In computer science and AI when we say "reasoning" we mean that we have a
theory and we can derive the consequences of the theory by application of some
inference procedure.
A theory is a set of facts and rules about some environment of interest: the
real world, mathematics, language, etc. Facts are things we know (or assume)
to be true: they can be direct observations, or implied, guesses. Rules are
conditionally true and so most easily understood as implications: if we know
some facts are true we can conclude that some other facts must also be true.
An inference procedure is some system of rules, separate from the theory, that
tells us how we can combine the rules and facts of the theory to squeeze out
new facts, or new rules.
There are three types of reasoning, what we may call modes of inference:
deduction, induction and abduction. Informally, deduction means that we start
with a set of rules and derive new unobserved facts, implied by the rules;
induction means that we start with a set of rules and some observations and
derive new rules that imply the observations; and abduction means that we
start with some rules and some observations and derive new unobserved facts
that imply the observations.
It's easier to understand all this with examples.
One example of deductive reasoning is planning, or automated planning and
scheduling, a field of classical AI research. Planning is the "model-based
approach to autonomous behaviour", according to the textbook on planning by
Geffner and Bonnet. An autonomous agent starts with a "model" that describes
the environment in which the agent is to operate as a set of entities with
discrete states, and a set of actions that the agent can take to change those
states. The agent is given a goal, an instance of its model, and it must find
a sequence of actions, that we call a "plan", to take the entities in the
model from their current state to the state in the goal. This is usually
achieved by casting the planning problem as pathfinding over a graph with a
search algorithm like A*. Here, the agent's model is a theory, the search
algorithm is the inference procedure, and the plan is a consequence of the
theory. Deductive reasoning can be sound, as long as the facts and rules in
the theory are correct: from correct premises we can deduce correct
conclusions. We know of sound deductive inference rules, e.g. A*, and
Resolution, used in automated theorem proving and SAT-Solving, are sound.
The classic example of inductive reasoning is inferring the colour of swans.
Most swans are white (apparently) so if we have only seen white swans we have
no reason to believe there are any other colours: we are forced to infer that
all swans are white. We may only be disabused of our fallacy if we happen to
observe a swan that is not white, e.g. a black swan. But who is to say when
such a magnificent creature will grace us with its presence, outside of
Tchaikovsky's ballets? Induction is thus revealed to be unsound: even given
true premises we can still arrive at the wrong conclusions. Another example is
the scientific method: imagine an idealised scientist, perfectly spherical, in
a frictionless vacuum. She starts with a scientific theory, then goes out into
the world and makes new observations about a phenomenon not described by her
theory. She constructs a hypothesis to extend her theory so as to explain the
new observations. The hypothesis is a set of rules, where the premises are the
consequences of the rules in her initial theory. Then, being an idealised
scientist, she goes looking for new observations to refute her hypothesis.
Science only gives us the tools to know when we're wrong.
Abductive reasoning is the mode of inference exemplified by Sherlock Holmes.
We can imagine Sherlock and Watson standing outside a tavern in London,
watching as a gentleman of interest steps out of the tavern with egg on his
lapel. "Ah, my dear Watson, what can we conclude from this observation?". "Why
my dear Holmes, we can conclude that the man had eggs for breakfast". Holmes
and Watson can arrive at this conclusion, about a fact that they have not
directly observed, because they have a theory with a rule that says "if one
eats eggs, one may get some on one's lapels". Working backwards from this
rule, and their observation of egg on the man's lapels, they can guess that
he had eggs even if they didn't directly observe him doing so. Abduction is
also unsound: the man may have swapped coats with an accomplice, who was the
one who had eggs for breakfast instead.
And now you know what "reasoning" means. So the next time someone asks: "what
is reasoning?", you can let them know and turn the discussion to more
interesting, more productive directions.
>> Even if one throws that aside, spending time exploring and building with the most state of the art LLMs is just as instructive. I'm watching the implementation - whats working is ML models trained on specific domains (not much different than 5+ years ago), and whats not working is a general model that humanity can let go to work on its own. Sit in front and observe ideas turn to the samey intellectual, high-syllable mush. Its productive, but not in any way that's promised.
Important point. LLMs were early on hailed as the first general-puprose AIs that can perform any task (remember "Sparks of AGI"?). Today they're increasingly promoted for specialised applications - coding, as a for instance.
Let me stand here on the Skeptic's Corner and be skeptical, so that the users who complain about skeptical comments have someone to direct their ire at. You're welcome.
Right, so, first, I haven't looked at the proof. Graph theory is not my subject and it would probably take me a few days to get my head around the whole thing. If OpenAI's LLM was used to prove an important graph theory result, then that's very good for them and graph theory.
However, I have to note that it's been 52 days since 20 May, the last date that OpenAI announced their previous mathematical result (a disproof of the unit distance conjecture).
What have OpenAI been doing all this time? I am willing to bet a good percentage of my money that they were trying, and failing, to produce the current result, or possibly something even juicier (one of the Millenium prize problems maybe?). They are hell bent on showing that their models are good for maths and science so they're very unlikely to have sat there twiddling their thumbs until they suddenly sprang into action and prompted their LLM once to generate just one proof. They must have been running the thing constantly, multiple instances of it, over that entire period.
Going by the instruction to run for eight hours before returning or giving up in their released prompt [1], that means they could have made at most 156 attempts to solve this problem, each of which failed except the last one [2].
So what happened to those other 156 attempts? Are we ever going to see them?
More importantly, who was it that selected the announced result? Who decided that this result is an actual proof? Until now, every proof generated by an LLM has been verified either by human mathematicians, or by human mathematicians x a proof assistant. What happened this time?
Obviously, any claims that this result were produced "autonomously" must be evaluated according to the answer to that last question. So far, LLMs have been incapable of distinguishing between a correct and an incorrect proof, which is also why they need to be run multiple times until they generate a correct one. If something has changed, it'd be interesting to know.
Finally, a magic eight ball that's correct one time out of 156 may be useful; or it may not. I honestly have no idea. I think time will tell.
__________________
[1] "Spend at least 8 hours on this before even thinking of returning or giving up"
[2] That's 52 days from 20 May, times 3 for each eight-hour attempt in a 24-hour day.
But note well that the X post says that the solution was produced in "just under one hour" so that means the model didn't really stick to the prompt's time limit. Which means there may have been considerably more than 156 attempts that we'll probably never know of.
Or even considerably more if the model ignored the time limit going the other way.
This is spot on. And yet, when I try to publish my papers on P = NP with the proof reducing to "trust me bro, I checked this out carefully" I get shot down by irrate reviewers who demand to see my work. Why can't those people just believe what I say?
For example, there's all the problems that the same off-the-shelf model hasn't solved despite OpenAI running it for many hours on them. Don't forget you're only seeing the results of successful runs.
We can estimate that those unsolved problems must number in the dozens, or even hundreds, given the amount of time that passed since the last announcement of a solution to an interesting problem by an OpenAI model: i.e. the unit distance problem which was announced solved in 20 May this year. That's a couple of months, yes?
We can be fairly certain that OpenAI have been trying to solve other problems all this time, first because they are hell bent on demonstrating that their models can do maths and second because we just got another result, but it took that long. They were obviously not twiddling their thumbs all this time.
So if OpenAI are running their model on a single proble for eight hours at a time (according to the prompt they released) they could be easily have run a few hundred instances of their model on the same number of open problems 156 times for each instance (53 days since 20 May, with a model running in three eight-hour sessions per 24 hour day). I mean the only restriction is the cost they're willing to pay for the inference.
So yeah, there's a lot left to do still, don't worry.
>> Try to interact with the Greek government and they might ask you to spell your name using only their characters. An interesting challenge when your name contains sounds that don't exist in the local language (sh, hu).
Seen from the other side, a friend of mine called Γωγώ (short for Γεωργία, i.e. Georgia) spelled her name "Roro" when she went to France. The standard transliteration would be "Gogo" but the French would pronounce that like "go-go", whereas they pronounce the "R/r" like Greeks pronounce the "Γ/γ".
And how about all the Greek women who take on their father's spelling of the family name in English-speaking languages (as have I)? E.g. Olympia Dukakis: that's a male form (Δουκάκης); the female is "Doukaki" (Δουκάκη). But, try to explain that to speakers of a language without grammatical genders. Sounds more like a spelling error.
I understand that Icelanding families have a similar problem, with surnames that name the parent, so that if the father's first name e.g. Bjorn, the son's surname would be Bjornsson and the daughter's name would be Bjornsdottir, with the father and mather's surname being whatever -son or -dottir reflects their ancestry. Can cause trouble when going through passport control as a family with underage kids all with different surnames.
Basically, those guys trained a drone to beat human FPOV racers but they had access to the race course layout before the race and trained extensively on it. Can't do that on a battlefield.
Also: no shooting at enemy drones during FPOV races. Makes surviving to the end of the race simpler.
If you make a hammer, it can always be used to murder someone, but if you make an AK-47, there's only one way it can be used. So if you don't want what you make to be used for killing, don't make an AK-47. If you 're good at toolmaking, choose to make tools that are not weapons.
The claim is very specifically that it's SOTA on the R2R-CE benchmark, which is a bunch of 3D environments in a simulation. So, yes, it's SOTA; no, it's not very different than a maze. And it's sure not anywhere near anything that could be considered SOTA in the real world... if such a SOTA was even possible to define objectively.
(it's not because evaluation in the real world is very, very tricky).
To be clear, R2R-CE is a benchmark consisting of simulated environments.
So what this means is that beating this benchmark is about as useful as getting a robot to play Minecraft, or some other video game. Great, but a robot must run in the real world, in physical reality: not in a digital environment.
Unfortunately it's extremely hard to evaluate the performance of robotic systems in physical reality. First of all because if they don't do well you need lots of spare robots to complete the evaluation.
The article above does include the obligatory video of a physical robot navigating a virtually empty, uncluttered "office" environment with nice, smooth surfaces, at 2x speed; virtually a trademark of the entire research field by now. Brownie points for having three guys shuffle carefully across the robot's path towards the end of the video (they're shuffling at 2x speed so they're going reeeaaaally carefully in real life, probably ready to jump out of the way if say a heavy metallic object hurtles towards them randomly).
But, this is like all the fanfare and hype about Aloha a couple of years ago: great stuff if you want your team to be bought by one of the large tech corps, or to get more funds to play with your cool tech (I mean who doesn't?). Not so great for anyone who's expecting this to be a step forward (or ahem a roll forward) on the way to having robot maids/butlers going 'round your house or office.
Shaheds (some models) have loitering ability, and other "autonomy" features. Tbh the term is as fuzzy as "AGI" or "self-driving" these days because there are a bunch of automatisms that a drone can have that are often labelled so. However, an autonomous system should do much more than go to a designated location and fire at a target that looks like it might be the designated target. I mean to say, pathfinding and image recognition do not autonomy make; or they shouldn't be said to anyway.
As I like to say of course, self-guided missiles are arguably autonomous; but that's just because their whole job is to reach a target while causing maximum damage on hit. That removes many of the requirements of other "autonomous" systems (e.g. self-driving cars).
P.S. I honestly don't know much about Predators but I expect they're going to have the most advanced features available.
Just to add to this, radio-controlled drones are also still used, it's just that those are relatively easy to jam while the fiber-optic ones aren't and that makes them very difficult to defend against.
Also, to my understanding, jamming works best against smaller, First Person View quadcopter-style drones that have a limited range and carry only limited firepower (e.g. one grenade basically) and are often used against personnel and armor.
Longer-range and better armed drones, like the US's Predators that can launch missiles, or Iran's Sahel drones that attack targets thousands of Kms away, fly at much greater heights and are -again, AFAICT- harder to jam, although I am saying this with some uncertainty.
In any case, I believe hkpack's comment above that Ukrainians have private tech that the world doesn't know about doesn't stand to reason. If any party had such tech, it would be the US, China, or possibly Israel, with Russia a distant second possibility. Ukrainians are not known for their AI output, to say the least. And we're talking here about major breakthroughs needed to endow drones with true autonomy, breakthroughs that require scientific advances and not just technological tweaks and R&D.
Also, if there was really useful drone autonomy, it would have now spread like wildfire in every possible theater. Despite a few announcements that this or that party (e.g. Turkey, last year) has used autonomous drones in a real combat situation, there is no shortage of real combat situations and yet there are no autonomous drones to be seen on any battlefield.
Finally, any side with autonomous killer robots would advertise their existence to high heaven. Half of the effect is the ability of such a weapon to cause terror to the enemy. Why keep quiet about it? The enemy already has samples of your tech, that's the only thing certain in modern warfare; you're not keeping any secrets that way.
This is a great introduction to all the technology that people have developed over the years (since the 1970's!) to make robots autonomous, that, unfortunately, have never quite worked. As I like to point out, if we knew how to make drones (or any kind of robot) really, actually autonomous you'd see them used first of all in Ukraine, and recently in Lebanon. You don't, all the drones used in warfare are remote-controlled. Autonomy doesn't work yet. Not well enough to deploy in a theater of war.
Btw, I did really enjoy the graphic sumarising Control Theory. I'd criticise the lack of Planning and Scheduling, i.e. the PDDL-based symbolic AI stuff which is the technology that works best and is used e.g. by NASA on Perseverance, but OK, there's basically three communities that attack the same problem from different angles: Model Predictive Control, Planning & Scheduling, and RL. Two out of three is not too bad (but I don't see how RL goes under CT; never mind).
What is reasoning?
In computer science and AI when we say "reasoning" we mean that we have a theory and we can derive the consequences of the theory by application of some inference procedure.
A theory is a set of facts and rules about some environment of interest: the real world, mathematics, language, etc. Facts are things we know (or assume) to be true: they can be direct observations, or implied, guesses. Rules are conditionally true and so most easily understood as implications: if we know some facts are true we can conclude that some other facts must also be true. An inference procedure is some system of rules, separate from the theory, that tells us how we can combine the rules and facts of the theory to squeeze out new facts, or new rules.
There are three types of reasoning, what we may call modes of inference: deduction, induction and abduction. Informally, deduction means that we start with a set of rules and derive new unobserved facts, implied by the rules; induction means that we start with a set of rules and some observations and derive new rules that imply the observations; and abduction means that we start with some rules and some observations and derive new unobserved facts that imply the observations.
It's easier to understand all this with examples.
One example of deductive reasoning is planning, or automated planning and scheduling, a field of classical AI research. Planning is the "model-based approach to autonomous behaviour", according to the textbook on planning by Geffner and Bonnet. An autonomous agent starts with a "model" that describes the environment in which the agent is to operate as a set of entities with discrete states, and a set of actions that the agent can take to change those states. The agent is given a goal, an instance of its model, and it must find a sequence of actions, that we call a "plan", to take the entities in the model from their current state to the state in the goal. This is usually achieved by casting the planning problem as pathfinding over a graph with a search algorithm like A*. Here, the agent's model is a theory, the search algorithm is the inference procedure, and the plan is a consequence of the theory. Deductive reasoning can be sound, as long as the facts and rules in the theory are correct: from correct premises we can deduce correct conclusions. We know of sound deductive inference rules, e.g. A*, and Resolution, used in automated theorem proving and SAT-Solving, are sound.
The classic example of inductive reasoning is inferring the colour of swans. Most swans are white (apparently) so if we have only seen white swans we have no reason to believe there are any other colours: we are forced to infer that all swans are white. We may only be disabused of our fallacy if we happen to observe a swan that is not white, e.g. a black swan. But who is to say when such a magnificent creature will grace us with its presence, outside of Tchaikovsky's ballets? Induction is thus revealed to be unsound: even given true premises we can still arrive at the wrong conclusions. Another example is the scientific method: imagine an idealised scientist, perfectly spherical, in a frictionless vacuum. She starts with a scientific theory, then goes out into the world and makes new observations about a phenomenon not described by her theory. She constructs a hypothesis to extend her theory so as to explain the new observations. The hypothesis is a set of rules, where the premises are the consequences of the rules in her initial theory. Then, being an idealised scientist, she goes looking for new observations to refute her hypothesis. Science only gives us the tools to know when we're wrong.
Abductive reasoning is the mode of inference exemplified by Sherlock Holmes. We can imagine Sherlock and Watson standing outside a tavern in London, watching as a gentleman of interest steps out of the tavern with egg on his lapel. "Ah, my dear Watson, what can we conclude from this observation?". "Why my dear Holmes, we can conclude that the man had eggs for breakfast". Holmes and Watson can arrive at this conclusion, about a fact that they have not directly observed, because they have a theory with a rule that says "if one eats eggs, one may get some on one's lapels". Working backwards from this rule, and their observation of egg on the man's lapels, they can guess that he had eggs even if they didn't directly observe him doing so. Abduction is also unsound: the man may have swapped coats with an accomplice, who was the one who had eggs for breakfast instead.
And now you know what "reasoning" means. So the next time someone asks: "what is reasoning?", you can let them know and turn the discussion to more interesting, more productive directions.