Re: Mental arithmetic as a test for Sentient AI

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Milton Ponson
Rainbow Warriors Core Foundation
CIAMSD Institute-ICT4D Program
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Aruba, Dutch Caribbean


On Tue, Jan 21, 2025 at 7:43 AM Dave Raggett <dsr@w3.org> wrote:

> Sentient AI differs from Generative AI in supporting continual learning
> and reasoning, mimicking human cognition. Sentient AI agents are thus able
> to acquire new skills. One way to explore this is to model how children
> learn basic arithmetic, something that is trivial for computers, but
> challenging for young children.
>
> Here is an explanation of how to add whole numbers:
>
> Step I: We arrange the given numbers in columns, ones under ones, tens
> under tens, hundreds under hundreds and so on.
>
> Step II: We add the digits in each column taking the carry over, if any,
> to the next column to the left, and adding it along with the digit in that
> column. We continue this process till we add the digits in all the columns.
>
>
> Taken from: https://www.math-only-math.com/addition-of-whole-numbers.html
>
> This explanation brushes over the details, e.g. how to add pairs of
> digits, where we can use our memory for a given pair, or if that fails,
> work it out step by step, by adding one progressively.
>
> Children are taught to write the numbers down, but as they gain
> confidence, are able to perform the algorithm mentally.  How can we
> replicate that with artificial neural networks?
>
> Christian Lebiere’s Ph.D thesis (1999) “The dynamics of cognition: An
> ACT-R model of cognitive arithmetic” [1], provides a symbolic model of
> mental addition. ACT-R is based upon the idea of “chunks” as sets of
> name/value pairs, along with the means to apply a sequence of
> transformations on chunks.
>
> [1]
> https://www.researchgate.net/publication/220173218_The_dynamics_of_cognition_An_ACT-R_model_of_cognitive_arithmetic
>
> Can ACT-R provide useful insights into how to design an artificial neural
> network with similar capabilities?  The idea here is to model addition in
> terms of understanding and generating sequences of tokens, sequential
> transformations applied to latent semantics, and an implementation of
> human-like memory.
>
> To demonstrate cognition, we require the agent to vocalise the sequence of
> steps the agent makes when working on the task (i.e. the chain of thought).
> This points to the idea of using autoregressive training as a basic for
> learning the cognitive steps. The teacher provides a worked example, and
> the student attempts to duplicate it. Repetition improves performance.
>
> Memory is key to all of this, including working memory and skill memory.
> For artificial neural networks this corresponds to the current values and
> model parameters. Continual learning implies that the model parameters are
> being continually updated as cognition proceeds. In principle, this can be
> arranged using a mix of local learning rules and gradient descent.
> Explicit memory involves cue based retrieval at the same level of the
> network.
>
> I am now looking for smaller steps to progress towards a full proof of
> concept for learning mental arithmetic. This could include memorising
> single digit addition, and understanding the columns for the digits in
> whole numbers.
>
> This overall approach seeks to mimic human cognition using modest levels
> of resources in stark contrast to approaches based upon exploiting large
> language models. This will allow us to build a whole new range of AI
> systems that can be taught like humans, learn on the job, explain
> themselves, reflect on their performance and so forth.
>
> Your comments are welcomed!
>
> Dave Raggett <dsr@w3.org>
>
>
>
>