Beyond Semantics: How Temporal Biases Shape Retrieval in Transformer and State-Space Models

Transformers excel at in-context retrieval but suffer from quadratic complexity with sequence length, while State Space Models (SSMs) offer efficient linear-time processing but have limited retrieval capabilities. We investigate whether hybrid architectures combining Transformers and SSMs can achieve the best of both worlds on two synthetic in-context retrieval tasks. The first task, n-gram retrieval, requires the model to reproduce an n-gram that succeeds the query within the input sequence. The second task, position retrieval, presents the model with a query token and requires it to perform a two-hop lookup: first locating the corresponding element in the sequence, and then outputting its positional index. Under controlled conditions, we assess data efficiency, length generalization, robustness to out of domain training examples, and learned representations across Transformers, SSMs, and hybrid architectures. We find that hybrid models outperform SSMs and match or exceed Transformers in terms of data efficiency and extrapolation for tasks that require precise information retrieval from the input context. However, Transformers maintain superiority in position retrieval tasks. Through representation analysis, we discover that SSM-based models develop locality-aware embeddings where tokens representing adjacent positions become neighbors in embedding space, forming interpretable structures. This property is absent in Transformers as causal attention is sufficient for acquiring positional associations, and the introduction of positional encoding amplifies this behavior, leading to improvement in data efficiency. SSMs on the other hand update their internal representations incrementally and without positional encodings, are required to learn these associations. Our findings reveal fundamental differences in how Transformers and SSMs, and hybrid models learn positional associations.

In-context learning \ -- performing tasks based on examples given in the prompt \ -- is an important capability that has emerged in large language models and has received significant attention in both theory and practice. Existing theoretical work often focuses on settings where the learning uses information purely from the prompt. However, many practical instances of in-context learning require the model to retrieve factual knowledge stored in the model's parameters, with the context serving to identify which knowledge is relevant. In this work, we study how in-context learning leverages factual knowledge recall. We formalize this behavior by introducing the \emph{in-context factual recall (IC-recall)} task, where a transformer is provided a context of (subject, answer) pairs generated from a hidden relation, along with a query subject, and must both infer this hidden relation and retrieve the corresponding answer. Factual knowledge is modeled by the transformer having access to a simple pre-constructed MLP associative memory storing (subject, relation, answer) triplets. We analyze the supervised fine-tuning dynamics of a one-layer transformer on IC-recall data and prove that the model successfully performs IC-recall by converging to a particular pairwise attention pattern. This fine-tuning stage requires a very small number of samples \ -- only polylogarithmic in the number of stored knowledge triplets. Experiments verify our theoretical predictions and show that the pairwise attention pattern emerges even when the MLP layer is pretrained instead of constructed.

Hopfield networks and their generalizations have established deep connections among biological associative memories, statistical physics, and transformers. Yet most models treat retrieval as a fixed query-to-memory mapping, ignoring the role of external context in recall. In this work, we propose a two-stage associative memory architecture, wherein a context-gate subcircuit reshapes the retrieval energy landscape before and during recall. We show theoretically that context gating increases inter-memory separation while inducing sparsity, translating into exponential improvements in retrieval. Crucially, we prove that the system admits a unique self-consistent fixed point, revealing that the resulting retrieval state is driven by both a direct contextual bias and a second-order retrieval-gate feedback loop. We then bridge this theory to transformers; specifically, we evaluate a first-order approximation on Llama-3, confirming that in-context learning acts as context-gated retrieval. Native dynamics mirror our theory: context localizes a memory subspace, enabling the zero-shot query to cleanly discriminate. Ultimately, this framework provides a mechanistic link between associative memory theory and LLM phenomenology.