We have now built a base of theory for why AI works, what Models are and how to create them, what Reductionism and Holism are, and what the process of Reduction is. These are the fundamentals of AI Epistemology. This base allows us to discuss various strategies to move towards Understanding Machines in a well understood and controlled manner.

We are now ready to discuss why Deep Learning (DL) works. This is the fifth and last entry in the AI Epistemology Primer.

Deep Learning Performs Reduction

This is an unsurprising claim, considering the preceding chapters. There are several mutually compatible theories for “how” Deep Learning works. But just as in the first chapter, we will now discuss the Epistemological aspects, “why” it works, from several viewpoints and levels, starting from the bottom. We will use examples from the TensorFlow system and API (as a library) as a stand-in for all Deep Learning-family algorithms and TF programs, because the available API functions heavily shape and constrain solutions that can be implemented in this space and the generalization should be straightforward enough.

Consider the following illustration of image Understanding using Keras (an excellent abstraction layer on top of TensorFlow):

I like to refer to the input layer as being “on the bottom” rather than at the far left as in this image. When viewing it my way, the low-to-high dimension we use in my rotated version of the above can be mentally mapped to a low-to-high stack of abstraction levels; I’m not the only one using this dimension this way. I hope this rotation isn’t too confusing.

We can see that there is an obvious data Reduction and an obvious complexity Reduction. Can we determine whether the system is also performing what I’d like to call “Epistemic Reduction”: Is it reducing away that which is unimportant, and if so, how does it accomplish this? How does an operator in a Deep Learning stack know what makes something important (Salient)?

A pure data “reduction” of sorts could be accomplished by compression schemes or even random deletion. This is undesirable. We need to discard the non-salient parts so that in the end, we are left with what is salient. Some people have not understood the importance of Salience based Reduction and use lossless compression power of reversible algorithms as a measurement of intelligence. Which is no more useful than believing a simple video camera can understand what it sees.

So let me conjure up, a bit like in the movie “Inside Out”, a fairytale of what goes on in a Deep Learning network, except we’ll do it “Bottom Up”. Suppose we have built a system for finding faces in an image, with the intent of incorporating that as a feature in a camera; many cameras have this feature already, so this is not a far-fetched example. We implement an image understanding neural network, show the system many kinds of images for a few days, perhaps using so-called supervised learning in order to improve this story, and then we show it an image of a family having a picnic in a park and ask the system to outline where the faces are so that the camera can focus sharply on them.

The input image is converted from RGB color values to an input array and the data in this array is then shuffled through many layers of operators. And for many of these layers, there are fewer outputs than there are inputs, as you can see in the above diagram. Which means some things have to be discarded by the processing. Each layer receives initially signals “from below”, i.e. from the input, or from lower levels of abstraction, and produces some reduced output to send to the next layer operator above.

To continue the tale, at some early level, some operator is given a few adjacent pixels and determines that there is a vertical, slightly curved line dividing a darker green area from a lighter green area, so it “tells” the operator above this simpler line/color based description using some encoding we don’t really care about.

The operator at the level above might have gotten another matching curve and says “these match what I saw a lot of when the label “blade of grass” was given as a ground truth label during (supervised) learning. If no label is known, then we again assume some other uninteresting representation. It is OK to propagate results without human-labeled signals because whatever signaling scheme is used will be learned by the level above.

The operator above that says “when I get lots of blades-of-grass signals I reduce all of that to a “lawn” signal as I send it upward.

And eventually we reach the higher operator layers and someone there says “We are a face finder application. We are completely uninterested in lawns” and discards the lawn as non-salient.

What remains after you discard all non-faces are the faces.

You cannot discard anything until you know what it is, or can at least estimate whether it’s worth learning. Specifically, until you understand it at the level of abstraction you are operating at. The low level blade-of-grass recognizers could not discard the grass because they had no clue about the high level saliencies of lawn-or-not and face-or-not that the higher layers specialize in.

You can only tell what’s Salient or not (important or not) at the level of Understanding and Abstraction you are operating at. Each layers receives “lower level descriptions” from below, discards what it recognizes as irrelevant, and sends its own version of “higher level descriptions” upward until we reach someone who knows what we are really looking for.

This is of course why Deep Learning is deep.

This idea itself is not new. It was discussed by Oliver Selfridge in 1959; he described an idea called “Pandemonium” which was largely ignored by the AI community because of its radical departure from the logic based AI promoted by people like John McCarthy and Marvin Minsky. But Pandemonium presaged, by almost 60 years, the layer-by layer architecture with signals passing up and down that is used today in all Deep Neural Networks. This is the reason my online handle is @pandemonica

— * —

So do any TensorFlow operators support this Reduction?

Let’s start by examining the Pooling operators; there are a few in the diagram. They are conceptually simple. There are over 50 pooling operators in TensorFlow. There is an operator named “2x2 Max-Pool Operator”. In this diagram, it is used four times:

It is given four inputs with varying values and propagates the highest value of those as its only output. Close to the input layer these four values may be four adjacent pixels where their values might be a brightness in some color channel, but higher up they mean whatever they mean. In effect, the Max-Pool 2x2 discards the “least important” 75% of its input data, preserving and propagating only one (highest) value.

In the case of pixels, it might mean the brightest color value. In the case of blades of grass, it might mean “there is at least one blade of grass here”. The interpretation of what is discarded depends on the layer, because in a very real sense, layers represent levels of Reduction; Abstraction levels, if you prefer that term.

And we should now be clearly seeing one of the most important ideas in Deep Neural Networks: Reduction has to be done at multiple levels of abstraction. Each set of decisions about what is reduced away as irrelevant and what is kept as possibly relevant can only be made at an appropriate abstraction level. We cannot yet abstract away the lawn if all we know is there are dark-and-light-green-areas levels.

This is a simplification; decisions made in this manner will be heeded only if they have contributed to positive outcomes in learning. Unreliable and useless decision makers will be ignored using any of several mechanisms that we may apply during learning. More later.

For now, we continue by examining the most popular subset of all TensorFlow operators – the Convolution family. From the TensorFlow Manual:

Note that although these ops are called “convolution”, they are strictly speaking “cross-correlation”

Convolution layers discover cross-correlations and co-occurrences of various kinds. Co-occurrences to known patterns in the image at various locations; spatial relationships within an image itself, like Geoff Hinton’s recent example of the mouth normally being found below the nose; and more obviously, in the supervised learning case, correlations between discovered patterns and the available meta-information (tags, labels) that correlate with the patterns the system may discover. This is what allows an an Image Understander to tag the occurrence of a nose in an image with the text string “nose”. Beyond this, such systems may learn to Understand concepts like “behind” and “under”.

The information that is propagated to the higher levels in the network now describes these correlations. Uncorrelated information is viewed as non-salient and is discarded. In the diagram above, this discarding is done by a max pooling layer after the convolution+ReLU layers. ReLU is a kind of layer operator that discards negative values, introducing a non-linearity that is important for DL but not really important for our analysis.

This pattern of three layers — convolution, then ReLU, then a pooling layer — is quite popular because this combination is performing one reliable Reduction step. These three layer types in this “packaged” sequence may appear many times in a DL computational graph. And each of these three-layer packages is reducing away things that levels below had no chance of evaluating for saliency because they didn’t “Understand” their input at the correct level.

Again,

This is why Deep Learning is deep… Because you can only do Reduction by discarding the irrelevant if you Understand what is relevant and irrelevant at each different level of Abstraction.

Is Deep Learning Science or not?

While the Deep Learning process can be described using mathematical notation, mostly using Linear Algebra, the process itself isn’t Scientific. We can not explain how this system is capable of forming any kind of Understanding by just staring at these equations, since Understanding is an emergent effect of repeated Reductions over many layers.

Consider the Convolution operators. As the TF manual quote clearly states, Convolution layers discover correlations. Many blades of grass together typically means a lawn. In TF, a lot of cycles are spent on discovering these correlations. Once found, the correlation leads to some adjustment of some weight to make the correct Reduction more likely to be re-discovered the next round (because this Reduction is done multiple times) but in essence, all correlations are forgotten and have to be re-discovered in every pass through the Deep Learning loop of upward signaling and downward gradient descent with minute adjustments to erring variables. The system is in effect learning from its mistakes, which is a good sign, since that may well be the only way to learn anything. At least at these levels. This up-and-down may be repeated many times for each image in the learning set.

This up-and-down makes some sense for image Understanding. Some are using the same algorithms for text. Fortunately, in the text case, there are very efficient alternatives to this ridiculously expensive algorithm. For starters, we can represent the discovered correlations explicitly, using regular “pointers” or “object references” in our programming languages. Or “synapses” in brains. “This (software) neuron correlates with that software neuron” says a synapse or reference connecting this to that. We shall discuss such systems in the Organic Learning series of blog entries; coming up next.

Neither the Deep Learning family of algorithms, or Organic Learning, are Scientific in any meaningful way. They jump to conclusions on scant evidence and trust correlations without insisting on provable causality; this is disallowed in scientific theory, where absolutely reliable causality is the coin of the realm. F=m*a or go home. Most Deep Neural Network programming is uncomfortably close to trial and error, with only minor clues about how to improve the system when reaching mediocre results. “Adding more layers doesn’t always help”. These kinds of problems are the everyday reality to most practitioners of Deep Neural Networks. With no a priori Models, there will be no a priori guarantees. The best estimate of the reliability and correctness of any Deep Neural Network, or even any Holistic system we can ever devise, is going to be extensive testing. More on this later, in future blogs.

Why would we ever use engineered systems that cannot be guaranteed to provide the correct answer? Because we have no choice. We only use Holistic methods when the reliable Reductionist methods are unavailable. As is the case when the task requires the ability to perform Autonomous Reduction of context-rich slices of our rich complex reality as a whole. When the task requires Understanding.

Don’t we have an alternative to these unreliable machines? Sure we do. There are billions of humans on the planet that are already masters of this complex task. Because they live in the rich world and need skills that are unavailable with Reductionist methods, starting with low level things like object permanence. So you can replace a well-performing but theoretically unproven contraption – a Holistic Understanding Machine built out of Deep Neural Networks – with a well-performing human being using a deeply mystical kind of Understanding hidden in their opaque heads. Who earns much more per hour. This doesn’t look like much of an improvement. The machine cannot be proven correct because it doesn’t function like normal computers. It is performing Reduction, the skill formerly restricted to animals.

A Holistic skill.

My favorite soundbite is a mere corollary to the Frame Problem by McCarthy and Hayes; you have seen it and you will see it again, since it is one of the stronger results of AI Epistemology. But we will, in but a few years, agree on a definition of intelligence that makes autonomous Reduction a requirement. This once semi-heretic soundbite will then be obvious to all. If it isn’t already.

All intelligences are fallible

Why Deep Learning Works was originally published in Artificial Understanding on Medium, where people are continuing the conversation by highlighting and responding to this story.

Until 2012, only humans and other animals with brains could perform Reduction. Now our Deep Neural Networks (DNN) can perform limited Reduction. How do brains and DNNs accomplish this, and how can we improve these algorithms?

This may be, to some readers, the most rewarding blog in this series because it provides you the opportunity to learn a new and useful skill. Most people never think about the world at this level. Knowledge of Reduction provides a new point of view that you can use to better understand your environment, other intelligent agents around you, and modern AI systems.

Definition of Reduction

Reduction is a process that discovers higher level abstractions in lower level data

We will initially note that Reduction is exactly the same as Abstraction. Why do we need a new word? Because the term “Abstraction” is mostly used by scientists already operating in a pure Model space, seeking a higher level of abstraction in that space. But to them, “Abstraction” is something that just magically happens in their heads, since there are no scientific theories for how Abstraction works. There cannot be, since Abstraction is a concept in Epistemology, not Science.

AI researchers are starting from something much closer to our rich mundane reality, where there is a lot of confounding context. We are solving the meta-problem of how to move from there into a space that is sufficiently abstract to solve the problem at hand. Here, Reduction is a much more appropriate term. We can’t abstract a red pixel or the letter “b”, but we can Reduce a rich context containing that pixel or letter into a higher level concept.

We Are Swimming In Reduction

Paradoxically, one of the hardest thing about teaching Reduction is that we don’t see the need to learn about it because we all do it all the time, every millisecond, and the resulting Reductions (Models) become available to our conscious minds as if “by magic”. Brains Reduce away 99.999% percent of their sensory input, but this process is subconscious and hence invisible to us. The situation is much like (supposedly) a fish swimming in water. We are all masters of Reduction, but we don’t know how we do it or that we even do it. We didn’t know this would ever matter. And generally, it doesn’t.

Well, it matters in Epistemology, and it matters in AI, since we need to actually implement that “magic”. We as Epistemologists must know how Abstraction is actually performed. And we give the Epistemology level equivalent of Abstraction the name “Reduction” because that’s the recipe for how to accomplish it. We Reduce our rich mundane Reality by discarding (reducing away) what’s irrelevant. And by using the name “Reduction” we (as AI Epistemologists) keep reminding ourselves how it is properly done.

Consider the following descriptions of a car. The slide is meant to be read from the bottom up, to match “abstraction levels” from low to high.

If I’m driving to work, I better be driving my car. If the police is looking for a stolen car they would be looking for a Red 2010 Toyota Celica. If I’m buying a new car then I might be looking for just a new Toyota Celica. And a self-driving car would likely only need to Understand whether an obstacle is a vehicle or not, in order to Model maximum speed for future movement.

We see that we want to pick the appropriate level of abstraction to deal with the same object (or topic) in different situations. But more importantly, we see that we can get from a more detailed description (at the bottom) to a more generic one (higher up) by simply discarding some detail.

I hasten to point out that Reduction is more complicated than this simple example of decreasing specificity shows, but we need to start somewhere and this image allows us to form intuitions that will serve for a while. True Reduction involves operations like shifting from syntax to semantics or from instance to type; the appearance of “car” as an abstraction of “Toyota”, and the step from “My Toyota” to “A Toyota” illustrate these steps. Algorithms for these things are known.

Salience

Part of the trick is to know what to discard. At each level of abstraction, something can typically be identified as the least important property. “Red” and “Celica” are more significant than “2010” for anyone looking for a car. If we had started from “My red 2010 Toyota truck”, then the word “truck” would not be discarded until the top level. Reduction requires Understanding what’s relevant; in Reduction we “keep that which is Salient”. More later.

Partial Reductions

Most of the time we do NOT perform Reduction all the way to Models. I cannot stress this enough. We discuss Reduction to Models for pedagogical reasons; it is easy to initially see the context-free Model as the goal of Reduction. In reality, in brains, we can stop Reducing the moment we recognize that we have a working answer or response, such as a command to contract some muscle or having Understood the meaning of a sentence subconsciously. At this point, there is still some residual context but we use that context productively rather than discard it to move to higher levels.

Some people claim we use Models for all our thinking, but I’m using (in these blogs) “Model” only to describe a completely context free Abstraction. F=ma is an example of that. There is no need to check whether a car is a Red car or a Toyota, the equation works not only for all cars but for all forces, masses and accelerations. We might come up with a special equation for acceleration of Tesla cars, which would require different inputs like battery charge level and software settings; that would not be a context free Model since it would not work on a Toyota. For almost all tasks — basically, in everything except Science, and even there, only rarely — we only perform as much Reduction as is necessary to get the job done. When learning to ski, you only figure out how you yourself need to perform given your body and equipment; we do not need to parameterize our skiing skills for someone with twice the body mass, because that would be useless to us for the purpose of our own skiing. But a scientist would have to go that far, in order to parameterize away one more piece of context from the Model they are creating. For instance, when creating a skiing video game or designing a new ski.

If we consider the enormous amount of subconscious activity that happens in the brain we can safely say that partial Reductions are the most common Reductions. For instance, when we take a step forward, our subconscious has analyzed our posture and velocity by using Reduction based on low level nerve signals and is commanding leg muscles to contract in a precisely timed sequence. This activity is something we are unaware of; most of us don’t even know what leg muscles we have. And there would be no time to perform Reduction all the way to Models. That process takes a minimum of a half second and you don’t have that kind of time available to respond to an imbalance when walking or skiing.

Reduction in Society

Most of us get paid to Understand whatever we need to Understand in order to perform our jobs. In other words, most of us get paid to do Reduction. If you are approving building permits, you Reduce a stack of forms to a one-bit verdict of “Approved” or “Rejected”. We excel at Reduction, and this is the main reason most of us haven’t been replaced by robots. But we see that when future Understanding Machines can perform Reduction by themselves, then we are unlikely to get paid for it.

Levels of Reduction

Suppose a young man and a young woman fall in love, something happens to mess it all up, and then they sort this out and re-unite.

This is what happened in the man’s “rich mundane reality”. Suppose the man wants to share this experience, because there was some moral to the story that he thinks would be interesting to others and possibly important.

He could analyze what happened and figure out which were the key events in the saga and then have actors on a stage re-enact the story as a play. This is a Reduction because the boring parts of the story would not be part of the play. They are discarded as irrelevant. But the story would be acted out by real people in front of a live audience. If you are in the audience, you can move your head to see behind any actor on the stage and you can clearly see everything on the stage, not just one actor speaking at a time.

He could make a movie about it. Now your point of view is predefined by the camera angle and cropping. You can no longer see behind an actor, and you can often only see those actors that are involved in the main action.

He could write a book about it. We no longer can see even the people described in the book, except in our imagination.

An critic reviewing the theatre play may Reduce it to “Boy meets girl, boy loses girl, boy gets girl”

A drama school graduate may summarise it as “A double-reversal plot”. This is a description that is so free from context (doesn’t even specify boys or girls) that it could be argued it qualifies to be called “A Model”.

Plays, Movies, Books, Stories, Tropes, etc are all Partial Reductions of Reality, and some are more Reduced than others. Just like in the My Red Toyota case, we need to find the appropriate level of Abstraction to work with.

The young man in the example, when writing a book or a screenplay, has much in common with a Scientist trying to describe something in nature in a re-usable context free manner by Reducing it to a Model. They are Model Makers, or are at least performing partial Reduction. They are discarding the irrelevant bits.

The Opposite of Reduction

We also need to be able to move in the opposite direction, from Models to Reality. Or at least from more abstract Partial Models to Partial Models closer to reality.

When an actor is given a screenplay they know it only contains rough directions for what to do and what lines to say. The actor’s job is to “give a little of themselves” to flesh out the screenplay to actual actions, including creating — synthesizing — the appropriate display of emotions, tone of voice, and body language. They use their experience as people and as actors ; they use elements of their past lives and skills they have acquired by training to create something people in the audience might relate to. For example, they may re-purpose a personal experience (“be as sad as when my hamster died”), things they learned in drama school (speaking, singing, dancing, swordplay), from other actors (“What would Bogart do”), from fiction, from other movies and plays, etc.

The actor’s art is to convey whatever the script intends to convey — emotions, a morality cookie, a political position, titillation, surprise, etc. starting from a simple Model (the screenplay). Their job is similar to an engineer’s when they are faced with a problem and use a Model to solve it. The engineer would use their experience to decide that “m” is the mass of the car and not the tire pressure. The actor decides that “sadness” is more appropriate than “grief” for a certain scene, etc.

I call this process, which is “the opposite of Reduction”, by the name it is used in problem solving: “Application”. We use a Model to simplify a problem situation, moving it into an abstract and purer “Model space”. We solve the problem there (by performing math, perhaps) and then “Apply” the answer to our rich reality, to the problem we are trying to solve.

Many of you may recognize the word “Application” or its abbreviation “App”. That’s not as farfetched as it might seem; apps are software based Models.

Reduction and Application in Brains

Back to the issue of Partial Reductions. Consider the actor reading a screenplay. They are using their eyes to gather “pixels” of color and orientation. The brain then performs pattern matching — Reduction — from these low level signals to letters, words, to language, to higher level concepts like love and separation, and eventually to a high level Understanding of the playwright’s intents. The actor then takes this high level Understanding and by performing Application he adds his own Experience to the script, to get closer to reality in their performance.

Our brains are capable of moving up and down many levels of abstraction at once. Perhaps it tracks all of them simultaneously, keeping layers of abstraction separate. This is a clue for why Deep Neural Networks perform better than shallow ones. Which is what we’ll discuss next.

Reduction was originally published in Artificial Understanding on Medium, where people are continuing the conversation by highlighting and responding to this story.

After having sorted out what Models are, we can now discuss two complementary problem solving strategies (or perhaps meta-strategies). They are in many ways each other’s opposites, but the classification can become an argument about meta-levels and definitions. I will initially pretend the division is clear and obvious, and will elaborate later.

Reductionism is the Use of Models

In this blog series we will use exactly the above definition of the word “Reductionism”. If you look up the definition elsewhere you may find that some sources divide the strategy into sub-strategies. They also seem to miss the most important sub-strategy, which we’ll discuss later. But what all these sub-strategies have in common is that they all provide ways to simplify observations of fragments of our rich mundane reality into much simpler Models, which we use for reasoning, computation, and sharing.

Reductionism is so central to how we do science — the heavy reliance on Models, such as theories, equations and formulas, in physics, chemistry, etc. — that we can speak of “Model Based sciences” or “Reductionist sciences” where such Model Making is easy and effective. And this classification excludes those sciences, like psychology, where such Model making is difficult and less often rewarded with reliable results.

After considering all the advantages of Models we might wonder why we even bother discussing it. To many people, especially those with a solid STEM (Science, Technology, Engineering, and Mathematics) education, it may well look like the only choice. But there is also the other strategy:

Holism is the Avoidance of Models

This is where the questions start. This is where the paradoxes surface. This is where your worldview may get shaken up. Seriously. Especially if you are a scientist or engineer with a solid STEM education and decades of professional success using science and Models.

In some sense, the goal of this entire blog series is to demonstrate that we need to use both problem solving strategies when creating our artificial Intelligences. Because that is what it is going to take. We need Holistic Understanding; we established that in the first chapter. As a sample of the new ideas that we will have to deal with I will just mention

• Reasoning is Reductionist
• Understanding is Holistic
• Neural Networks are Holistic
• Holistic systems can jump to conclusions on scant evidence
• Holistic systems can themselves know what is important and what isn’t
• Holistic systems can solve problems we ourselves cannot (or don’t care to) Understand
• Holistic systems are “Model Free”. They do not use any a priori Models of any problem domain
• Reasoning systems inherit all problems and benefits of Reductionism.
• Understanding systems inherit all problems and benefits of Holism
• Humans are born Holistic
• Humans each solve thousands of little problems every day, and we are solving almost all these problems Holistically, using Understanding, and without a need to Reason at all. This includes fluent language use.
• A STEM education instills a strict Reductionist discipline in order to mitigate problems with fallibility of Holistic human minds
• All intelligences are fallible

These claims all deserve individual treatments, and we’ll get to all of them in later blogs. But the major theme is clear:

Humans are mainly Holistic problem solvers. The same must be true for our Artificial Intelligences

We had several reasons for focusing on Reductionist Methods (Models) and Reasoning during the first 60 years of AI. Our computers were too small to make Neural Networks work at all. But there were also ideological reasons. AI was born out of the math and computer science departments of our universities. And therefore most of the people working on AI were solidly oriented towards the goal of creating a logic based Reductionist infallible artificial mind. To build early AIs, like expert systems, we entered rules or programmed in lots of facts to Reason about. But this was building Reductionist castles in the air, comprised of un-anchored facts that didn’t tie to any Understanding whatsoever. The troubles with classical AI, such as brittleness (the tendency to make spectacular and expensive mistakes at the edges of their competence), can be directly traced to the lack of foundational Understanding to support these attempts at Reasoning.

Understanding Machines will not suffer from this brittleness, but will fail gracefully at the edges of their competence, much like humans. Most of the time they will “know” the answer; beyond that they will guess. And the guesses they make are based on a lifetime of experience (gained through learning from a large corpus) and so they have a good chance of being at least a workable choice, if not perfect.

How can anyone solve problems without using Models?

A lot of people coming from a STEM background cannot even imagine how to solve problems without using Models. But it’s not hard, once you understand the difference. Mostly it’s a matter of doing what worked last time. The problem is now figuring out whether we are in a situation that’s similar enough that it will work again. This is mostly a pattern matching problem. More later.

What’s the result? The Holistic answer is a quick guess at the best action, based on experience with similar situations. Most of the time it’s correct, sometimes it’s a little wrong, and every now and then, there’s a noticeable mistake. And if we get things a little wrong, we may notice the outcome and correct the action. We learn from our mistakes. If we practice something a lot we will start doing it effectively and perfectly every time. Do we learn faster if we make more mistakes? Should we make mistakes on purpose? More later.

In situations where you cannot use Models, which are more common than many realize, the Holistic guess may also be your only option. Conversely, if you have an adequately well working Model based solution, just use that.

My video “Model Free Methods Workshop” demonstrates how the group solves four different problems, at a high level, using both Reductionist and Holistic Methods.

Why are these “Dirty words”?

Well, they are not dirty to Epistemologists.

Reductionism has been the default problem solving paradigm because it’s the one that has to be taught. We are born with a holistic problem solving apparatus. But Reductionist science doesn’t come naturally; therefore it has to be taught in schools, practiced, and carried out according to certain rules. Perhaps that’s why the sciences are called “disciplines”, because following the ideal scientific method requires practice and constant vigilance.

J. C. Smuts’ book “Holism and Evolution” (1926) established the terminology in the Epistemological literature. And Erwin Schrödinger wrote “What is Life” (1944), questioning the power of physics to provide useful explanations to the life sciences. Pirsig wrote “Zen and the Art of Motorcycle Maintenance” (1974) that contrasts something very Holistic, Zen Buddhism, with something very Reductionist, Motorcycle Maintenance. So the chasm between the strategies was identified a long time ago.

The strategies are each other’s opposites. Holism based strategies for Understanding can handle many important kinds of complexity and can quickly provide a guessed answer, but these guesses are fallible, and often more expensive to compute. Reductionist education and strategies brought benefits of cheap Model reuse and formal rigor to improve correctness, but cannot handle complexity and is therefore dependent on an external Understander to determine applicability in real-world complexity-rich situations. And as part of that education, we are told that Holistic methods (such as jumping to conclusions on scant evidence) are bad… in spite of the fact that our brains use Holistic methods thousands of times each day to successfully Understand the environment we live in.

We can all use either strategy as appropriate; if we don’t have a STEM education we will still sometimes make naïve Models. But sometimes there is a choice and different people may prefer one or the other. When playing pool, some people estimate and compute bouncing angles and some people shoot “by feel”.

But we have our preferences, and it might be tempting to label a person with an overly strong preference as “a Holist” or “a Reductionist”. This is sometimes received badly, if perceived as a limitation. Some dictionaries even flag “Reductionist” as derogatory; and yet, some people use it as a self-assigned label. I try to use these terms only as shorthand for “a person with a stated strong preference for Holistic (or Reductionist) Methods”.

The two terms were very useful in Epistemology. But then someone invented the concept of “Holistic Medicine”: Instead of just treating a single medical problem, you analyzed the patient’s entire situation, attempting to account for diet, exercise, sleep, work, habits, stress levels, allergies, family, friends, and environmental poisons. A good idea, in general. But the wide scope was unmanageable by the (traditionally Reductionist) medical establishment and the idea faded away. Instead, the whole idea of Holism became tainted as woo-woo when the term “Holistic Medicine” became associated with woo-woo merchants selling crystals and aromatherapy.

As explained above, “Holism is the avoidance of Models”, or better phrased, “Holism is the meta-strategy of avoiding a priori Models of the problem domain”. That extra precision rarely matters. There’s nothing woo-woo about it. It does say “science not required”, but…

You can make breakfast without Reasoning

It is important to note that Holistic methods are based on a lifetime of experience (in humans) and a training corpus’ worth of experience (in Neural Networks). When you are making breakfast, you are relying on this experience, mostly repeating whatever worked yesterday.

Some people claim they use Reasoning while making breakfast… but they can make their breakfast while speaking to someone else on the phone and as they hang up, they find themselves suddenly sitting at the breakfast table with their coffee and hot oatmeal. Same thing when driving to work; you may get lost in thought, and then you find yourself parked at work. You didn’t need to Reason, since all subproblems that occur in driving had been solved multiple times during years of driving. Subconscious Understanding is used for simple things like sequencing our leg muscles as we walk; you have no idea how you are doing that, it just works. Same thing with vision. You Understand that you are looking at a chair, but you do not have conscious access to the fifteenth rod/cone/pixel to the left of your center of vision, and have no idea how this Understanding works. Same thing with understanding and generating language. You do not have any explanation for how you are able to understand the meaning of this sentence. Understanding is Subconscious and Holistic.

So for the majority of things we do every day, we do not need Reasoning or Reductionist Methods. Some people would like to think they are “logical thinkers”, immune to most cognitive fallacies, but whether they are or not, at the lower levels, everyone is solving most of their problems Holistically.

I claimed that “Reductionist Reasoning requires Holistic Understanding”. In other words, I need to Understand the problem domain at hand before I can create and/or re-use Models to enable me to Reason about the domain.

So Holistic Understanding is much more important than Reductionist Reasoning because it is the most used strategy, by far, and the former is also a prerequisite for the latter. But the fallibility of Holistic Understanding forced us to create Reductionist science and to teach it in STEM educations. It is as if the purpose of science is to keep Holistic guessing in check. But this aversion to fallibility has a cost, because it means complexity-bound and “irreducible” problems cannot be solved. Like language Understanding, global resource allocation, and social interactions.

Reductionism and Model based science appeared around 1650 after a century of gestation. Excluding minor romantic interludes, it has held its position as the dominant paradigm for about 400 years. This is changing.

The Reductionist train is running out of track

The remaining hard problems facing humanity are problems of irreducible complexity in domains where Reductionist Model Based Methods simply cannot work. Whether we like the idea or not, we need to accept these Holistic methods into our AI toolkits, starting now. We will use these methods either in their raw form, as Model Free Methods, or as Understanding Machines at any level from component to robot co-worker.

Two Dirty Words was originally published in Artificial Understanding on Medium, where people are continuing the conversation by highlighting and responding to this story.

The first blog “Why AI Works” provided the big picture of AI and Understanding Machines. Next we will focus on how to actually implement Understanding in a computer. But before we can attack that core issue we need to simplify the journey a bit by defining four important words and concepts. I’ll define one in this blog, two in the next, and the concept of Reduction after that. We can then discuss the Epistemology-level algorithm for Understanding itself.

If you are already familiar with these concepts, just check the boldfaced headings and definitions below to ensure we are using these words roughly the way you use them.

You may have noticed I write certain (sometimes common) words, such as Model, with an uppercase first letter. This means I am using the word in a technical, well defined, unchanging sense. I will define all such technical terms over time and I will try not to use these terms until I have defined them. We defined 11 such terms in the first chapter, starting with Understanding and Reasoning. A dictionary of defined terms is in the works.

Models are simplifications of reality

In Epistemology and science, “Models” are simplifications of reality. Our rich mundane reality is too complex to lend itself directly to computation. In old TV science fiction shows, we would sometimes hear “… and then we fed all the information into the computer and this is what came out”. Well, not anymore; audiences now know that’s not how (regular) computers work.

Consider an automobile. It consist of thousands of parts, each with properties like materials, size, color, function, and sometimes complex interactions with other parts. What’s “all the information” here? We can’t just feed all of those properties and measurements and facts into a computer and expect to get “an answer”. We need to ask a question. And we also need to simplify the problem so that we can feed in just the facts or numbers that matter, so that our question can be answered with minimum effort. How do we do that?

We must identify or create, first in our minds, a very simple Model of some sort of a generic automobile, and use that Model for our computation. After we get the answer for the pure and simple Model case, we apply the answer, with some care, back to our complex reality where the real automobile (and the problem) exists.

What kind of Model we choose depends on our goals. As an example of a Model, Newton’s second law states that force equals mass times acceleration: “F = ma”. This equation is a classical scientific Model. If we measure mass and acceleration of a car then we can estimate how many horsepower the engine has. To use this equation, we engineers would model (in our minds) the car as a single small “point mass” with all the mass of the car in that point. Because if we don’t, then we’d have to worry about the car rotating and other problems.

This is how Model based science works. One or more scientists somehow derive a Model for some phenomenon. The Model is published as an equation, a formula, or a computer program. Scientists and engineers anywhere can now use this equation/program/Model, treating it as a quick shortcut that works every time, as long as they have correct input data and are competently applying the formula to a suitable problem in their reality.

Our Greatest Invention

Model Based Problem Solving (aka Reductionism) is the greatest invention our species has ever made. The general strategy of simplifying problems before solving them must be tens of thousands of years old. In some sense, it is a prerequisite for all other inventions, including the use of fire. If you see a forest fire then you need to first imagine the utility of fire, as a Model, before you can figure out that it might be useful to carry home a burning branch.

We don’t think of this problem solving strategy as an invention because it is already ubiquitous in our lives. We are all taught how to use Model based problem solving in school when we start solving story problems in math class. But most people never learn the names of these strategies and are missing the big Epistemology level picture; this rarely matters… until you start working with AI, where lack of an Epistemological grounding may lead you astray into failing strategies. These blogs are an attempt to remedy that.

Naïve Model based methods were examined and refined into scientific methods over the past 450 years. Science is now a collection of thousands of Models that taken together allow science-competent people to solve problems quickly and efficiently without having to re-do all the work that scientists (like Newton) put into creating these Models in the first place. And the sum total of those Models covers many problems we want to solve scientifically, such as how to build a bridge, or travel to the moon. This reuse is what makes science so effective.

But not all sciences can benefit equally from this Model making; it works well for physics, chemistry, and most of biochemistry. As I’m fond of saying, “Physics is for simple problems”. But as you get to more and more complex sciences — as you get further away from physics and closer to life — it gets harder to make decent Models. The Models used by for instance psychology, ecology, physiology, and medicine are generally more complex but also less powerful than Models in physics. Given some solid data, a physicist can compute the mass of the proton to six decimal places but we would have a harder time predicting the number of muskrats in New England next summer because that outcome depends on millions of parameters. The life sciences base many of their Models on statistics. Statistical Models are among the weakest Models used in science. We use statistical Models when more powerful Models with better predictive capabilities cannot be used for complexity reasons.

Models are

• hypotheses (unverified Models)
• scientific theories (Models verified by peer review)
• equations
• formulas
• complex scientific Models (simulations of climate, weather, etc.)
• naïve models (that we create to simplify our own lives)
• computer programs

And what is Mathematics? It is a system that allows us to manipulate our Models to cover more cases. Mathematics is the purest, most context free of all scientific disciplines. As such, its greatest value to humanity is in its role as a help discipline to all other disciplines. Einstein’s famous E=mc² Model was derived using mathematical manipulation of other Models known to Einstein at the time. But perhaps mathematics isn’t as much a scientific discipline as an Epistemological one; I may explore this aside later.

Model use requires Understanding

A good Model is context free, since that maximizes the number of contexts it can be applied in. Newton’s second law F=ma works pretty much everywhere we have forces, masses, and accelerations. The tradeoff for this flexibility is that we ourselves need to Understand the problem domain. In rocket science, when maneuvering in space, F=ma will often work perfectly, but when you are applying it to the acceleration of your car you need to account for lots of effects like friction between the road and the wheels, wind resistance, and the like. So F=ma applied naïvely would give you the wrong answer if friction is involved. This demonstrates the main disadvantage with Models. They require that both the Model Maker (scientists like Newton) and the Model users (STEM competent people everywhere) Understand enough about the problem domain to know whether the Model is applicable or not, and how to use it. This Understanding is the expensive part of science, since using science requires first getting a solid science education in order to avoid mistakes when using Models.

And since Models require Understanding, they cannot be used to create Understanding. This is a major problem for AI implementers.

Our Greatest Invention was originally published in Artificial Understanding on Medium, where people are continuing the conversation by highlighting and responding to this story.

This is an attempt to explain the current state of AI to a general audience without using mathematics, computer science, or neuroscience; discussions at these levels would focus on how AI works. Here I will discuss this at the level of Epistemology and will try to explain why it works.

“Epistemology” sounds scary, but it really isn’t. It’s mostly scary because it is unknown; it is not taught in schools anymore. Which is a problem, because we now desperately need this branch of Philosophy to guide our AI development. Epistemology discusses things like Reasoning, Understanding, Learning, Novelty, problem solving in the abstract, how to create Models of the world, etc. These are all concepts one would think would be useful when working with artificial intelligences. But most practitioners enter the field of AI without any exposure to Epistemology which makes their work more mysterious and frustrating than it has to be.

I think of Epistemology as the general base for everything related to knowledge and problem solving; Science forms a small special case subset domain where we solve well-formed problems of the kind that Science is best at. In Epistemology outside of Science we are free to productively also discuss pre-scientific problem solving strategies, which is what brains are using most of the time. More later.

Intelligence = Understanding + Reasoning

In his book “Thinking Fast and Slow”, Daniel Kahneman discusses the idea that human minds use two different and complementary processes, two different modes of thinking, which we call Understanding and Reasoning. The idea has been discussed for decades and has been verified using psychological studies and by neuroscience.

“Subconscious Intuitive Understanding” is the full name of the “Fast Thinking” or “System 1” thinking. It is fast because the brain can perform many parts of this task in parallel. The brain spends a lot of effort on this task.

“Conscious Logical Reasoning” is the full name of “Slow Thinking” or “System 2” thinking. To many people’s surprise, this is very rarely used in practice. My soundbite for this is “You can make breakfast without Reasoning”. Almost everything we do on a daily basis in our rich mundane reality is done without a need to reason about it. We just repeat whatever worked last time we performed this task; we are experience driven.

“Intuitive” means that the system can very quickly “provide solutions” to very complex problems but those solutions may not be correct every time.

“Logical” means that answers are always correct as long as input data is correct and sufficient. Which is not true in our rich mundane reality; it can only be true in a mathematically pure “Model” space. If you like Logic, you must also like Models.

“Subconscious” means we have no conscious (“introspective”) access to the these processes. You are reading this sentence and you understand it fully but you cannot explain to anyone, including yourself, how or why you understand it.

“Conscious” means we are aware of the thought; we can access it through introspection and we may find reasons to why we believe a certain idea.

“Expensive” is on the list because brains spend most of their effort on this Understanding part. We really shouldn’t be surprised that AI now requires very powerful computers. More later.

In contrast, Reasoning is “Efficient”. It is most useful when you are stuck in a novel situation where experience and Understanding doesn’t help you. Or perhaps you need to plan ahead, or need to find reasons for why something happened after the fact. It is used at a formal level in the sciences. Reasoning is important, but just rarely needed or used.

Finally, Understanding is “Model Free” and Reasoning is “Model Based”. This is likely the most important distinction to people who are implementing intelligent systems since it provides a way to keep the implementation on the correct path when the going gets rough. We cannot discuss these issues quite yet, but if you are curious you can watch the videos at http://videos.syntience.com which discuss this distinction at length. Think of their appearance in this table as a kind of foreshadowing.

All of this groundwork allows me to state the main point of this blog. We have known for a long time that brains use these two modes. But the AI research community has been spending overmuch effort on the Reasoning part and has been ignoring the Understanding part for sixty years.

We had several good reasons for this. Until quite recently, our machines were too small to run any useful sized neural network. And also, we didn’t have a clue about how to implement this Understanding. But that is exactly what changed in 2012 when a group of AI researchers from Toronto effectively demonstrated that Deep Neural Networks could provide a simple kind of shallow and hollow proto-Understanding (well, they didn’t call it that, but I do). I will look just a little into the future, and overstate this just a little, in order to make it more memorable:

Deep Neural Networks can provide Understanding

This new phase of AI took decades to develop, but it would never have happened without people like the group led by Geoffrey Hinton at the University of Toronto, who spent 34+ years to develop the Deep Neural Network technology we now call “Deep Learning”. A number of breakthroughs from 1997 to 2006 led to a number of successful demonstrations (including first prizes in AI competitions) in 2012, and we therefore count this year as the birth year of Machine Understanding.

To an outsider, it may look like an older program or phone app might be “Understanding” whatever the app is doing, but that Understanding really only happened in the mind of the programmer creating the app. The programmer first simplified the problem in their own head by discarding a lot of irrelevant detail using “Programmer’s Understanding”. This simplified mental “Model” of the problem domain could then be explained to a computer in the form of a computer program.

What is changing is that computers are now making these Models themselves.

The first bullet point describes regular programming, including “old style AI” programs. AI has, since 1955, provided many novel and brilliant algorithms that we now use in programs everywhere. But when you contrast old style AI to Understanding systems, the old kind of AI is basically indistinguishable from any other kind of programming we do nowadays.

The second bullet point describes the recent developments. Deep Neural Networks are so different from regular programs that we have to acknowledge them as a different computational paradigm. This is why they took almost four decades to develop. And the paradigm, being pre-scientific and Model Free, is difficult to grasp if you received a solid Reductionist and Model Based education; it takes a long time for an established AI practitioner or experienced programmer to switch. People who are just starting out in AI have an easier time assimilating this new paradigm since they haven’t had a full career’s worth of experience and success using old style AI techniques.

The amount of work we have to do to get a Deep Neural Network to Understand is surprisingly small, and companies like Google and Syntience are working on eliminating the remaining effort of programming Neural Networks. This is where things will get really weird: when the Deep Neural Network (DNN) Understands enough about the world and about the problem it is faced with, then we no longer need a programmer to acquire this Understanding. Let me elaborate.

Programmers are employed to bridge two different domains. They first have to study whatever application domain they are working on. For instance, if they are writing an airline ticket reservation system they will have to learn a lot of detailed information about airlines, airline tickets, flights, luggage, etc. and then know to provide features for unusual cases such as canceled flights. And then the programmer uses their Understanding of the problem domain to explain to a computer how it can Reason about these things… but the programmer cannot make the system Understand, it can only put in a hollow and fragile kind of Reasoning, as a program with many if-then cases. And any misunderstandings the programmer has about the problem domain will become “bugs” in the computer program. Notice the shift in terminology; more later.

But today, for certain classes of moderately complex problems, we can use a DNN to automatically learn for itself how to Understand the problem.

Which means we no longer need a programmer to Understand the problem.

We have delegated our Understanding to a machine.

And if you think about that for a minute you will see that that’s exactly what an AI should be doing. It should Understand all kinds of things so that we humans won’t have to.

And there are two common situations where this will be a really good idea. One is when we have a problem we cannot Understand ourselves. We know a lot of those, starting with cellular biology.

The other common case will be when we Understand the problem well, but making a machine Understand it well enough to get the job done is cheaper and easier than any alternative. Roombas accomplish this level using old style AI methods, but I predict we will one day be flooded with similar but DNN based devices that Understand several aspects of domestic maintenance as well as we do.

Do machines really Understand ?

If we give a picture like this to a DNN trained on images it will identify the important objects in the image and provide the rectangles, called “bounding boxes” as approximations to where the objects are. The text on the right says “Woman in white dress standing with tennis racket two people in green behind her”. Which is not a bad description of the image. It could be used as the basis for a test for English skill level for adult education placement.

For all practical purposes, this is Understanding.

We had no idea how to make our computers do this before 2012. This is a really big deal. This feat requires not only a new algorithm, it requires a new computational paradigm.

An image is, to a computer, a single long sequence of numbers denoting values for red, blue, and green colors in values from 0 to 255; it also knows how wide the image is. How does it get from this very low level representation to knowing that there is a woman with a tennis racket in the image?

This is what William Calvin has called “A river that flows uphill”. There are very few mechanisms that can go in this direction, from low levels to
high levels. Calvin used the term to describe Evolution, and I can use this quote to describe Understanding.

I like to think of Evolution as “Nature’s Understanding” because the phenomena are very similar at several levels. Evolution of species can bring forth advanced species starting from simpler species in the same manner that Understanding is the discovery and re-use of high level concepts in low level input.

In contrast, Reasoning proceeds by breaking problems into subproblems and solving those, which is a “flowing downhill” kind of strategy. In mathematics we accept (and many mathematicians only accept this reluctantly) that we need to use induction to move “uphill” in abstractions. And that’s a very limited uphill movement at that. Epistemology allows for much stronger uphill moves. This is known as “jumping to conclusions on scant evidence” and it’s allowed in Epistemology based pre-scientific systems.

As an aside, here’s a pretty deep related thought: Nature/Evolution re-uses anything that works. I like to think that Understanding is a spandrel of Evolution itself. Neural Darwinism certainly straddles this gap. Could be coincidence, or the only answer that will work at all. More later.

We Doubled Our AI Toolkit in 2012

We can now use these Deep Neural Networks as components in our systems to provide Understanding of certain things like vision, speech, and other problems that require that we discover high level concepts in low level data. The technical (Epistemology level) name for this uphill flowing process is “Reduction” and we’ll be using that term later after we explain what it means.

Let’s look at what the industry is doing with their newfound toys.

This is my view of what I think Tesla is doing (based on public sources) in their self-driving (“Autopilot”) cars. Cameras feed Vision Understanding components based on Deep Learning, and Radar feeds to Radar Understanding components. These supply bounding boxes in 2D or 3D with additional information like “There’s a woman with a tennis racket ahead” to a Traffic Reasoning Component that uses regular programming or some old style AI like a rule-based system to actually control the car based on the vision and radar inputs, and the driver’s desires.

But this is not the only possible configuration. George Hotz at Comma.ai, a team at nVidia corporation, and the DeepTesla class at MIT are using a
simpler architecture with just a neural network that implements lane following and other simple driving behaviors directly in one single Deep Neural Network. There is room for improvement, but they are a big step in the direction we want to move in.

Future automotive systems will likely integrate everything about driving into one single neural network, or something that effectively behaves as one. Vision, traffic, the car itself including various functionality like windscreen wipers, lights, and entertainment, how to drive in a safe and polite manner, and to understand also the driver’s (or “car owner’s”) desires. And if we’ve gotten that far, then it is a given that we will have speech input and output so that the driver can have a conversation with the car while driving, and can chastise it in case it does something wrong.

We are nowhere close to this today. But after a DNN breakthrough or two, who knows how quickly these kinds of systems become available. We can already see an increasing stream of new features built using Understanding components.

This article (and the next) are expansions of a talk given at BIL conference on June 10th 2017 in San Francisco.

More at http://videos.syntience.com and http://syntience.com/links

A decade ago I created http://artificial-intuition.com . I now have a lot more to say, but I need to split this meme-package into digestible chunks; this takes a lot of effort to get right. If you liked this article and would like to see more like it then you can support my writing and my research in many ways, small to large:

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Why AI Works was originally published in Artificial Understanding on Medium, where people are continuing the conversation by highlighting and responding to this story.