#+title: =CORTEX=

 #+author: Robert McIntyre

 #+email: rlm@mit.edu

 #+description: Using embodied AI to facilitate Artificial Imagination.

 #+keywords: AI, clojure, embodiment

 

 

 * Empathy and Embodiment as problem solving strategies

   

   By the end of this thesis, you will have seen a novel approach to

   interpreting video using embodiment and empathy. You will have also

   seen one way to efficiently implement empathy for embodied

   creatures. Finally, you will become familiar with =CORTEX=, a system

   for designing and simulating creatures with rich senses, which you

   may choose to use in your own research.

   

   This is the core vision of my thesis: That one of the important ways

   in which we understand others is by imagining ourselves in their

   position and emphatically feeling experiences relative to our own

   bodies. By understanding events in terms of our own previous

   corporeal experience, we greatly constrain the possibilities of what

   would otherwise be an unwieldy exponential search. This extra

   constraint can be the difference between easily understanding what

   is happening in a video and being completely lost in a sea of

   incomprehensible color and movement.

 

 ** Recognizing actions in video is extremely difficult

 

    Consider for example the problem of determining what is happening

    in a video of which this is one frame:

 

    #+caption: A cat drinking some water. Identifying this action is 

    #+caption: beyond the state of the art for computers.

    #+ATTR_LaTeX: :width 7cm

    [[./images/cat-drinking.jpg]]

    

    It is currently impossible for any computer program to reliably

    label such a video as ``drinking''. And rightly so -- it is a very

    hard problem! What features can you describe in terms of low level

    functions of pixels that can even begin to describe at a high level

    what is happening here?

   

    Or suppose that you are building a program that recognizes chairs.

    How could you ``see'' the chair in figure \ref{hidden-chair}?

    

    #+caption: The chair in this image is quite obvious to humans, but I 

    #+caption: doubt that any modern computer vision program can find it.

    #+name: hidden-chair

    #+ATTR_LaTeX: :width 10cm

    [[./images/fat-person-sitting-at-desk.jpg]]

    

    Finally, how is it that you can easily tell the difference between

    how the girls /muscles/ are working in figure \ref{girl}?

    

    #+caption: The mysterious ``common sense'' appears here as you are able 

    #+caption: to discern the difference in how the girl's arm muscles

    #+caption: are activated between the two images.

    #+name: girl

    #+ATTR_LaTeX: :width 7cm

    [[./images/wall-push.png]]

   

    Each of these examples tells us something about what might be going

    on in our minds as we easily solve these recognition problems.

    

    The hidden chairs show us that we are strongly triggered by cues

    relating to the position of human bodies, and that we can determine

    the overall physical configuration of a human body even if much of

    that body is occluded.

 

    The picture of the girl pushing against the wall tells us that we

    have common sense knowledge about the kinetics of our own bodies.

    We know well how our muscles would have to work to maintain us in

    most positions, and we can easily project this self-knowledge to

    imagined positions triggered by images of the human body.

 

 ** =EMPATH= neatly solves recognition problems  

    

    I propose a system that can express the types of recognition

    problems above in a form amenable to computation. It is split into

    four parts:

 

    - Free/Guided Play :: The creature moves around and experiences the

         world through its unique perspective. Many otherwise

         complicated actions are easily described in the language of a

         full suite of body-centered, rich senses. For example,

         drinking is the feeling of water sliding down your throat, and

         cooling your insides. It's often accompanied by bringing your

         hand close to your face, or bringing your face close to water.

         Sitting down is the feeling of bending your knees, activating

         your quadriceps, then feeling a surface with your bottom and

         relaxing your legs. These body-centered action descriptions

         can be either learned or hard coded.

    - Posture Imitation :: When trying to interpret a video or image,

         the creature takes a model of itself and aligns it with

         whatever it sees. This alignment can even cross species, as

         when humans try to align themselves with things like ponies,

         dogs, or other humans with a different body type.

    - Empathy         :: The alignment triggers associations with

         sensory data from prior experiences. For example, the

         alignment itself easily maps to proprioceptive data. Any

         sounds or obvious skin contact in the video can to a lesser

         extent trigger previous experience. Segments of previous

         experiences are stitched together to form a coherent and

         complete sensory portrait of the scene.

    - Recognition      :: With the scene described in terms of first

         person sensory events, the creature can now run its

         action-identification programs on this synthesized sensory

         data, just as it would if it were actually experiencing the

         scene first-hand. If previous experience has been accurately

         retrieved, and if it is analogous enough to the scene, then

         the creature will correctly identify the action in the scene.

    

    For example, I think humans are able to label the cat video as

    ``drinking'' because they imagine /themselves/ as the cat, and

    imagine putting their face up against a stream of water and

    sticking out their tongue. In that imagined world, they can feel

    the cool water hitting their tongue, and feel the water entering

    their body, and are able to recognize that /feeling/ as drinking.

    So, the label of the action is not really in the pixels of the

    image, but is found clearly in a simulation inspired by those

    pixels. An imaginative system, having been trained on drinking and

    non-drinking examples and learning that the most important

    component of drinking is the feeling of water sliding down one's

    throat, would analyze a video of a cat drinking in the following

    manner:

    

    1. Create a physical model of the video by putting a ``fuzzy''

       model of its own body in place of the cat. Possibly also create

       a simulation of the stream of water.

 

    2. Play out this simulated scene and generate imagined sensory

       experience. This will include relevant muscle contractions, a

       close up view of the stream from the cat's perspective, and most

       importantly, the imagined feeling of water entering the

       mouth. The imagined sensory experience can come from a

       simulation of the event, but can also be pattern-matched from

       previous, similar embodied experience.

 

    3. The action is now easily identified as drinking by the sense of

       taste alone. The other senses (such as the tongue moving in and

       out) help to give plausibility to the simulated action. Note that

       the sense of vision, while critical in creating the simulation,

       is not critical for identifying the action from the simulation.

 

    For the chair examples, the process is even easier:

 

     1. Align a model of your body to the person in the image.

 

     2. Generate proprioceptive sensory data from this alignment.

   

     3. Use the imagined proprioceptive data as a key to lookup related

        sensory experience associated with that particular proproceptive

        feeling.

 

     4. Retrieve the feeling of your bottom resting on a surface, your

        knees bent, and your leg muscles relaxed.

 

     5. This sensory information is consistent with the =sitting?=

        sensory predicate, so you (and the entity in the image) must be

        sitting.

 

     6. There must be a chair-like object since you are sitting.

 

    Empathy offers yet another alternative to the age-old AI

    representation question: ``What is a chair?'' --- A chair is the

    feeling of sitting.

 

    My program, =EMPATH= uses this empathic problem solving technique

    to interpret the actions of a simple, worm-like creature. 

    

    #+caption: The worm performs many actions during free play such as 

    #+caption: curling, wiggling, and resting.

    #+name: worm-intro

    #+ATTR_LaTeX: :width 15cm

    [[./images/worm-intro-white.png]]

 

    #+caption: =EMPATH= recognized and classified each of these poses by

    #+caption: inferring the complete sensory experience from 

    #+caption: proprioceptive data.

    #+name: worm-recognition-intro

    #+ATTR_LaTeX: :width 15cm

    [[./images/worm-poses.png]]

    

    One powerful advantage of empathic problem solving is that it

    factors the action recognition problem into two easier problems. To

    use empathy, you need an /aligner/, which takes the video and a

    model of your body, and aligns the model with the video. Then, you

    need a /recognizer/, which uses the aligned model to interpret the

    action. The power in this method lies in the fact that you describe

    all actions form a body-centered viewpoint. You are less tied to

    the particulars of any visual representation of the actions. If you

    teach the system what ``running'' is, and you have a good enough

    aligner, the system will from then on be able to recognize running

    from any point of view, even strange points of view like above or

    underneath the runner. This is in contrast to action recognition

    schemes that try to identify actions using a non-embodied approach.

    If these systems learn about running as viewed from the side, they

    will not automatically be able to recognize running from any other

    viewpoint.

 

    Another powerful advantage is that using the language of multiple

    body-centered rich senses to describe body-centerd actions offers a

    massive boost in descriptive capability. Consider how difficult it

    would be to compose a set of HOG filters to describe the action of

    a simple worm-creature ``curling'' so that its head touches its

    tail, and then behold the simplicity of describing thus action in a

    language designed for the task (listing \ref{grand-circle-intro}):

 

    #+caption: Body-centerd actions are best expressed in a body-centered 

    #+caption: language. This code detects when the worm has curled into a 

    #+caption: full circle. Imagine how you would replicate this functionality

    #+caption: using low-level pixel features such as HOG filters!

    #+name: grand-circle-intro

    #+begin_listing clojure

    #+begin_src clojure

 (defn grand-circle?

   "Does the worm form a majestic circle (one end touching the other)?"

   [experiences]

   (and (curled? experiences)

        (let [worm-touch (:touch (peek experiences))

              tail-touch (worm-touch 0)

              head-touch (worm-touch 4)]

          (and (< 0.55 (contact worm-segment-bottom-tip tail-touch))

               (< 0.55 (contact worm-segment-top-tip    head-touch))))))

    #+end_src

    #+end_listing

 

 

 **  =CORTEX= is a toolkit for building sensate creatures

 

    I built =CORTEX= to be a general AI research platform for doing

    experiments involving multiple rich senses and a wide variety and

    number of creatures. I intend it to be useful as a library for many

    more projects than just this one. =CORTEX= was necessary to meet a

    need among AI researchers at CSAIL and beyond, which is that people

    often will invent neat ideas that are best expressed in the

    language of creatures and senses, but in order to explore those

    ideas they must first build a platform in which they can create

    simulated creatures with rich senses! There are many ideas that

    would be simple to execute (such as =EMPATH=), but attached to them

    is the multi-month effort to make a good creature simulator. Often,

    that initial investment of time proves to be too much, and the

    project must make do with a lesser environment.

 

    =CORTEX= is well suited as an environment for embodied AI research

    for three reasons:

 

    - You can create new creatures using Blender, a popular 3D modeling

      program. Each sense can be specified using special blender nodes

      with biologically inspired paramaters. You need not write any

      code to create a creature, and can use a wide library of

      pre-existing blender models as a base for your own creatures.

 

    - =CORTEX= implements a wide variety of senses, including touch,

      proprioception, vision, hearing, and muscle tension. Complicated

      senses like touch, and vision involve multiple sensory elements

      embedded in a 2D surface. You have complete control over the

      distribution of these sensor elements through the use of simple

      png image files. In particular, =CORTEX= implements more

      comprehensive hearing than any other creature simulation system

      available. 

 

    - =CORTEX= supports any number of creatures and any number of

      senses. Time in =CORTEX= dialates so that the simulated creatures

      always precieve a perfectly smooth flow of time, regardless of

      the actual computational load.

 

    =CORTEX= is built on top of =jMonkeyEngine3=, which is a video game

    engine designed to create cross-platform 3D desktop games. =CORTEX=

    is mainly written in clojure, a dialect of =LISP= that runs on the

    java virtual machine (JVM). The API for creating and simulating

    creatures and senses is entirely expressed in clojure, though many

    senses are implemented at the layer of jMonkeyEngine or below. For

    example, for the sense of hearing I use a layer of clojure code on

    top of a layer of java JNI bindings that drive a layer of =C++=

    code which implements a modified version of =OpenAL= to support

    multiple listeners. =CORTEX= is the only simulation environment

    that I know of that can support multiple entities that can each

    hear the world from their own perspective. Other senses also

    require a small layer of Java code. =CORTEX= also uses =bullet=, a

    physics simulator written in =C=.

 

    #+caption: Here is the worm from above modeled in Blender, a free 

    #+caption: 3D-modeling program. Senses and joints are described

    #+caption: using special nodes in Blender.

    #+name: worm-recognition-intro

    #+ATTR_LaTeX: :width 12cm

    [[./images/blender-worm.png]]

 

    Here are some thing I anticipate that =CORTEX= might be used for:

 

    - exploring new ideas about sensory integration

    - distributed communication among swarm creatures

    - self-learning using free exploration, 

    - evolutionary algorithms involving creature construction

    - exploration of exoitic senses and effectors that are not possible

      in the real world (such as telekenisis or a semantic sense)

    - imagination using subworlds

 

    During one test with =CORTEX=, I created 3,000 entities each with

    their own independent senses and ran them all at only 1/80 real

    time. In another test, I created a detailed model of my own hand,

    equipped with a realistic distribution of touch (more sensitive at

    the fingertips), as well as eyes and ears, and it ran at around 1/4

    real time. 

 

    #+BEGIN_LaTeX

    \begin{sidewaysfigure}

    \includegraphics[width=9.5in]{images/full-hand.png}

    \caption{Here is the worm from above modeled in Blender, 

    a free 3D-modeling program. Senses and joints are described

    using special nodes in Blender. The senses are displayed on 

    the right, and the simulation is displayed on the left. Notice

    that the hand is curling its fingers, that it can see its own 

    finger from the eye in its palm, and thta it can feel its own 

    thumb touching its palm.}

    \end{sidewaysfigure}

    #+END_LaTeX

 

 ** Contributions

 

    I built =CORTEX=, a comprehensive platform for embodied AI

    experiments. =CORTEX= many new features lacking in other systems,

    such as sound. It is easy to create new creatures using Blender, a

    free 3D modeling program.

 

    I built =EMPATH=, which uses =CORTEX= to identify the actions of a

    worm-like creature using a computational model of empathy.

    

 * Building =CORTEX=

 

 ** To explore embodiment, we need a world, body, and senses

 

 ** Because of Time, simulation is perferable to reality

 

 ** Video game engines are a great starting point

 

 ** Bodies are composed of segments connected by joints

 

 ** Eyes reuse standard video game components

 

 ** Hearing is hard; =CORTEX= does it right

 

 ** Touch uses hundreds of hair-like elements

 

 ** Proprioception is the sense that makes everything ``real''

 

 ** Muscles are both effectors and sensors

 

 ** =CORTEX= brings complex creatures to life!

 

 ** =CORTEX= enables many possiblities for further research

 

 * Empathy in a simulated worm

 

   Here I develop a computational model of empathy, using =CORTEX= as a

   base. Empathy in this context is the ability to observe another

   creature and infer what sorts of sensations that creature is

   feeling. My empathy algorithm involves multiple phases. First is

   free-play, where the creature moves around and gains sensory

   experience. From this experience I construct a representation of the

   creature's sensory state space, which I call \Phi-space. Using

   \Phi-space, I construct an efficient function which takes the

   limited data that comes from observing another creature and enriches

   it full compliment of imagined sensory data. I can then use the

   imagined sensory data to recognize what the observed creature is

   doing and feeling, using straightforward embodied action predicates.

   This is all demonstrated with using a simple worm-like creature, and

   recognizing worm-actions based on limited data.

 

   #+caption: Here is the worm with which we will be working. 

   #+caption: It is composed of 5 segments. Each segment has a 

   #+caption: pair of extensor and flexor muscles. Each of the 

   #+caption: worm's four joints is a hinge joint which allows 

   #+caption: 30 degrees of rotation to either side. Each segment

   #+caption: of the worm is touch-capable and has a uniform 

   #+caption: distribution of touch sensors on each of its faces.

   #+caption: Each joint has a proprioceptive sense to detect 

   #+caption: relative positions. The worm segments are all the 

   #+caption: same except for the first one, which has a much

   #+caption: higher weight than the others to allow for easy 

   #+caption: manual motor control.

   #+name: basic-worm-view

   #+ATTR_LaTeX: :width 10cm

   [[./images/basic-worm-view.png]]

 

   #+caption: Program for reading a worm from a blender file and 

   #+caption: outfitting it with the senses of proprioception, 

   #+caption: touch, and the ability to move, as specified in the 

   #+caption: blender file.

   #+name: get-worm

   #+begin_listing clojure

   #+begin_src clojure

 (defn worm []

   (let [model (load-blender-model "Models/worm/worm.blend")]

     {:body (doto model (body!))

      :touch (touch! model)

      :proprioception (proprioception! model)

      :muscles (movement! model)}))

   #+end_src

   #+end_listing

   

 ** Embodiment factors action recognition into managable parts

 

    Using empathy, I divide the problem of action recognition into a

    recognition process expressed in the language of a full compliment

    of senses, and an imaganitive process that generates full sensory

    data from partial sensory data. Splitting the action recognition

    problem in this manner greatly reduces the total amount of work to

    recognize actions: The imaganitive process is mostly just matching

    previous experience, and the recognition process gets to use all

    the senses to directly describe any action.

 

 ** Action recognition is easy with a full gamut of senses

 

    Embodied representations using multiple senses such as touch,

    proprioception, and muscle tension turns out be be exceedingly

    efficient at describing body-centered actions. It is the ``right

    language for the job''. For example, it takes only around 5 lines

    of LISP code to describe the action of ``curling'' using embodied

    primitives. It takes about 8 lines to describe the seemingly

    complicated action of wiggling.

 

    The following action predicates each take a stream of sensory

    experience, observe however much of it they desire, and decide

    whether the worm is doing the action they describe. =curled?=

    relies on proprioception, =resting?= relies on touch, =wiggling?=

    relies on a fourier analysis of muscle contraction, and

    =grand-circle?= relies on touch and reuses =curled?= as a gaurd.

    

    #+caption: Program for detecting whether the worm is curled. This is the 

    #+caption: simplest action predicate, because it only uses the last frame 

    #+caption: of sensory experience, and only uses proprioceptive data. Even 

    #+caption: this simple predicate, however, is automatically frame 

    #+caption: independent and ignores vermopomorphic differences such as 

    #+caption: worm textures and colors.

    #+name: curled

    #+begin_listing clojure

    #+begin_src clojure

 (defn curled?

   "Is the worm curled up?"

   [experiences]

   (every?

    (fn [[_ _ bend]]

      (> (Math/sin bend) 0.64))

    (:proprioception (peek experiences))))

    #+end_src

    #+end_listing

 

    #+caption: Program for summarizing the touch information in a patch 

    #+caption: of skin.

    #+name: touch-summary

    #+begin_listing clojure

    #+begin_src clojure

 (defn contact

   "Determine how much contact a particular worm segment has with

    other objects. Returns a value between 0 and 1, where 1 is full

    contact and 0 is no contact."

   [touch-region [coords contact :as touch]]

   (-> (zipmap coords contact)

       (select-keys touch-region)

       (vals)

       (#(map first %))

       (average)

       (* 10)

       (- 1)

       (Math/abs)))

    #+end_src

    #+end_listing

 

 

    #+caption: Program for detecting whether the worm is at rest. This program

    #+caption: uses a summary of the tactile information from the underbelly 

    #+caption: of the worm, and is only true if every segment is touching the 

    #+caption: floor. Note that this function contains no references to 

    #+caption: proprioction at all.

    #+name: resting

    #+begin_listing clojure

    #+begin_src clojure

 (def worm-segment-bottom (rect-region [8 15] [14 22]))

 

 (defn resting?

   "Is the worm resting on the ground?"

   [experiences]

   (every?

    (fn [touch-data]

      (< 0.9 (contact worm-segment-bottom touch-data)))

    (:touch (peek experiences))))

    #+end_src

    #+end_listing

 

    #+caption: Program for detecting whether the worm is curled up into a 

    #+caption: full circle. Here the embodied approach begins to shine, as

    #+caption: I am able to both use a previous action predicate (=curled?=)

    #+caption: as well as the direct tactile experience of the head and tail.

    #+name: grand-circle

    #+begin_listing clojure

    #+begin_src clojure

 (def worm-segment-bottom-tip (rect-region [15 15] [22 22]))

 

 (def worm-segment-top-tip (rect-region [0 15] [7 22]))

 

 (defn grand-circle?

   "Does the worm form a majestic circle (one end touching the other)?"

   [experiences]

   (and (curled? experiences)

        (let [worm-touch (:touch (peek experiences))

              tail-touch (worm-touch 0)

              head-touch (worm-touch 4)]

          (and (< 0.55 (contact worm-segment-bottom-tip tail-touch))

               (< 0.55 (contact worm-segment-top-tip    head-touch))))))

    #+end_src

    #+end_listing

 

 

    #+caption: Program for detecting whether the worm has been wiggling for 

    #+caption: the last few frames. It uses a fourier analysis of the muscle 

    #+caption: contractions of the worm's tail to determine wiggling. This is 

    #+caption: signigicant because there is no particular frame that clearly 

    #+caption: indicates that the worm is wiggling --- only when multiple frames 

    #+caption: are analyzed together is the wiggling revealed. Defining 

    #+caption: wiggling this way also gives the worm an opportunity to learn 

    #+caption: and recognize ``frustrated wiggling'', where the worm tries to 

    #+caption: wiggle but can't. Frustrated wiggling is very visually different 

    #+caption: from actual wiggling, but this definition gives it to us for free.

    #+name: wiggling

    #+begin_listing clojure

    #+begin_src clojure

 (defn fft [nums]

   (map

    #(.getReal %)

    (.transform

     (FastFourierTransformer. DftNormalization/STANDARD)

     (double-array nums) TransformType/FORWARD)))

 

 (def indexed (partial map-indexed vector))

 

 (defn max-indexed [s]

   (first (sort-by (comp - second) (indexed s))))

 

 (defn wiggling?

   "Is the worm wiggling?"

   [experiences]

   (let [analysis-interval 0x40]

     (when (> (count experiences) analysis-interval)

       (let [a-flex 3

             a-ex   2

             muscle-activity

             (map :muscle (vector:last-n experiences analysis-interval))

             base-activity

             (map #(- (% a-flex) (% a-ex)) muscle-activity)]

         (= 2

            (first

             (max-indexed

              (map #(Math/abs %)

                   (take 20 (fft base-activity))))))))))

    #+end_src

    #+end_listing

 

    With these action predicates, I can now recognize the actions of

    the worm while it is moving under my control and I have access to

    all the worm's senses.

 

    #+caption: Use the action predicates defined earlier to report on 

    #+caption: what the worm is doing while in simulation.

    #+name: report-worm-activity

    #+begin_listing clojure

    #+begin_src clojure

 (defn debug-experience

   [experiences text]

   (cond

    (grand-circle? experiences) (.setText text "Grand Circle")

    (curled? experiences)       (.setText text "Curled")

    (wiggling? experiences)     (.setText text "Wiggling")

    (resting? experiences)      (.setText text "Resting")))

    #+end_src

    #+end_listing

 

    #+caption: Using =debug-experience=, the body-centered predicates

    #+caption: work together to classify the behaviour of the worm. 

    #+caption: while under manual motor control.

    #+name: basic-worm-view

    #+ATTR_LaTeX: :width 10cm

    [[./images/worm-identify-init.png]]

 

    These action predicates satisfy the recognition requirement of an

    empathic recognition system. There is a lot of power in the

    simplicity of the action predicates. They describe their actions

    without getting confused in visual details of the worm. Each one is

    frame independent, but more than that, they are each indepent of

    irrelevant visual details of the worm and the environment. They

    will work regardless of whether the worm is a different color or

    hevaily textured, or of the environment has strange lighting.

 

    The trick now is to make the action predicates work even when the

    sensory data on which they depend is absent. If I can do that, then

    I will have gained much,

 

 ** \Phi-space describes the worm's experiences

    

    As a first step towards building empathy, I need to gather all of

    the worm's experiences during free play. I use a simple vector to

    store all the experiences. 

    

    #+caption: Program to gather the worm's experiences into a vector for 

    #+caption: further processing. The =motor-control-program= line uses

    #+caption: a motor control script that causes the worm to execute a series

    #+caption: of ``exercices'' that include all the action predicates.

    #+name: generate-phi-space

    #+begin_listing clojure

    #+begin_src clojure

 (defn generate-phi-space []

   (let [experiences (atom [])]

     (run-world

      (apply-map 

       worm-world

       (merge

        (worm-world-defaults)

        {:end-frame 700

         :motor-control

         (motor-control-program worm-muscle-labels do-all-the-things)

         :experiences experiences})))

     @experiences))

    #+end_src

    #+end_listing

 

    Each element of the experience vector exists in the vast space of

    all possible worm-experiences. Most of this vast space is actually

    unreachable due to physical constraints of the worm's body. For

    example, the worm's segments are connected by hinge joints that put

    a practical limit on the worm's degrees of freedom. Also, the worm

    can not be bent into a circle so that its ends are touching and at

    the same time not also experience the sensation of touching itself.

 

    As the worm moves around during free play and the vector grows

    larger, the vector begins to define a subspace which is all the

    practical experiences the worm can experience during normal

    operation, which I call \Phi-space, short for physical-space. The

    vector defines a path through \Phi-space. This path has interesting

    properties that all derive from embodiment. The proprioceptive

    components are completely smooth, because in order for the worm to

    move from one position to another, it must pass through the

    intermediate positions. The path invariably forms loops as actions

    are repeated. Finally and most importantly, proprioception actually

    gives very strong inference about the other senses. For example,

    when the worm is flat, you can infer that it is touching the ground

    and that its muscles are not active, because if the muscles were

    active, the worm would be moving and would not be perfectly flat.

    In order to stay flat, the worm has to be touching the ground, or

    it would again be moving out of the flat position due to gravity.

    If the worm is positioned in such a way that it interacts with

    itself, then it is very likely to be feeling the same tactile

    feelings as the last time it was in that position, because it has

    the same body as then. If you observe multiple frames of

    proprioceptive data, then you can become increasingly confident

    about the exact activations of the worm's muscles, because it

    generally takes a unique combination of muscle contractions to

    transform the worm's body along a specific path through \Phi-space.

 

    There is a simple way of taking \Phi-space and the total ordering

    provided by an experience vector and reliably infering the rest of

    the senses.

 

 ** Empathy is the process of tracing though \Phi-space 

 

    Here is the core of a basic empathy algorithm, starting with an

    experience vector: First, group the experiences into tiered

    proprioceptive bins. I use powers of 10 and 3 bins, and the

    smallest bin has and approximate size of 0.001 radians in all

    proprioceptive dimensions.

    

    Then, given a sequence of proprioceptive input, generate a set of

    matching experience records for each input. 

 

    Finally, to infer sensory data, select the longest consective chain

    of experiences as determined by the indexes into the experience

    vector. 

 

    This algorithm has three advantages: 

 

    1. It's simple

 

    3. It's very fast -- both tracing through possibilites and

       retrieving possible interpretations take essentially constant

       time. 

 

    2. It protects from wrong interpretations of transient ambiguous

       proprioceptive data : for example, if the worm is flat for just

       an instant, this flattness will not be interpreted as implying

       that the worm has its muscles relaxed, since the flattness is

       part of a longer chain which includes a distinct pattern of

       muscle activation. A memoryless statistical model such as a

       markov model that operates on individual frames may very well

       make this mistake.

 

    #+caption: Program to convert an experience vector into a 

    #+caption: proprioceptively binned lookup function.

    #+name: bin

    #+begin_listing clojure

    #+begin_src clojure

 (defn bin [digits]

   (fn [angles]

     (->> angles

          (flatten)

          (map (juxt #(Math/sin %) #(Math/cos %)))

          (flatten)

          (mapv #(Math/round (* % (Math/pow 10 (dec digits))))))))

 

 (defn gen-phi-scan 

   "Nearest-neighbors with binning. Only returns a result if

    the propriceptive data is within 10% of a previously recorded

    result in all dimensions."

   [phi-space]

   (let [bin-keys (map bin [3 2 1])

         bin-maps

         (map (fn [bin-key]

                (group-by

                 (comp bin-key :proprioception phi-space)

                 (range (count phi-space)))) bin-keys)

         lookups (map (fn [bin-key bin-map]

                        (fn [proprio] (bin-map (bin-key proprio))))

                      bin-keys bin-maps)]

     (fn lookup [proprio-data]

       (set (some #(% proprio-data) lookups)))))

    #+end_src

    #+end_listing

 

 

    #+caption: Program to calculate empathy by tracing though \Phi-space

    #+caption: and finding the longest (ie. most coherent) interpretation

    #+caption: of the data.

    #+name: longest-thread

    #+begin_listing clojure

    #+begin_src clojure

 (defn longest-thread

   "Find the longest thread from phi-index-sets. The index sets should

    be ordered from most recent to least recent."

   [phi-index-sets]

   (loop [result '()

          [thread-bases & remaining :as phi-index-sets] phi-index-sets]

     (if (empty? phi-index-sets)

       (vec result)

       (let [threads

             (for [thread-base thread-bases]

               (loop [thread (list thread-base)

                      remaining remaining]

                 (let [next-index (dec (first thread))]

                   (cond (empty? remaining) thread

                         (contains? (first remaining) next-index)

                         (recur

                          (cons next-index thread) (rest remaining))

                         :else thread))))

             longest-thread

             (reduce (fn [thread-a thread-b]

                       (if (> (count thread-a) (count thread-b))

                         thread-a thread-b))

                     '(nil)

                     threads)]

         (recur (concat longest-thread result)

                (drop (count longest-thread) phi-index-sets))))))

    #+end_src

    #+end_listing

 

 

 There is one final piece, which is to replace missing sensory data

 with a best-guess estimate. While I could fill in missing data by

 using a gradient over the closest known sensory data points, averages

 can be misleading. It is certainly possible to create an impossible

 sensory state by averaging two possible sensory states. Therefore, I

 simply replicate the most recent sensory experience to fill in the

 gaps. 

 

    #+caption: Fill in blanks in sensory experience by replicating the most 

    #+caption: recent experience.

    #+name: infer-nils

    #+begin_listing clojure

    #+begin_src clojure

 (defn infer-nils

   "Replace nils with the next available non-nil element in the

    sequence, or barring that, 0."

   [s]

   (loop [i (dec (count s))

          v (transient s)]

     (if (zero? i) (persistent! v)

         (if-let [cur (v i)]

           (if (get v (dec i) 0)

             (recur (dec i) v)

             (recur (dec i) (assoc! v (dec i) cur)))

           (recur i (assoc! v i 0))))))

    #+end_src

    #+end_listing

 

   

 ** Efficient action recognition with =EMPATH=

 

    In my exploration with the worm, I can generally infer actions from

    proprioceptive data exactly as well as when I have the complete

    sensory data. To reach this level, I have to train the worm with

    verious exercices for about 1 minute.

 

 ** Digression: bootstrapping touch using free exploration

 

 * Contributions

 

 

 

 

 # An anatomical joke:

 # - Training

 # - Skeletal imitation

 # - Sensory fleshing-out

 # - Classification