Neural Networks Hide a Symbolic Structure, New Study Shows
The Emergent Symbolic Structure of Artificial Neural Networks
A new paper proposes that neural networks, despite their vector-based nature, may implicitly encode symbolic structures. The authors show that the internal representations of various networks, including large language models, can be closely approximated by closed-form equations that instantiate symbolic structures, without significantly changing behavior. This holds for tasks like arithmetic, logic, code, and language. Moreover, precise interventions on these symbolic structures allow targeted modifications of an LLM's behavior, suggesting a path to reconcile symbolic AI with modern deep learning.
Despite appearances, perhaps the internal representations of neural networks implicitly realize symbolic structure.
- sigpwned
The big questions I’m taking away are:
(1) they are claiming to produce apparently bijective closed-form symbolic representations/approximations of, among other things, LLMs. Is evaluating these closed-form representations more computationally efficient? The implications of that are potentially huge. It would be essentially analytic distillation. Fable on a chip and not a data center would be important — and disruptive - in many ways.
(2) Unsupervised, and even supervised, symbolic approaches to problem solving break down due to combinatorial explosion, among other things. This could potentially allow us to treat LLM training and inference as a search algorithm for novel symbolic approaches to solving new classes of complex problems hitherto unreachable through other approaches. If that works, I suspect it’s a feedback loop, too - the learnings from one representation push advances in the other. This would also increase the economic value of large training runs, since the model itself is now valuable, not just its inference.
(3) Per the above, can this push LLM design to greater capabilities?
The relationship between this and Anthropic’s J-space observation is also interesting. This is much, much deeper and more directly actionable, though.
EDIT: I ran my questions through Sonnet — yes, I appreciate the irony — and it was none too sanguine about questions (1) and (2), but thought (3) was reasonable. In any case, this is quite the paper. On reflection, I do think that the appa […]
- jsrozner
A big problem with some of these supervised* interpretability approaches is that they can find spurious structure. (There are lots of ways to make the model do what you want; which is roughly what Hewitt and Liang 2019 showed). This paper draws a contrast to a previous method, DAS (distributed alignment search) on page 20. These and related methods rest on theories of causal abstraction, which are great in theory, but harder in practice. DAS, for example, has faced numerous recent criticisms (Makelov 2024, Meloux 2025, Sutter 2025, Grant 2026, Kumon 2026). My favorite is the quite approachable Meloux et al.; Sutter 2025 is also really good, but relies on a sort of real number argument that allows a lossless encoding of every input.
My forthcoming paper at EMNLP offers an alternative that instead grounds the notion of representation in a very simple notion of the effect it has on model learning/behavior when you adversarially perturb it. For example, if I tell a model that in the context "I saw a duck quacking" it should replace 'duck' with 'glam', how much does it desire to replace 'duck' with 'glam' in "I need to duck out of the meeting" vs. "At the park a duck protected her ducklings." This method turns out to work quite well, and as we use only a single example, avoids the need for supervision.
The linked paper argues that their method, DISCOVER, is not supervised in the same way as DAS, since it does not directly optimize for causal effect. I have only skimmed this, but I […]
- gps372
As I am going through the article, I was wondering why is this more interesting than having the ability to recover java programs from byte code. So I asked copilot the same question. It told me that - "Honestly this is where the difference between an engineer and researcher shows up!" .
- jkingsman
The math and core experimentation here is beyond my abilities, but what I think I understand is that there are possible deeper patterns of representation that exist in LLMs that are distillations of core conceptual relations in grammar that we can get our heads around in a mathematical sense rather than apparent layer-smeared noise that somehow, un-interpretably (in a meaningful sense), resolve to correct grammar/inferences.
That's pretty cool. I hope I've got that kinda-right.
- 4b11b4
Sounds reasonable... That the model is sometimes learning a lossy vector representation of something symbolic in nature... Sure, a NN can approximate a function?
They say this holds in... Some examples they found?
I don't enough about this area