Understanding the Limitations of Mathematical Reasoning in Large Language Models
The paper "GSM-Symbolic" examines the limitations of Large Language Models in mathematical reasoning, introducing a new benchmark and revealing performance variability and struggles with logical reasoning in LLMs.
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The paper titled "GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models" explores the mathematical reasoning capabilities of Large Language Models (LLMs) using the GSM8K benchmark. Despite improvements in LLM performance on this benchmark, the authors question the reliability of these metrics, suggesting that LLMs may not have genuinely advanced in mathematical reasoning. To address this, they introduce GSM-Symbolic, a new benchmark that generates diverse questions from symbolic templates, allowing for more controlled evaluations. The study reveals significant performance variability in LLMs when faced with different instantiations of the same question, particularly when numerical values are altered. The research indicates that LLMs struggle with logical reasoning, as their performance declines sharply (up to 65%) with the addition of irrelevant clauses in questions. This suggests that LLMs replicate reasoning steps from training data rather than performing true logical reasoning. Overall, the findings provide a deeper understanding of the limitations of LLMs in mathematical reasoning tasks.
- The GSM8K benchmark is commonly used to evaluate LLMs' mathematical reasoning.
- The new GSM-Symbolic benchmark offers improved evaluation metrics for LLMs.
- LLMs show significant performance drops when numerical values in questions are changed.
- The addition of irrelevant clauses can drastically reduce LLM performance.
- The study highlights the difference between replicating reasoning steps and genuine logical reasoning in LLMs.
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LLMs still can't reason like humans
Recent discussions reveal that large language models (LLMs) struggle with basic reasoning tasks, scoring significantly lower than humans. A project called "Simple Bench" aims to quantify these shortcomings in LLM performance.
- Many commenters draw parallels between LLM performance and human reasoning, suggesting that both exhibit similar limitations, especially when faced with complex or irrelevant information.
- There is a consensus that LLMs struggle with logical reasoning and mathematical tasks, particularly when the questions are altered or contain extraneous details.
- Some argue that the current benchmarks for LLMs may not accurately reflect their reasoning capabilities, indicating potential overfitting and a need for better evaluation methods.
- Several comments emphasize the importance of developing systems that integrate LLMs with other reasoning tools to enhance their performance.
- There is a call for more research and investment in improving mathematical reasoning capabilities in LLMs rather than focusing solely on advanced AI concepts like AGI.
32 commentsSo while I don't take a stance on what an LLM does should be considered reasoning, I do think that SOTA LLMs like GPT-4o perform about as good as high school graduates in America with average intelligence. In other words, average Americans exhibit similar limitations on their reasoning as good LLMs. Which on the one hand is a little disappointing to me in terms of the human performance but is kind of good news for LLMs- they aren't doing graduate-level research but they are already capable of helping a large portion of the population.
I don't find this very impressive. Forget LLMs for a second. Let's say _you_ read a question of that kind with some bit of irrelevant information. There are two possibilities you have to consider: the question may as well have excluded the irrelevant information, or the question was miswritten and the irrelevant information was meant to be relevant. The latter is a perfectly live possibility, and I don't think it's a dramatic failure to assume that this is correct. I have to confess that when I read some people's LLM gotcha questions, where they take some popular logic puzzle and invert things, I think I would get them "wrong" too. And not wrong because I don't understand the question, but wrong because with no context I'd just assume the inversion was a typo.
You could argue that the issue lies in the models being in an intermediate state between pattern matching and reasoning.
To me, such results indicate that you can't trust any LLM benchmark results related to math and reasoning when you see, that changing the characters, numbers or the sentence structure in a problem alter the outcome by more than 20 percentage points.
I'd offer a simpler explanation: Tokenization.
If you tokenize "12345 * 27271" you will get the following:
"123", "45", " *", " ", "272", "71"
You can argue that this is where tool use comes in (and I would be inclined to agree), but I don't think this bodes well for "genuine logical reasoning".
Eventually they will run out of exponential cash to pour in, and investors will start asking questions, stocks are already valued at 60x+ their earnings, whenever it pops you don't want to be the one who bought the top.
Guess it's still gonna take a while more for the layman to realize the issues with LLMs, but it'll happen.
> Specifically, the performance of all models declines when only the numerical values in the question are altered in the GSM-Symbolic benchmark.
This seems like irrefutable evidence of overfitting, that in the best case scenario is epidemic among current LLMs (and in the worst case interpretation, is covering up fundamental inabilities to learn mathematical reasoning from the training data).
(And yes, I know people are hard at work adding other types of thinking to work along with the pure language models)
For example, just as a dog will never understand a fourier transform, there are likely ideas that humans cannot understand. If we know what our limits are, I wonder if we could build machines that can reason in ways we aren't capable of?
LLMs don't do formal reasoning - https://news.ycombinator.com/item?id=41812523 - Oct 2024 (70 comments)
Brains have various structures that have distinct architectures. I don’t see any indication that the best way forward is to try to shoehorn everything into a single computational paradigm.
It’s like trying to make a flying submarine car. It might technically be possible, but it might not be worth the trouble, and it’s unlikely to result in a vehicle that works excellently in any of its environments.
Maybe the benchmark Qs/As snuck into training sets accidentally. Is it still Goodhart's Law if it's unintentional?
Daniel Lemire has blogged about being impressed with how well the LLM answers his CS problem questions. I was impressed too. Not sure where the line of competence lies.
An LLM is very good at recovering rules, but being good at pattern recognition is not the same thing as being good at unambiguously following rules in the appropriate context.
edit: Natural language is far from an efficient/sufficient/necessary intermediate representation for doing math, just ask any general-purpose computer. Sometimes, it's worth "putting rules in stone," and it seems unreasonable to believe that there is always an unambiguous rule for this that you can mechanically recover from a corpus of language use.
Having said that, we can still get semantically and logically idempotent output that makes sense but with lots of work outside of the LLM, which contrasts with the current hyper focus on the LLM itself as the be all and end all. It is just one component in what ought to be a larger and more involved system for reasoning.
Look at what we were able to accomplish here for Legal AI, not so mathematical logic per se but mimicking (capturing) axiomatic logic in the legal domain:
https://www.youtube.com/watch?v=_9Galw9-Z3Q
marc at sunami dot ai
until that happens .. I think RL startups focused on real problems are much undervalued : https://quantblog.wordpress.com/2024/10/11/llm-hype-means-th...
EDIT: Had there been an ounce of actual true reasoning emerging in LLMs, openai would have been running this thing privatly 24/7 to produce new science and capture pattents that would give them economic dominance. Not trying to sell tokens to us all.
Consider that in a LLM, language inputs are tokenized and fed as inputs into the neural network, and connections in the network create output sequences that are not just syntactically correct (trivial) or form semantically plausible sentences (early transformers did this). LLM output sequences follow the deep patterns of language which include sometjhing that resembles reasoning as the model has learnt from its training data.
LLMs seem to fall short because they often fail at truly abstract reasoning tasks that humans find easy. If trained properly, LLMs can develop advanced representations of logical systems that will surely outpace what humans can do in terms of raw reasoning.
However, human mathematicians have not even unified around constructive mathematics as a must for the study of mathematics. This reveals that even highly evolved mathematical disciplines rely on objects whose characteristics do not lend themselves to full logical scrutiny and are in a way socially constructed and effectively hard to audit.
While notation in mathematics is incredible technology it is also a highly limiting factor that suffers major tradeoffs. Humans struggle to invent new notation fast enough and to discard outdated notation fast enough. If we do see an AI-powered boom in mathematics, I suspect our notion of notation and the fluidity we demand from it will change dramatically.
Whatever happened with that result which found some representation of the state of a game inside an LLM? That indicated some degree of model-building. Haven't heard about that again/
tl;dr - the best open model dropped from 89.7% on GSM8K(full) to 30% on Symbolic-NoOp, while o1-preview dropped from 94.9% to 77.4%, respectively.
I think all this paper shows is that LLMs need space to "think" outside of their inference layer, (for the current architectures at least).
It's similar to the "draw a room, but DO NOT put an elephant in the corner" prompts that people were using with image models.
This is something that practitioners have been doing for awhile (via CoT, ToT, etc.) and the whole rationale behind OpenAI's newly launched o1-series "model."
There's another post that says this paper proves LLMs can't be used to build "reliable agents" -- which doesn't appear to be true when you look at o1's stellar performance here.
They have none. Literally zero. That’s the limit. Thank you for reading my paper.
Related
Reasoning in Large Language Models: A Geometric Perspective
The paper delves into how large language models reason geometrically, linking self-attention graph density to expressive power. Higher intrinsic dimensions enhance LLMs' capacity, supported by theoretical, toy examples, and empirical evidence.
Does Reasoning Emerge? Probabilities of Causation in Large Language Models
The paper investigates the reasoning capabilities of large language models, focusing on probability of necessity and sufficiency, and proposes a framework to evaluate their reasoning through mathematical examples.
Can Large Language Models Understand Symbolic Graphics Programs?
The study evaluates large language models' understanding of symbolic graphics programs, introducing a benchmark and Symbolic Instruction Tuning to enhance reasoning and instruction-following capabilities in visual content comprehension.
Inductive or Deductive? Rethinking the Fundamental Reasoning Abilities of LLMs
The paper examines reasoning abilities of Large Language Models, distinguishing inductive from deductive reasoning. It introduces SolverLearner, showing LLMs excel in inductive reasoning but struggle with deductive tasks, particularly counterfactuals.
LLMs still can't reason like humans
Recent discussions reveal that large language models (LLMs) struggle with basic reasoning tasks, scoring significantly lower than humans. A project called "Simple Bench" aims to quantify these shortcomings in LLM performance.