The impetus for this paper comes from two sources.
Firstly, the very short 1966 paper: Counterexample to Euler’s Conjecture, which reads as follows:
Euler’s conjecture is that at least n nth powers are required to sum to an nth power, n>2.
However, the counterexample
27⁵+84⁵+110⁵+133⁵=144⁵
in which four fifth powers sum to a fifth power, disproves the conjecture.
This paper reminds us that a definitive counterexample unambiguously disproves a conjecture.
Secondly, the 2017 Google paper: Attention Is All You Need.
This paper shows us that improvements in approximating techniques are often possible with new insights and greater processing power, and it was such improvements that have led to the current Generative AI systems. Unfortunately, because Generative AI systems are so impressive for some applications, where good approximations are ‘good enough’, some commentators now believe that Generative AI systems can achieve Artificial General Intelligence (AGI). I do not!
Origin of the Conjecture
There are numerous proponents of Generative AI that believe it is capable of AGI, but for brevity I will only directly refer to four.
i) An extract from Nature (9 Feb 2023) page 224:
“ChatGPT has caused excitement and controversy because it is one of the first models that can convincingly converse with its users in English and other languages on a wide range of topics.”
Comment: Whereas a naive user may anthropomorphise ChatGPT, it certainly can not converse. Human-quality conversations require the ability to create unstructured long-term memories – a capability that ChatGPT lacks.
ii) A LinkedIn post (2023): GPT-4: A significant step towards AGI, …
Comment: My own everyday use of English would imply that a significant step was a step forwards along a path that leads to one’s ultimate destination. I don’t believe a step towards a precipice can be regarded as significant. Again the writer would seem to support the conjecture I seek to disprove.
iii) OpenAI – various comments:
Comment:
OpenAI uses the term AGI to such an extent, that one could seemingly easily believe that the company believes that its Generative AI systems provide a path to AGI, which is the conjecture I seek to disprove with a counterexample.
iv) DeepMind has developed some truly impressive, but memoryless, applications.
Comment: I assume that the result of this focus on memoryless applications is the reason why there is no DeepMind AI Conversational Assistant.
Language Understanding
The problems with Generative AI systems can be difficult to appreciate given that one needs a reasonable knowledge of language, cognition, memory and mathematics.
Language is used to describe our physical and social world and as such it must of necessity be complex, but at the simple level language consists of three key ideas:
animate things,
inanimate things,
events (hence verbs).
The basic unit of language used in conversations is the sentence, and there are many types of sentence. However the three most common types are
Command
Question
and Statement.
As a result of humanity’s attachment to the ‘Principle of Least Effort’ it is usually the case that the meaning of a sentence can only be understood by understanding the context in which it occurs; this results in the following equation:
sentence ⊕ context = meaning
this reads: a sentence when mediated by context, i.e. the set of existing memories, resolves to meaning.
In the past there has been a strange interest in Question Answering systems, strange because of claims that such research provides a path to Artificial General Intelligence (AGI). However this research ignored the importance of Statements and their essential role in creating the long term, precise and discoverable memories required for context.
It takes only a little effort to appreciate the role of memory in providing the essential context for understanding human quality intelligent conversations. These memories must of necessity be clear, unambiguous, long-term and discoverable, and, for maximum economic value, such memories must also use standardised and verifiable cognitive representations.
This would also seem to be a clear requirement for Document Comprehension systems – where interoperability and third-party verification tools must surely be essential for commercial success.
A further problem with previous systems and current Generative AI systems is that they lack a verifiable mathematical theory for anaphor resolution. Given that Generative AI systems operate in a very high dimensional space this is yet another reason why they will always hallucinate.
Disproving the Conjecture
To disprove the conjecture, I have adopted a three part approach:
1) This paper – which provides a brief overview of the issues.
2) A set of counterexamples: see https://preciseai.co.uk/counterexamples
3) Eight talks on problems of Generative AI – see YouTube channel Precise Intelligence
Logically the counterexamples I have collected should be sufficient to disprove the conjecture that Attention Is All You Need. However the lessons from Semmelweis, Sally Clark and Lucia de Berk inform us that logical inference is not a strong point in scientific analysis. I discuss Semmelweis and Sally Clark in my book Precise AI. The sad story and poor mathematics involved in the case of Lucia de Berk can be found in the book ‘Math on Trial’ by Leila Schneps and Coralie Colmez. This perfectly highlights the problem of confirmation bias, also common in Generative AI.
Generative AI systems are built up from historic data using available text, and so, as is quickly apparent from some simple tests, the structures so created are not based on cognitive concepts and they have no explicit knowledge of things, and this issue extends to people they will only meet in the future.
An example of this lack of cognitive concepts is given by my first counterexample – as ChatGPT is unaware that ‘a brother of a brother is also a brother’.
Another example is given by ChatGPT’s response to the question:
Could my sister-in-law be a king? ChatGPT’s response of over 100 words failed to include the word ‘no’. However even a child knows that a sister-in-law is female and a king is male.
The sibling problem arises because Generative AI systems lack a sibling concept and one should note that such structures must be handled actively not passively because these systems will meet such individuals in their future interactions.
The gender confusion arises because Generative AI systems lack a specific vector dimension for gender, this is likely why in one of my test conversations ChatGPT decided that ‘Alan was a policewoman’, despite all evidence to the contrary in the conversation.
If future memories are formed of a person, then such memories may contain substantive information, as would be the case for a user input such as:
‘Tom is married to Kate and they have two
children’ or ephemeral information may be memorised, as would be the case with a user input of the form: ‘The first time I met Susan, who is a blonde, it was one afternoon in the local park and she was crying.’
These two examples show that as a minimum, an intelligent system must be able to precisely memorise personal information and event information.
Although it is possible to envisage a Generative AI system building a close approximation to a model of Tom – which it could do by laying down Tokens in appropriate positions in memory. The problem of memorising the event seems more difficult. I find it hard to envisage that a Generative AI used as a AI Conversational Assistant would be surprised if the next time I describe Susan she was a brunette.
This is perhaps a good point in this paper to remind ourselves of two simple facts.
Firstly, Generative AI systems cannot do simple multiplication!
Secondly, after many years of development, and apparently many $billions, the high tech companies seem determined to ignore both the importance of unstructured Statements and the essential requirement for a mathematical theory for anaphor resolution. I have an early 2024 newsletter from Amazon that gives 19 examples of simple Alexa interactions – and not one of them is a Statement, which is very strange given claims that Amazon wants to monetise Alexa. Also despite Microsoft’s interest in Voice Assistants for business applications, I have found no evidence that they have any interest in a provable theory of anaphor resolution. I mention these examples, there are many others, because the field of languages and AI is permeated with many strange belief systems – when the focus should surely be on verifiable mathematics.
Cognitive Memory
A Generative AI system stores its Knowledge in the weights of its network – or more precisely, given the fact that the vector dimensions are approximations, the weights hold approximate representations of the Knowledge provided.
However, we should ask what happens in the AI Conversational Assistant case – when the user now inputs Information in unstructured statements over a number of years.
Clearly the attention mechanism will record this new information in Token memory using a combination of explicit Tokens and their position in memory. Unfortunately this is another approximation approach and given the number of cognitive concepts that humans use, accurate retrieval of information over 50 years seems highly unlikely.
This brief analysis then leads onto a fascinating question – if a Generative AI system has to keep user information in Token memory then why don’t such systems keep all Information and Knowledge in such (cognitive) memory.
I suspect the answer to this question is very simple – the designers of Generative AI systems don’t know how to do so, and it is this lack of precision which leads such systems to hallucinate.
Summary
It is always useful to ask simple questions. If generative AI systems are so amazing and intelligent, then why can’t I just walk up to one and hold a conversation – remembering of course that conversations include unstructured Statements that must be reliably remembered and be discoverable, for at least 50 years.
Why do the ones I can test textually make such simple errors?
How can anyone believe that systems that hallucinate are intelligent?
The key issue is that memorising statements requires precision not approximations – it really is that simple. Intelligence will not magically appear from historic data.
Please read the counterexamples. They show problems with the simple concepts of
Siblings
Parents
Relatives
Names
Alive
to_Meet
Birthday
Marriage
and there are clearly many more similar cognitive concepts.
I find my evidence clearly disproves the conjecture.
However, many individuals, as with the discoveries of Semmelweis, find accepting alternate views to be very difficult – which is why we have stories such as The Emperor’s New Clothes. If my proof is insufficient for you, I hope that I have at least created doubt – and hopefully enough doubt before we spend further $billions going in the wrong direction.
My personal interest is in human quality intelligence not imprecise imitations of it.
Postscript
Applications that require ‘good enough’ approximations are often very suitable for Generative AI systems and so we find impressive results in Recommendation Systems, Games, Search, Image Creation and very simple short-term conversations – these can seem to demonstrate intelligence, but when probed with a counterexample only display excellent mimicry, with NO signs of innate intelligence and NO verifiable, discoverable memories. Hence NO precise context – and so NO understanding of meaning.
Even more concerning from a commercial perspective is the inability of such systems to produce a standardised representation of a document – for the simple reason that each Generative AI system uses its own proprietary approximating representations.
The commercial analogy would be to consider container ships in a different world, where despite the enormous economic benefits of standardisation, each country decides to use only its own distinct non-standard shipping container. Ouch!
My view is that standardisation is to be preferred.
