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Transformers are very bad at counting in one feed forward pass, you need to explicitly tell them to use a counter in autoregressive fashion like here:

https://chatgpt.com/share/6775cb37-4198-8007-82cb-e897220827...


Transformers are very bad at counting due to how their internals work. But if you ask them to use explicit counter the problem disappears:

https://chatgpt.com/share/6775c9a6-8cec-8007-b709-3431e7a2b2...

Basically one feed forward is not Turing complete, but autoregressive (feeding previous output back into itself) are Turing complete.


This makes it worse IMO. I was starting to think it didn’t have a letter by letter representation of the tokens. It does. In which case the fact it didn’t decide to use it speaks even more towards its unsophistication.

Regardless, I’d love if you would explain a bit more why the transformer internals make this problem so difficult?


When Can Transformers Count to n?

https://arxiv.org/html/2407.15160v2

The Expressive Power of Transformers with Chain of Thought

https://arxiv.org/html/2310.07923v5

Transformer needs to retrieve letters per each token while forced to keep internal representation still aligned in length with the base tokens (each token also has finite embedding, while made out of multiple letters), and then it needs to count the letters within misaligned representation.

Autoregressive mode completely alleviate the problem as it can align its internal representation with the letters and it can just keep explicit sequential count.

BTW - humans also can't count without resorting to sequential process.


Thanks!

Reasoning is not a binary skill.

And failure modes of other types of reasoners do not need to be the same as the failure modes of humans.


It's widely accepted that reasoning is not a binary skill.

You can make mistakes and still reason. Very often people given the same premises will disagree in thier reasoning as we are doing right here.


BTW - the model may be wrong depending on the example. More voluminous objects displace more air and due to buoyancy are lighter for the same mass.

The proper way to ask it would be to ask which object has more mass.


For what it’s worth, I asked it the following:

Q:

Which weighs more on earth: 100kg of steel or a 100kg polystyrene ball? Be as technically correct as possible

A: Technically, 100 kg of steel and 100 kg of polystyrene weigh the same on Earth when measured on a scale, as they both experience the same gravitational force due to their equal mass. However, there are some nuances to consider:

Buoyancy Effect

Earth’s atmosphere exerts an upward buoyant force on objects, proportional to the volume of the object and the density of the surrounding air. Since polystyrene has a much lower density than steel, a 100 kg polystyrene ball will have a significantly larger volume and experience a greater buoyant force compared to 100 kg of steel.

As a result: • Effective weight (apparent weight): The steel will weigh slightly more than the polystyrene on a scale because the buoyant force acting on the polystyrene reduces its apparent weight more.

Actual Weight

Weight is the gravitational force on an object and is given by:

Where and . Without considering buoyancy, both objects have the same weight of approximately (newtons).

Conclusion • True weight (in a vacuum): Both are identical at 981 N. • Apparent weight (in air): Steel is slightly heavier due to reduced buoyant force acting on it compared to the polystyrene ball.


Yup, the models are smart, but are trained to follow standard human patterns for this type of questions. And even on hackernews vast majority will not think that they would need to correct for buoyancy when actually attempting the experiment in standard conditions.

They very often get popular "tricky" questions wrong because they saw it so many times that they switch from internal reasoning to memorization/retrieval.


The task of Russian navy was to invade Odessa and sabotage Ukrainian grain trade. They didn't even attempt Odessa desant, because they knew it was futaile. And they failed at sabotaging Ukrainian grain trade, but not for a lack of effort.

Otherwise these ships served as missile lunchers, but even then they had to widraw to ports far away from Ukraine, because of drone attacks.

Ukraine won the naval battle at tiny fraction of the Russian navy cost.


The ship has long sailed. EU decided that our laws will be applied maximally - to all EU citizens regardless of their location and for everyone within our territorial control.

And if other countries like USA have conflicting laws like Patriot Act then companies can be even forced to divest from EU or split their businesses so that USA branch can not enforce USA spy laws in EU. Google Privacy Shield.


> The ship has long sailed. EU decided that our laws will be applied maximally - to all EU citizens regardless of their location and for everyone within our territorial control.

Ships that have sailed can still be sunk.

> And if other countries like USA have conflicting laws like Patriot Act then companies can be even forced to divest from EU or split their businesses so that USA branch can not enforce USA spy laws in EU.

How is this supposed to apply to a small business with one employee?


Depends on the benchmarks. AI that can actually do end to end the job of software developers, theoretical computer scientists, mathematicians etc. would be significantly more impactful than this.

I want to see AI moving the state of the art of the world understanding - physics, mathematics etc. - the way it moved state of the art of the Go game understanding.


Doing these end to end jobs still falls on user experience and UI, if we are talking about getting to mass market.

This GPT-4o model is a classic example. It is essentially the same model as GPT-4 but these multimodal features, voice conversations, math, and speed is revolutionary as the creation of the model itself.

Open Source LLM will end up as a model in GitHub and will be used by developers but it looks like even if GPT-4o is only 3 months ahead of other models in terms of benchmarks, the UI + Usecase + Model is 2 years ahead of the competition. And I say that because there is still no chat product that is close to what ChatGPT is delivering now, even though there are models that is close to ChatGPT 4o today.

So if it is sticky for 2 more years, their lead will just grow and we will just end up with more open source models that are technically behind by 3 months but behind product-wise by 2 years.


> probably the atomic cooperation is even more important

That's why I don't understand why Budapest Memorandum signatories allow Russia for breaking the security guarantees.

Ukraine gave up fully the third biggest nuclear arsenal for security guarantees from Russia, USA, France and UK.

To me it seems pretty clear that if Ukraine falls then nuclear disarmament and nonproliferation is dead. And that my country, Poland, should seek to develop nuclear weapons.


i agree that nuclear disarmament and nonproliferation is dead. and clearly it is the case that countries that do not develop nuclear weapons will not enjoy westphalian sovereignty as they did for the previous few centuries, but it's not clear that westphalian sovereignty in the nuclear age was the stable equilibrium that it was in the gunpowder age, and now drones have probably made nuclear weapons obsolete, with so-far-unforeseeable consequences for the contours of international relations

it's possible that pursuing the will-o'-the-wisp of westphalian sovereignty under those circumstances will just make the situation worse and increase the chances of human extinction, which (i feel safe in saying) would be a worse outcome for poland


On the basic premise EU is working wonderfully.

It's the longest period in our thousand years history that we Poles have not had to fight Germans.

We have lost maybe even 1/3 of population in wars with Sweden, 1/5 of population in war with Germany.

Poland didn't exist or 123 years under Russian, Prussian and Austrian occupation.

Given that as a baseline, I'm really grateful for the EU.


Even within the EU it is clear that low income countries have worse life than high income countries, just like everywhere in the world. And Europe's real median income is decreasing in most of the countries. Surely, it will have effect in few decades.

[1]: https://www.euronews.com/next/2023/08/21/real-wages-are-down...


Yes. But are you implying that the EU is making this worse? After all, the economic slowdown in Europe can almost fully be explained by the terrible demographics in Europe.

It is easy to imagine a war torn Europe without the EU. Then we would definitely be worse off.


Maybe I'm about to display my ignorance, but until 1990 wasn't Poland under the USSR's umbrella? And the US was all but occupying Germany until ... it is almost possible to make that claim up to today. There are 50k US troops in Germany and 60k in the German army. That and the Southwestern Europeans being broken like twigs after WWII.

I don't think it is the EU that is keeping the peace; I reakoon it is the Haber process + the US more than anything else. Although if it was it is failing IMO, there is a land war in Europe right now that is at risk of fighting WWIII. And everyone is arming up again because of it.


The Haber process was the single most important thing that brought us WW1 and WW2. War at an industrial scale was suddenly possible because munitions were possible to produce at and industrial scale.

The EU is what changed in Europe.

US "occupation" in Europe after WW2 was weak compared to the influence of the EU. The EU emanates all regulation in Europe. The US certainly didn't create the single market in the EU.

Also the brutal occupation of Easter Europe by the USSR is exactly an example of what the EU peace project is about solving.


If someone was going to start a fight in Europe after WWII, they had a choice of either attacking in the East and going toe-to-toe with the USSR, or the West and going toe-to-toe with the US. That calculation held for the Germans, British and French too if they wanted to start something.

The common market has probably been a net force for peace, but superpowers staking out areas where they were involved can hardly be brushed aside. After the fall of the USSR it hasn't been 30 years and we see land wars in their former sphere of influence.

Economics doesn't stop armies. We saw in WWII that insane politicians are perfectly capable of destroying everything in sight, economic consequences for their own citizens be damned.


Indeed. You're displaying your ignorance.


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