Why LLMs Continue to Generate Errors in Code - and Scaling Won't Fix It

Imagine a typical situation: you ask a model to write a data processing function for a corporate project. The code appears in seconds, looks neat, and passes local tests. But in production, hidden problems emerge: the logic slightly diverges from the requirements under edge cases, or the code ignores specific constraints of an internal library that the model has never seen in the training data.

The same happens with legacy code: the model suggests methods from a new release of a framework that is not yet supported in your environment. The code does not compile, and it has to be rewritten manually. In modern projects, the situation is mirrored: the generated code stubbornly clings to an outdated API, even though safe and efficient alternatives have long been available.

Errors are particularly noticeable in less popular languages. In Python or JavaScript, the model confidently constructs complex constructs. But when switching to Rust or Haskell, logical missteps occur: incorrect handling of borrowing, missed edge cases. Sometimes the model simply does not know about syntactic changes that came out after its training and misses new opportunities that would perfectly fit the task.

In real projects, especially with proprietary code and internal libraries, the model regularly suggests solutions that miss the mark by a little bit. All these examples share one thing: such errors are not accidental—they are systemic. The model is guided by statistical patterns from publicly available data, rather than the strict logic of your task and environment.

Benchmarks confirm the same picture. At SWE-bench Verified, where tasks are taken from real GitHub repositories, the best models in early 2026 achieve 70-80%. The numbers are increasing, but there remains a significant gap to complete reliability of the generated code.

The reason lies not in the volume of training data or the number of parameters. It runs deeper—in the very nature of modern LLMs: they approximate probabilities of continuations, rather than constructing logically consistent solutions. It is in the mathematical foundation that lies the explanation for why bugs are inevitable—not due to the "stupidity" of the model, but because of how it transforms a query into a response. One should not expect that the next versions of models will radically change the situation.

LLM model: what's under the hood

To understand where these systemic errors come from, it is worth setting aside all external enhancements. Let’s discard everything that is layered on top of the base model: chat interfaces, integrations with editors, agents with their chains of reasoning, additional checks. What remains is the bare neural network — it is the heart of any modern LLM.

At its core lies the transformer architecture proposed in 2017. But if we set aside the attention mechanism and other tricks, topologically the transformer is equivalent to a multilayer perceptron — a construction that emerged in the 1960s. The history goes deeper: the first artificial neuron, which performs a weighted sum of inputs followed by a nonlinear transformation, was described in 1943. In 1958, Frank Rosenblatt introduced the single-layer perceptron — a network with one computational layer. Later, additional layers were added, resulting in the multilayer perceptron, where the signal passes sequentially from one layer to the next, and the output of one layer becomes the input for another. The weights of the connections between neurons are the parameters of the network that adjust during training to minimize error.

An important feature of this architecture is that the signal propagates strictly in one direction — from input to output. There are no feedbacks as in biological neural networks. The network cannot "look back" at its output, cannot reflect on the intermediate result and correct it before the final answer. It lacks the ability for internal verification — it simply transforms input into output without checking the meaningfulness of the result.

The transformer introduced an attention mechanism that allows for the consideration of relationships between tokens at large distances. But at its core, it remains the same: unidirectional signal propagation through weighted sums and nonlinearities, billions of frozen weights after training.

And here arises a fundamentally important distinction that is often overlooked: training a neural network and using it are two entirely different processes. During training, the weights are dynamically adjusted: millions of examples are fed into the network, and complex algorithms compare its output with the correct answers and adjust the parameters to reduce the error. This stage requires colossal computational resources and can take weeks.

But once training is complete, the weights are fixed. When generating code, the network is no longer learning—it is simply applying the frozen parameters. A sequence of tokens is input, the signal passes in one direction through the layers, and the next token appears at the output. There is no "magic" in this: no reasoning, no consistency checking, no understanding of the task. There is only the transformation of input into output based on patterns learned from a fixed training set.

An natural question arises: if the network merely approximates the patterns it has seen, what tasks is it capable of handling, and where are errors inevitable? The answer lies in the mathematical foundation—the universal approximation theorem.

Mathematical Foundation: Universal Approximation Theorem

The structure of deep neural networks relies on a powerful mathematical result that explains why such models are capable of generating meaningful code at all. This concerns the universal approximation theorem, proven in the late 1980s and early 1990s.

The history of this theorem goes back to the depths of nineteenth-century mathematics. As early as 1885, Karl Weierstrass proved that any continuous function on an interval can be approximated by polynomials with arbitrary precision. This idea — approximating the complex with simple elements — laid the foundation for many subsequent results. A direct predecessor for neural networks was the theorem proved by George Cybenko in 1989: a multilayer network with nonlinear sigmoid activation is capable of approximating any continuous function on a compact area with arbitrary precision. A couple of years later, Kurt Hornik generalized the result — universality is provided by the multilayer architecture itself, not by the specific form of the activation function. Subsequent works relaxed the requirements for the activation function, expanding the applicability of the theorem.

In essence, a deep neural network can serve as a universal approximator. If we consider the task of predicting the next token as a function — mapping the prefix of a sequence to a probability distribution of continuations — the network can reproduce it with arbitrary accuracy. But only under the condition that: the input area must be compact, and the function must be continuous.

This is what happens during the training phase. The model sees billions of examples and adjusts the weights so that its output corresponds as closely as possible to the actual distributions in the data. In popular scenarios — typical Python constructs or using standard libraries — the code turns out almost perfect. Millions of examples from open repositories form a dense area of training data. In it, approximation achieves high accuracy.

But the theorem speaks specifically about approximation, not exact equality. Behind this lie three fundamental limitations that are often overlooked.

First, approximation never implies exact equality. Even with an infinite number of neurons, there always remains a non-zero error, however small it may be.

Second, the guarantee applies only to a compact area of inputs — that is, to data similar to those encountered in the training set. Outside this area, the behavior of the network is not mathematically controlled. In new versions of languages, rare libraries, or proprietary code, the behavior of the network becomes unpredictable.

And thirdly, the theorem is an existence theorem: it says nothing about how to train the network or how many layers and neurons are necessary to achieve a given accuracy.

These limitations manifest directly when generating code. The network does not "understand" the logic of the program and does not verify its correctness — it approximates the statistical distribution of tokens learned from the data. When you ask it to write a function in a familiar language with typical patterns, the network confidently interpolates within the dense area. But as soon as it goes beyond its limits — using a niche library, new syntax, or a proprietary framework — the approximation loses reliability. The network continues to generate plausible tokens, but their combination no longer guarantees logically correct code. It cannot guarantee this due to its very mathematical nature.

Verification remains with the human

The universal approximation theorem not only describes the capabilities of the neural network — it clearly delineates its limits. The model approximates statistics but does not verify logic. It generates tokens but does not prove the correctness of the algorithm. And this is not a shortcoming of a specific implementation — it is a consequence of the very mathematical nature of approximation.

From this follows the inevitable conclusion: the responsibility for the logical correctness of the code remains with the human. Not because the models "have not matured yet," but because their architecture does not provide a mechanism for self-checking. The model cannot answer the question "Is this code correct?" — it simply lacks the tool for such judgment. It merely continues the sequence of tokens that is most probable according to the learned patterns. Assessing correctness, however, requires going beyond statistics: understanding requirements, analyzing boundary conditions, checking for safety, taking into account the context of a specific system.

And here an important paradox arises. The better the model handles routine tasks — typical patterns, standard libraries, template code — the more difficult the tasks remain for humans. Errors move from the realm of the obvious to the realm of the non-trivial: rare combinations of conditions, non-obvious interactions of components, vulnerabilities in input processing, logical contradictions in distributed systems. It is these areas that require a deep understanding of the subject matter, design experience, and the ability to see what does not fit into statistical patterns.

This is not a threat to the profession of a developer — on the contrary, it shifts its focus. Routine is automated, but the responsibility for complexity increases. The future of programming lies not in writing every line, but in managing complexity: designing architecture, verifying critical parts, making decisions under uncertainty. A human is not replaced by a model — they become its verifier, architect, and judge of correctness.

That is why a human will not disappear with the growth of parameters or improvement of training data. Their necessity is embedded not in the current state of technology, but in the very mathematical nature of modern LLMs. As long as the architecture remains a statistical approximation without logical understanding, as long as the weights freeze after training, the responsibility for ensuring that the code does exactly what is intended remains human.