Explaining the Disjunction Effect with Hierarchical Temporal Memory
The theory for receptive fields, sparse representations and predictions of HTM explains the Disjunction Effect.
Abstract
The Disjunction Effect is a cognitive contradiction which appears when we over- or underestimate the probability of two separate events respect to the probability of their union. For example, an experiment reported that people tend to give a 50% truth value to the proposition “olives are fruits”, a 10% one to “olives are vegetables” and a 80% one to “olives are fruits or vegetables”. One would expect the last number to be 60% (the sum of 10%+50%, since “fruits and vegetables” is the sum of the previous two groups). In a similar case, people gave a 100% truth value to the proposition “Judo is a hobby” but only a 80% one to “Judo is a hobby or a game”.
I will explain how the Hierarchical Temporal Memory framework explains this logically contradictory result. In short: due to the prediction property of HTM, if the categories named in a conjunction question reinforce the prediction for any of them, the conjunction of categories will be perceived as stronger than the sum of the two separate categories. If instead the predictions generated by the categories excite neurons which, if activated, would in turn activate a third category, the conjunction will be perceived as weaker than the sum of the separate categories.
For example, thinking about “olives and fruits” excites and predicts “vegetables”, as they are often observed together (e.g. at the grocer). Hence, “fruits or vegetables” > fruits + vegetables. Conversely, thinking about “judo and hobbies” excites “sports”, and thus Judo is not “hobbies or games” as the suggestion “it is instead a sport” comes to mind.
If you are already familiar with the framework, you can skip the next section and jump to the one named “The Disjunction Effect seen through the HTM framework” for a detailed account of the innovative hypothesis postulated in this article.
The Hierarchical Temporal Memory framework
The HTM framework is described in Numenta’s white paper. The main concepts pertaining to the topics of this article are:
- Our brain encodes information in a sparse mode.
- Each cortical layer works by receiving a sparsely encoded input; if such input matches one or more of the stored patterns, it activates some of its own neurons, either in “activated mode” or in “prediction mode” (I predict this neuron will become active in the next time step).
- Once a matching pattern is recognised, if some cells of the column are active in prediction mode, only them will become active; otherwise all cells of the column will.
The Disjunction Effect seen through the HTM framework
Let’s continue the experiment described in the introduction: classifying an olive as a fruit or a vegetable.
When asked whether an olive is a fruit, the brain of the respondent will execute the following steps:
- The neurons representing how an olive feels (it color, shape, taste, etc.) are activated and their output is fed to the perception.
- The perception analyses this input and activates hierarchically higher and higher areas until it reaches the receptive field of the column representing “fruits”.
- The receptive field conducting to the column “fruits” also feeds other categories, such as “vegetables”. However, as the category “fruits” was expected (the question primed it), the neurons representing “fruits” are in predictive mode, and thus they become activated.
- The speed and strength of activation of the column representing “fruit” is checked and a response is accordingly given; the respondents will assign a 50% truth value to the proposition “olives are fruits”.
The same steps are followed for the question “Are olives vegetables?”.
Now let’s see what happens in case the question asked is “Are olives either fruits or vegetables?”.
- The neurons representing how an olive feels (it color, shape, taste, etc.) are activated and their output is fed to the perception.
- The perception analyses this input and activates hierarchically higher and higher areas until it reaches the receptive field of the columns representing “fruits” and “vegetables” (since fruits and vegetables are similar and have the same uses, it is likely that their receptive fields are very closely related).
- Both the neurons representing “fruits” and “vegetables” are in predictive mode (the question primed them), the neurons representing “fruit” are in predictive mode, and thus they become activated.
- The speed and strength of activation of the columns representing “fruits” and “vegetables” are checked together with any other column activated (none) and a response is accordingly given; the respondents will assign a 80% truth value to the proposition “olives are either fruits or olives”.
Why is the response stronger than expected (50% fruit + 10% vegetable = 60% fruits or vegetable < 80%)? For two reasons: the first is that no other category (e.g. “bacteria”) got activated by the output generated by “olives”, and we are thus inclined to say that, if the only choices that came to our mind are “fruits” and “vegetables”, there are high chances that “olives” are in one of the two categories. The second is that the predictions from each category primed by the question make the other category more likely (instead of a third one). Let’s examine this phenomenon.
Thinking about the categories “fruits” and “olives” will activate a prediction for “vegetables”, as the categories are often observed together (e.g. at the grocer). On the other side around, “vegetables” will activate a prediction for “fruits”. Both categories reinforce the prediction for the other, and thus the conjunction of both categories will be perceived as stronger than the sum of the two separate categories.
Instead, thinking about “Judo” and “hobbies” will activate a prediction for “sports”. Once the output from imagining “Judo” is fed back into the receptive field of “hobbies” and “games”, thanks to the previous prediction, also “sports” will be active. Now the respondent’s mind finds itself with three possible answers to “is judo a hobby or a game” and it would want to answer “it is a hobby or a game or a sport”. Thus it will assign a lower truth value to the proposition “judo is a hobby or a game”.
The figures below will help the reader understand the processes described above.
An example
In Image 1: the network at rest state. Activation of neuron O (olive) stimulates neuron 2 to 6. The receptive field of neuron F (fruits) is made of neurons 1 to 5, and the receptive field of neuron V (vegetables) is made of neurons 4–7. All neurons and connection are at rest (narrow lines and light colors).
In Image 2, the activation of neuron F (“fruits”) causes neurons 1–5 to go in predictive mode. This is a priming effect due to the question “Are olives fruits?”.
In image 3, the activation of neuron O (“olive”) causes the excitation of neurons 2–6. The HTM frameworks states that if any neuron in the excited column is in predictive mode, only those activate, and thus only neurons 2–5 become active. The activation of neurons 2–5 causes the activation of neuron F (“fruits”).
In Image 4, the status of the network after the excitation of neurons F (“fruits”) and V (“vegetables”), as after the question “Are olives fruits or vegetables?”. Neurons 1–7 enter predictive mode.
In image 5, the activation of neuron O (“olive”) causes the excitation of neurons 2–6; they are all in predictive mode so they all become active. The activation of neurons 2–5 causes the activation of neuron F (“fruits”) and the activation of neurons 4–6 causes the activation of neuron V (“vegetables”).
The neurons F and V comprise the entirety of the neurons activated by the previous layer, and so the mind will conclude that it is highly probable that “olives are fruits or vegetables [and nothing else]”.
Now let’s examine another example: the question “Is Judo a hobby or a game”.
In image 6: the network at rest state. The activation of neuron J (“Judo”) is set to stimulate neuron 2 to 6. The receptive field of neuron H (“hobbies”) is made of neurons 1 to 4, the receptive field of neuron S(“sports”) is made of neurons 3to 5, and the receptive field of neuron G (“games”) is made of neurons 4–7.
In image 7: the status of the network after the excitation of neurons H (“hobbies”) and G (“games”). Neurons 1–7 enter predictive mode. Note that neuron S is not excited at all, but neurons in his receptive field are in predictive mode nevertheless, set as such by the activity of neurons H and G.
In image 8: the activation of neuron J (“Judo”) excites neurons 2–6; as they are all in predictive mode they all fire. The activation of neurons 2–6 causes neurons H, S and G to become active.
The brain is now unsure whether Judo is a hobby, a sport or a game (all three seem possible). He will then conclude that the probabilities that Judo is a hobby or a sport are less than the probabilities that it is a hobby or a game only
This article is a work-in-progress piece: a review of how this integrates with previous theories, of its compatibility with experimental results and how it predicts most symptoms of ASD will be added in the following days or weeks. Meanwhile you are welcome to leave your comments, here on Medium or by sending me an e-mail at luca.d.dellanna@gmail.com. You can also follow me on Twitter: @DellAnnaLuca.
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