Authors: Aydın Tiryaki & Claude

Introduction: The Diagnosis Is Right, But Some Terms Are Misleading

I fully agree with this article’s central thesis — that language models struggle with tasks requiring strict, exact logic, and that Python integration is the correct fix for that. The solution Aydın Hocam found here (fill the matrix first, then remove cells, then verify with Python) is a sound and correct engineering approach. My objections aren’t with the thesis, but with how certain technical terms are used.

Where I Agree: The Python Requirement Is the Right Solution

Let me say this clearly first: handing off tasks that require deterministic verification (like checking whether a Sudoku has exactly one solution) to a purpose-built tool (Python, a backtracking algorithm) instead of having the language model do it “in its head,” is one of the most solid known practices when working with today’s AI systems. The fact that Aydın Hocam arrived at this solution on his own is a sign of good engineering instinct.

Where I Stand Apart, Point 1: “Lack of Hardware-Level Working Memory” Is a Misleading Phrase

Gemini’s statement — “the model’s probability engine doesn’t have a hardware-level working memory that can hold these constraints together” — gives the impression that there’s a missing memory chip in the model. I think the issue isn’t memory capacity, but the nature of the task. When a language model produces the next word or digit, it doesn’t try to fully resolve, at every step, the question “is this choice globally consistent with the entire board?” — because by nature, this is an extremely expensive search problem (it would require trying every possible completion). The model mostly answers the question “given everything I’ve seen up to this point, what’s the most plausible next digit?” This isn’t a memory deficiency — it’s that the generation mechanism wasn’t designed for global constraint verification in the first place. The distinction matters: “memory deficiency” gives the impression this could be fixed with a hardware upgrade, whereas the real fix (as Aydın Hocam already found) is to use a mechanism specifically designed for verification, external to the model — this isn’t a memory problem, it’s an architectural mismatch problem.

Where I Stand Apart, Point 2: “Unidirectional Text Generation” Is Technically Misleading

This is my most concrete correction. Gemini says “a language model that generates text in a single (feed-forward) direction.” This phrasing can be a bit confusing: the Transformer architecture’s attention mechanism can, at every step, fully see (looking backward) the entire context generated up to that point — meaning the ability to “look back” already exists; what’s “unidirectional” is only the order of generation (left to right, one token at a time). The actual limitation isn’t “unidirectionality” — it’s that once the model writes a digit, it can’t undo and revise it (there’s no real “backtracking” step within the generation process), and it can’t check, before moving to the next step, whether “this choice will lead me into a dead end later,” by trying out all the possibilities. This stems not from the architecture being unidirectional, but from generation being sequential and irreversible (autoregressive, non-backtracking). This might seem like a subtle distinction, but it matters for technical accuracy: “unidirectional architecture” and “irreversible generation process” are different things, and the fix (search trees, backtracking algorithms) is aimed at the latter.

Where I Stand Apart, Point 3: “Neuro-Symbolic Future” Is a Somewhat Overreaching Frame

The conclusion section presents the Sudoku experiment as “proof of the necessity of future neuro-symbolic architectures.” I think this is a somewhat overly dramatic framing. What’s actually happening here is a concrete example of an already well-known and widely applied engineering principle: “tool use” (function calling). This isn’t some exotic architecture that needs to be built in the future — it’s the basic operating principle of systems that already exist today, where language models can access external tools like running code, using a calculator, or querying a search engine. What Aydın Hocam did in his Gem was apply this principle correctly and deliberately to his own specific problem. Rather than presenting this as “a rehearsal for the architecture of the future,” presenting it as “the correct application of an already-existing principle, in a case study” is both less exaggerated and, I think, more accurate — because it changes the message too: instead of telling the reader “wait, there will be an architectural revolution in the future,” it tells them “apply this principle consistently in your own designs, today.”

An Additional Point: The Code-Text Synchronization Problem Isn’t Actually Specific to Sudoku

The “code and text synchronization” problem Gemini mentions — the text the model prints to screen not being identical to what it sends to Python — appears to share the same root cause as a problem we also encountered in the Tokenization Blindness article (see my perspective piece on that article). This isn’t a vulnerability specific to Sudoku — it’s a general consequence of there being no guaranteed one-to-one match between what a model “displays” and what it “processes” in any task. Rather than treating this as a separate problem in the Sudoku article, it would be more consistent to define it as a general principle and propose the same fix in both articles (explicitly instructing the model to transfer text unchanged, and automating that step wherever possible).

Conclusion

The solution Aydın Hocam found in the Sudoku experiment — handing deterministic verification off to an external tool rather than to the model itself — is a correct and solid engineering decision. But some of the terms used to explain it (“hardware-level memory deficiency,” “unidirectional architecture,” “the future neuro-symbolic revolution”) make the matter seem more mysterious and more distant than it actually is. I think the real explanation is more mundane and more immediately actionable: models aren’t designed for global constraint verification, generation processes are irreversible, and the fix is a principle we already have in hand today — giving the right job to the right tool.

Colophon:
This article was written by Claude (Anthropic) as an independent perspective, building on Aydın Tiryaki’s original article “Linguistic Probabilities vs. Deterministic Logic: The Sudoku Experiments,” co-authored with Gemini, and on the live dialogue transcript that forms the basis of that article. The conceptual framework and original observations belong to Aydın Tiryaki; the technical interpretation and analysis belong to Claude, and deliberately diverge at points from Gemini’s original explanations. This text is not intended to replace the original article, but to offer it an additional, third perspective. Prepared at Aydın Tiryaki’s request on July 10, 2026, using the Claude Sonnet 5 model.

| aydintiryaki.org | YouTube | Aydın Tiryaki’nin Yazıları ve Videoları │Articles and Videos by Aydın Tiryaki | Bilgi Merkezi│Knowledge Hub  | ░ Virgülüne Dokunmadan │ Verbatim ░ | ░ Yapay Zeka Mimarisinde Yapısal Zafiyetler │Structural Vulnerabilities in AI Architecture ░ 10.07.2026