Three specific goals for AI memory are mathematically incompatible, proving that a perfect long-context model can never exist.
No sequence model can simultaneously achieve constant-time computation, constant-size memory, and the ability to recall every fact it has seen. This mathematical speed limit proves that there is always a trade-off between how much an AI can remember and how fast it can work. We have been chasing infinite-memory models, but this research shows that such a goal is theoretically impossible. Every future AI architecture will have to pick two of these traits and sacrifice the third. This discovery defines the boundaries of what is possible for the next generation of large language models.
The Impossibility Triangle of Long-Context Modeling
arXiv · 2605.05066
We identify and prove a fundamental trade-off governing long-sequence models: no model can simultaneously achieve (i) per-step computation independent of sequence length (Efficiency), (ii) state size independent of sequence length (Compactness), and (iii) the ability to recall a number of historical facts proportional to sequence length (Recall). We formalize this trade-off within an Online Sequence Processor abstraction that unifies Transformers, state space models, linear recurrent networks, a