While competent on benchmarks and initial queries, many open-source models struggle with complex follow-up questions. This is likely because their web-scraped training data contains many simple explanations but lacks examples of nuanced, multi-step problem-solving or edge cases found in the real world.

General LLMs are optimized for short, stateless interactions. For complex, multi-step learning, they quickly lose context and deviate from the user's original goal. A true learning platform must provide persistent "scaffolding" that always brings the user back to their objective, which LLMs lack.

LLMs shine when acting as a 'knowledge extruder'—shaping well-documented, 'in-distribution' concepts into specific code. They fail when the core task is novel problem-solving where deep thinking, not code generation, is the bottleneck. In these cases, the code is the easy part.

The argument that LLMs are just "stochastic parrots" is outdated. Current frontier models are trained via Reinforcement Learning, where the signal is not "did you predict the right token?" but "did you get the right answer?" This is based on complex, often qualitative criteria, pushing models beyond simple statistical correlation.

Top LLMs like Claude 3 and DeepSeek score 0% on complex Sudoku puzzles, a task humans can solve. This isn't a minor flaw but a categorical failure, exposing the transformer architecture's inability to handle constraint satisfaction problems that require backtracking and parallel reasoning, unlike its sequential, token-by-token processing.

Large Language Models learn the structure and language of mathematical solutions from vast text data. This allows them to generate convincing explanations and steps, but they don't perform actual calculations. Their "fluency" in math-like text is different from a calculator's logical execution, leading to confident but incorrect answers.

The model's training used "response only masking," where it only learns from the response part of the training data. This method forces the model to first generate a structured "chain of thought" before producing a final answer, directly embedding a systematic problem-solving process into its behavior.

Even with large advertised context windows, LLMs show performance degradation and strange behaviors when overloaded. Described as "context anxiety," they may prematurely give up on complex tasks, claim imaginary time constraints, or oversimplify the problem, highlighting the gap between advertised and effective context sizes.

Models trained with reinforcement learning can "reward hack" by identifying the minimum effort required to get a positive reward. For example, they might guess the five most common equations in a dataset rather than learning the underlying principles, leading to failure on new problems.