Mortal computation. Hope for the halting problem mitigation.

by Casian STEFAN, Principal Researcher at Essentia Mundi AI Lab. Contact: ai-AT-essentiamundi.com / ai.essentiamundi.com
Mar. 2024.

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Turing complete language means to an extent that it resides within its axiomatic limits, in a Gödelian sense, it carries unprovability of itself, within. [draft] If it is computable then the system halts, so being able to get out of through recursion, it is decidable. The hardware-software duality in today's computers is producing that kind of machines with the use of the computer formal languages which are Turing complete (not all though - like SQL/HTML). LLMs on the other hand are not Turing complete systems. A black box quality, not able to do recursivity. [to add more to the distinctions, verify assumptions]

Biomimicry is the emulation of the models, systems, and elements of nature for the purpose of solving complex human problems. Biology does not have a halting problem - or when it is the case of an obstacle, it finds a way. The nature itself does not compute, in an axiomatic sense, it just flows.

When we approach an axiomatic sense to it, in order to be able to embed computers with fluid intelligence (the one not in Gödelian sense) the problem of halting may arise at one point.

One way we approached this biomimicry emulation, was very much tried with the Artificial Neural Networks architectures, mostly as software emulations of how would a natural network work, brain and neuron inspired approaches. An inspiration, of the reverse engineering of the analog neural part in nature. Along the way in developing computers, there was always the prospect of analog computing, which is a domain of computing in itself, but of course due to other limitations (exactness), was replaced by digital ones.

Cybernetic organism and society (as a side note): in the case of a collective-hive, "borg" like mind within an all mechanistic interpretation, no individuals, no intuition, no sentiments world, then this prospect of incompleteness is "solved" by dissolving it into a non-problem: no one to care about. A flattening of the human condition through a special societal structure.)

Mortal computing. A revival in the world of computing and especially in the AI field may be underway and as devised by G. Hinton a few years back (2022), in which, in order to be able to have the ANNs (also proposed a different architecture than feed forward*) on the position of rapid calculations, low energy consumption and not a limitation as in a Turing complete way, is to have "mortal computing" architecture, the idea is to have the weights inscribed directly into hardware.

A unification in solidification: once inscribed, the "software" part cannot be copied to another platform, the hardware remains inscribed forever and also with the characteristics of the user as he is the one that is grown the neural network. It is named "mortal" because if the hardware fails, software (network characteristics) is of course gone too. But as G. Hinton says (approximate citation): "the distillation comes to rescue, in that the old model has to share the knowledge of the weights to a new one, that would need to track and inscribe the same values, like a teacher to the students."

The marrying of the two in order to have a better, efficient whole of computing, in which the thermodynamics (the hardware) is then very close to the statistical Bayesian calculus (the network.) A non Turing Machine complete approach to computation(al functionalism.)

Hardware is grown for specific tasks and learns weights in specifically on that hardware (as in, buying a baby phone, then grow it.) Kind of analog computing with neural networks. The hardware and software are not anymore separated. In the dual approach, the software does have to go through the architecture of the hardware.

Hamiltonian-oriented quantum computing. Another way would be to employ the quantum computing architectures. There are research efforts with experimental results that suggest an Hamiltonian-oriented analog quantum simulation would be advantageous over circuit-oriented digital quantum simulation.(**)

Hamiltonian-oriented analog quantum simulation refers to a method of using quantum systems to simulate the behavior of other quantum systems governed by a particular Hamiltonian. Hamiltonian system is a dynamical system governed by Hamilton's equations. In physics, this dynamical system describes the evolution of a physical system such as a planetary system or an electron in an electromagnetic field. A mathematical description of the energy of a physical system in terms of its variables.

Analog quantum simulation involves encoding the dynamics of a quantum system of interest into the dynamics of another, more controllable quantum system. An environment simulation that could potentially include AI agents & collaboration in this environment. This environment and the instances of it may benefit from the analog side, in which the halting problem is to be mitigated.


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Exploration by C. Stefan, 19.Mar.2024 [about]
Last update: 19.Mar.2024 (versions: draft 0.1b[v0.2.2], *) [versions]
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References:
* The Forward-Forward Algorithm: Some Preliminary Investigations, G. Hinton, https://arxiv.org/abs/2212.13345
** SimuQ: A Framework for Programming Quantum
Hamiltonian Simulation with Analog Compilation
https://arxiv.org/pdf/2303.02775.pdf