within the network layers are interesting but secondary to the broad use of back-propagation or Gibb’s sampling combined with autoencoding. This is a critique that goes back to the early days of connectionism, of course, and why it was somewhat sidelined after an initial heyday in the late eighties. Then came statistical NLP, then came hybrid methods, then a resurgence of corpus methods, all the while with image processing getting more and more into the hand-crafted modular space.

But we can see some interesting developments that start to stir more Cognitivism into this stew.… Read the rest

Evolving Visions of Chaotic Futures

Mark Davis1 Comment

FlutterbysMost artificial intelligence researchers think unlikely the notion that a robot apocalypse or some kind of technological singularity is coming anytime soon. I’ve said as much, too. Guessing about the likelihood of distant futures is fraught with uncertainty; current trends are almost impossible to extrapolate.

But if we must, what are the best ways for guessing about the future? In the late 1950s the Delphi method was developed. Get a group of experts on a given topic and have them answer questions anonymously. Then iteratively publish back the group results and ask for feedback and revisions. Similar methods have been developed for face-to-face group decision making, like Kevin O’Connor’s approach to generating ideas in The Map of Innovation: generate ideas and give participants votes equaling a third of the number of unique ideas. Keep iterating until there is a consensus. More broadly, such methods are called “nominal group techniques.”

Most recently, the notion of prediction markets has been applied to internal and external decision making. In prediction markets,  a similar voting strategy is used but based on either fake or real money, forcing participants towards a risk-averse allocation of assets.

Interestingly, we know that optimal inference based on past experience can be codified using algorithmic information theory, but the fundamental problem with any kind of probabilistic argument is that much change that we observe in society is non-linear with respect to its underlying drivers and that the signals needed are imperfect. As the mildly misanthropic Nassim Taleb pointed out in The Black Swan, the only place where prediction takes on smooth statistical regularity is in Las Vegas, which is why one shouldn’t bother to gamble.… Read the rest

On Woo-Woo and Schrödinger’s Cat

Mark Davis1 Comment

schrodingers-cat-walks-into-a-bar-memeMichael Shermer and Sam Harris got together with an audience at Caltech to beat up on Deepak Chopra and a “storyteller” named Jean Houston in The Future of God debate hosted by ABC News. And Deepak got uncharacteristically angry back behind his crystal-embellished eyewear, especially at Shermer’s assertion that Deepak is just talking “woo-woo.”

But is there any basis for the woo-woo that Deepak is weaving? As it turns out, he is building on some fairly impressive work by Stuart Hameroff, MD, of University of Arizona and Sir Roger Penrose of Oxford University. Under development for more than 25 years, this work has most recently been summed up in their 2014 paper, “Consciousness in the universe: A review of the ‘Orch OR’ theory” available for free (but not the commentaries, alas). Deepak was even invited to comment on the paper in Physics of Life Reviews, though the content of his commentary was challenged as being somewhat orthogonal or contradictory to the main argument.

To start somewhere near the beginning, Penrose became obsessed with the limits of computation in the late 80s. The Halting Problem sums up his concerns about the idea that human minds can possibly be isomorphic with computational devices. There seems to be something that allows for breaking free of the limits of “mere” Turing Complete computation to Penrose. Whatever that something is, it should be physical and reside within the structure of the brain itself. Hameroff and Penrose would also like that something to explain consciousness and all of its confusing manifestations, for surely consciousness is part of that brain operation.

Now, to get at some necessary and sufficient sorts of explanations for this new model requires looking at Hameroff’s medical speciality: anesthesiology.… Read the rest

Bayesianism and Properly Basic Belief

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Kircher-Diagram_of_the_names_of_GodXu and Tenebaum, in Word Learning as Bayesian Inference (Psychological Review, 2007), develop a very simple Bayesian model of how children (and even adults) build semantic associations based on accumulated evidence. In short, they find contrastive elimination approaches as well as connectionist methods unable to explain the patterns that are observed. Specifically, the most salient problem with these other methods is that they lack the rapid transition that is seen when three exemplars are presented for a class of objects associated with a word versus one exemplar. Adults and kids (the former even more so) just get word meanings faster than those other models can easily show. Moreover, a space of contending hypotheses that are weighted according to their Bayesian statistics, provides an escape from the all-or-nothing of hypothesis elimination and some of the “soft” commitment properties that connectionist models provide.

The mathematical trick for the rapid transition is rather interesting. They formulate a “size principle” that weights the likelihood of a given hypothesis (this object is most similar to a “feb,” for instance, rather than the many other object sets that are available) according to a scaling that is exponential in the number of exposures. Hence the rapid transition:

Hypotheses with smaller extensions assign greater probability than do larger hypotheses to the same data, and they assign exponentially greater probability as the number of consistent examples increases.

It should be noted that they don’t claim that the psychological or brain machinery implements exactly this algorithm. As is usual in these matters, it is instead likely that whatever machinery is involved, it simply has at least these properties. It may very well be that connectionist architectures can do the same but that existing approaches to connectionism simply don’t do it quite the right way.… Read the rest

Entanglement and Information

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shannons-formula-smallResearch can flow into interesting little eddies that cohere into larger circulations that become transformative phase shifts. That happened to me this morning between a morning drive in the Northern California hills and departing for lunch at one of our favorite restaurants in Danville.

The topic I’ve been working on since my retirement is whether there are preferential representations for optimal automated inference methods. We have this grab-bag of machine learning techniques that use differing data structures but that all implement some variation on fitting functions to data exemplars; at the most general they all look like some kind of gradient descent on an error surface. Getting the right mix of parameters, nodes, etc. falls to some kind of statistical regularization or bottlenecking for the algorithms. Or maybe you perform a grid search in the hyperparameter space, narrowing down the right mix. Or you can throw up your hands and try to evolve your way to a solution, suspecting that there may be local optima that are distracting the algorithms from global success.

Yet, algorithmic information theory (AIT) gives us, via Solomonoff, a framework for balancing parameterization of an inference algorithm against the error rate on the training set. But, first, it’s all uncomputable and, second, the AIT framework just uses strings of binary as the coded Turing machines, so I would have to flip 2^N bits and test each representation to get anywhere with the theory. Yet, I and many others have had incremental success at using variations on this framework, whether via Minimum Description Length (MDL) principles, it’s first cousin Minimum Message Length (MML), and other statistical regularization approaches that are somewhat proxies for these techniques.… Read the rest