The Impossibility Triangle of Long-Context Modeling

Long-context recall in linear-time sequence models highlights a tradeoff in how they write to memory. State-based linear models, such as state-space models (SSMs) and linear Transformers, write densely, updating the entire state for each newly arrived token, which leads to interference and makes specific past tokens hard to recover. Sliding-window attention (SWA) exhibits the opposite behavior: it writes sparsely by storing explicit token representations, but only within a fixed window, so recall drops once the relevant token is evicted. Interpolating between these models, we introduce Raven, a linear-time sequence model that maintains a fixed set of memory slots and, at each step, decays and updates only a selected subset via learned, input-dependent routing. This lets Raven mitigate SWA's position-based overwriting and hard eviction while reducing interference from dense state updates in SSMs, thereby preserving long-range content much more effectively. Across recall-intensive benchmarks, Raven is competitive with or outperforms prior linear-time baselines, achieving strong long-context recall where both SWA and SSMs sharply degrade. It remains effective when extrapolating to context lengths as large as 16x its training length, with similar gains in hybrid architectures.

Modern sequence modeling is dominated by two families: Transformers, whose self-attention can access arbitrary elements of the visible sequence, and structured state-space models, which propagate information through an explicit recurrent state. These mechanisms face different limitations on long contexts: when attention is diffuse, the influence of individual tokens is diluted across the effective support, while recurrent state propagation can lose long-range sensitivity unless information is actively preserved. As a result, both mechanisms face challenges in preserving and selectively retrieving information over long contexts. We propose Sessa, a decoder that places attention inside a recurrent feedback path. This creates many attention-based paths through which past tokens can influence future states, rather than relying on a single attention read or a single recurrent chain. We prove that, under explicit assumptions and matched regimes, Sessa admits power-law memory tails $O(\ell^{-β})$ for $0 < β< 1$, with slower decay than in the corresponding Transformer and Mamba-style baselines. We further give an explicit construction that achieves this power-law rate. Under the same assumptions, Sessa is the only model class among those considered that realizes flexible selective retrieval, including profiles whose influence does not decay with distance. Consistent with this theoretical advantage, across matched experiments, Sessa achieves the strongest performance on long-context benchmarks while remaining competitive with Transformer and Mamba-style baselines on short-context language modeling.

Transformers owe much of their strong long-context retrieval capability to a token-level memory that grows with context length. This flexibility, however, incurs a quadratic computation complexity during training and a key--value cache that grows linearly during autoregressive inference. Recurrent alternatives offer efficient decoding by compressing the entire history into a fixed-size state, but often underperform on recall-intensive tasks since earlier associations usually get overwritten by subsequent updates, and only the most recent contextual information is retained. In this paper, we introduce Memory-Anchor Routing across Context History (MARCH), a network architecture that effectively scales state-space models beyond a fixed-size dimension, while maintaining computational efficiency over long-sequences. MARCH periodically caches cumulative recurrent-state checkpoints as state anchors and associates each anchor with a compact, content-conditioned anchor key. This lets MARCH maintain a memory bank, which can grow as context length increases, providing a controllable trade-off between historical resolution and memory cost. At each token, MARCH produces an anchor query to attend all causally available state anchors, and the output is calculated as an attention-style aggregation over all historical anchors along the current state. We show that after standard pretraining, MARCH consistently outperforms multiple linear attention variants across commonsense reasoning, LongBench, and in-context retrieval. These results demonstrate that content-routed state caching substantially strengthens recurrent long-range memory while preserving its native computation path.