Lifelong In-Context Learning with Transformers Requires Parametric Forms of Attention

Large language models (LLMs) exhibit a strong capacity for in-context learning: Given labeled examples, they can generate good predictions without parameter updates. However, many interactive settings go beyond static prediction to online decision-making, in which effective behavior demands adaptation over long multi-turn horizons in response to feedback, and efficient algorithms in these domains must use compact representations of what they have learned. Recently, continuous transformer architectures with latent chain of thought have shown promise for offline iterative tasks such as directed graph-reachability. Motivated by this, we study whether continuous latent context tokens equip transformers to more effectively realize online learning. We give explicit constructions of constant-depth transformers that implement two foundational online decision-making procedures -- the weighted majority algorithm and $Q$-learning -- by storing their algorithmic state as linear combinations of feature embeddings, using a small number of latent context tokens. We further train a small GPT-2-style transformer with latent contexts using a multi-curriculum objective that does not directly supervise the latent states. On long synthetic online prediction sequences, this model outperforms larger and more complex LLMs, including Qwen-3-14B and DeepSeek-V3. Our results suggest that continuous latent contexts provide a simple and effective persistent state for transformers to implement online learning algorithms.

In-context learning (ICL) derives its power from enabling Large Language Models to adapt to new tasks via prompt-based reasoning alone, entirely bypassing the need for parameter updates. Existing theories primarily study ICL in single-task settings, while real-world prompts often contain sequences of heterogeneous tasks, leaving a gap in understanding whether Large Language Models implicitly perform continual learning during inference. To bridge this gap, we propose the first theoretical framework for in-context continual learning, modeling how a pretrained Transformer processes multiple sequential tasks within a single prompt through shared attention mechanisms. Focusing on linear and masked linear self-attention, we derive error expressions for model predictions under sequential task prompts and analyze their generalization and forgetting behavior. Our results reveal that standard attention mechanisms inevitably induce intertask interference by uniformly or causally aggregating historical contexts, leading to systematic bias. We further provide a bias-variance-interference decomposition of prediction error, characterizing when historical in-context information yields positive transfer or provable negative transfer. This analysis exposes fundamental limits of attention-based continual inference and offers theoretical explanations for order sensitivity and performance degradation in long prompts.

Long-running assistants and agents consume interaction streams that eventually outgrow the context. Existing context retention, summarization, and retrieval preserve access to selected history, but do not provide a persistent state over the full lifecycle when working context changes. We formulate this missing inference capability as \emph{state continuity under context turnover}: carrying computation forward through a fixed-capacity memory state whose lifetime is independent of the active context. We introduce an intrinsic memory method, \textbf{LiveMem}, which augments a pretrained full-attention LLM with a memory state that preserves the historical information over the whole lifecycle while the main attention path retains a bounded KV window. Context turnover and memory state maintaining, memory-oriented post-training, and state-aware serving jointly make this memory state load bearing after its originating tokens are released. Our experiments show that LiveMem achieves leading overall performance among evaluated systems and other intrinsic memory methods. Experiments on LongMemEval show that LiveMem is able to answer the question based on the memory state, even when the supporting evidence has been removed from the current context, and evidence-distance analysis shows that useful information persists beyond the active window. LiveMem thus establishes state continuity as a distinct and complementary abstraction for continual LLM inference.