Working Memory in Language Models

Large language models (LLMs) reproduce a human working-memory signature on the N-back task: performance declines as memory load N increases, and errors concentrate on lures, items that repeat the current stimulus at a neighboring but incorrect serial position. We ask whether this shared behavioral signature reflects a shared mechanism. The literature offers two candidate accounts. On a precision account, softmax attention cannot concentrate its weight on the item N positions back, so adjacent items are retrieved instead. On an interference account, attention selects the correct item, but the content of competing items corrupts the decision. We dissociate these accounts in 15 pretrained LLMs from three families (70 million to 14 billion parameters) and in minimal transformers trained from scratch. In all three families, the attention heads that carry the task attend to the target on most missed matches. Linear probes decode near-perfectly whether a matching letter occurred at the target or at a lure position, even on trials where the model false-alarms to the lure, although its own decisions barely distinguish the two. Sharpening attention yields negligible gains, whereas suppressing the letter identity of non-target items improves sensitivity (d') in nearly all model-by-load conditions. In larger models the task is spread over more heads, and removing interference helps more. In minimal transformers, precision limits a single attention layer, but a second layer removes this constraint. The working-memory limit of LLMs therefore lies in reading items out under interference rather than in locating them, consistent with interference accounts of human working memory.

How many assignments can a language model recall before it loses track of which value belongs to which entity? We measure this limit using continuous recall curves for 12 models at or below 3B parameters and a threshold sweep over 30 open models up to 12B. On the continuous curves, the load at which recall falls halfway to chance follows $K_{50}=cN^α$, with $α=0.820$ and $R^2=0.73$. The broader sweep shows an eightfold range associated with pretraining recipe, although the continuous curves show no detectable recipe effect after controlling for scale, with few modern models in the fit. We derive why interference can lower measured capacity by reducing single-binding recall even when the load-dependent recall profile is unchanged. Direct task training also exceeds the extrapolated zero-shot law, but different measurement criteria prevent interpreting that comparison as a capacity gain. Its formation times follow a power-law form in two independent codebases, conditional on runs that succeed. Together, these results characterize capacity at the model's query interface. Bounds on joint recall and a decomposition of policy errors connect this measurement to working memory and instruction following, without treating recall as a measure of alignment. The controlled task also provides a baseline for testing whether binding limits constrain world-state tracking; the present experiments do not measure state updates or downstream transfer.

A language model with a bounded working memory must repeatedly decide which stored items to keep. Every deployed method decides the moment an item arrives, from the past (StreamingLLM, H2O) or from a guess about the future (SnapKV). We recast the choice as an estimation problem on a hidden signal, whether an item will be reused, placing existing methods on one axis, the commit lag $H$: online filters and learned predictors commit at $H=0$, while Belady's offline optimum sits where the whole future is known. The missing regime in between, fixed-lag smoothing, waits a bounded number of steps, observes which items a correct near-future prediction attended to, and only then commits. This measurement, demonstrated utility, turns Belady's unobservable future request into something we read off the model itself. We instantiate it as a training-free policy, RMM, a strict generalization of H2O that reduces to it exactly when the measurement is uniform. In controlled settings where reuse is endogenous and separated in time, demonstrated utility identifies used memory far better than accumulated attention, and a small bounded memory behaves like a much larger one. But on independent third-party benchmarks, run inside NVIDIA's KVPress harness against its own SnapKV, H2O, and StreamingLLM implementations, the advantage mostly disappears: RMM is on par with H2O for single-turn question answering and loses to both H2O and SnapKV in a streaming multi-turn setting. The cause is simple: on natural text the model is correct about most tokens, so weighting attention by correctness barely changes it, and demonstrated utility collapses onto accumulated attention unless reuse is sharp and endogenous, which standard benchmarks do not exercise. Our contribution is the framework and an honest map of when measuring beats accumulating, not a new state of the art.

Language agents that interleave reasoning and tool use degrade sharply as reasoning chains lengthen, even when each individual step is easy. We trace this to context dilution: an agent's investigative state (what it has confirmed, what it suspects, and what it still needs) lives only implicitly in a growing context window, where early discoveries are buried under later retrievals. We introduce SLEUTH, which makes this state explicit and actionable through a structured epistemic working memory: the agent maintains Confirmed Facts grounded to sources, Active Hypotheses ranked by evidence, and Open Questions that directly drive its next action. Across five multi-hop benchmarks and five established baselines, SLEUTH's advantage grows with difficulty, from +5 points on HotpotQA to +11 on 4-hop chains, surpassing Reflexion without multiple episodes. Analyzing where the remaining gap lies, we identify the evidence sufficiency problem: agents often find the answer but fail to commit, exhausting their budget on needless verification. A lightweight commitment trigger fixes this, but only when the agent already maintains structured state: the identical trigger applied to an unstructured agent yields no improvement, isolating organized epistemic state as the necessary condition for effective commitment. Finally, enforcing protocol adherence on a weaker model recovers up to +19 points on the hardest problems, showing that how an agent organizes its reasoning, not raw model capability, is the active ingredient for scaling multi-hop reasoning.

Language agents run a loop - observe, reason, act - but the memory they reason over sits outside it: a store queried at most once per turn. We study the regime where memory moves inside the loop, read and written on every step. The obstacle has always been latency: networked stores answer in tens to hundreds of milliseconds, and in-loop retrieval can inflate end-to-end latency by up to 83x when retrieval is expensive. Prior work manages that cost rather than questioning it: serving-layer scheduling hides it, "memory-first" designs ration retrieval to once per turn. We argue latency is a property of where the store lives, not the in-loop pattern: an in-process store answers in ~100us, three orders of magnitude below the network regime, and at that speed the per-step tax collapses. By the extended-mind thesis's parity principle, a store fast enough to be constantly and directly available becomes extended working memory, not a tool the agent merely consults. The premise is causal: holding a fixed per-turn memory-latency budget and varying only the store's answer speed, redundant actions rise monotonically with latency - 0.0 of 12 at in-process speed, 7.2 of 12 at a 110ms cloud round trip (gpt-5-nano, gpt-5-mini; exact permutation p=0.0079). We demonstrate the regime end-to-end: across four GPT-5-class models under a bounded window, recall improves from 0/5 to 3.6-4.8/5 with in-loop memory, store ops at p50 80-165us - though an instructed restate-every-reply baseline also solves it perfectly, at a token cost that grows with the working set. The store never lost a fact in any run (244 of 244 writes kept); every miss traces to the agent's read policy, not the store. Our measurements also relocate the bottleneck: the dominant per-step cost is embedding (~200-400ms over the network); pairing the in-process store with a small local embedder returns the complete operation to a measured ~40us.

To improve the reasoning capabilities of large language models, test-time compute is typically scaled by generating intermediate tokens before the final answer. However, this couples reasoning to autoregressive generation and thereby conflates internal computation with external communication. In contrast, human cognition can use working memory to hold and manipulate information internally without the need to externalize intermediate thoughts. Drawing on this principle, we introduce Reasoning in Memory (RiM), a latent reasoning method that replaces the autoregressive generation of reasoning steps with memory blocks. These memory blocks are fixed sequences of special tokens that unlock the working-memory capacity of large language models. Since they are fixed rather than generated, they can be processed in a single forward pass, enabling compute-efficient latent reasoning. To operationalize these memory blocks, we employ a two-stage curriculum. First, we ground them by predicting explicit reasoning steps after each memory block. Second, we discard this step-level supervision and iteratively refine the final answer after each memory block. Our experiments on reasoning benchmarks show that, across language models of different families and sizes, RiM matches or exceeds existing latent reasoning methods while avoiding the autoregressive generation of thoughts. These results demonstrate that large language models can be trained to use working memory as an effective mechanism for latent reasoning.

Language models (LMs) behave more like humans when their cognitive resources are restricted, particularly in predicting sentence processing costs such as reading times. However, it remains unclear whether such constraints similarly affect sentence comprehension strategies. Besides, existing methods do not directly target the balance between memory storage and sentence processing, which is central to human working memory. To address this issue, we propose a dual-task paradigm that combines an arithmetic computation task with a sentence comprehension task, such as "The 2 cocktail + blended 3 =..." Our experiments show that under dual-task conditions, GPT-4o, o3-mini, and o4-mini shift toward plausibility-based comprehension, mirroring humans' rational inference. Specifically, these models show a greater accuracy gap between plausible sentences (e.g., "The cocktail was blended by the bartender") and implausible sentences (e.g., "The bartender was blended by the cocktail") in the dual-task condition compared to the single-task conditions. These findings suggest that constraints on the balance between memory and processing resources promote rational inference in LMs. More broadly, they support the view that human-like sentence comprehension fundamentally arises from the allocation of limited cognitive resources.

We investigate the integration of human-like working memory constraints into the Transformer architecture and implement several cognitively inspired attention variants, including fixed-width windows based and temporal decay based attention mechanisms. Our modified GPT-2 models are trained from scratch on developmentally plausible datasets (10M and 100M words). Performance is evaluated on grammatical judgment tasks (BLiMP) and alignment with human reading time data. Our results indicate that these cognitively-inspired constraints, particularly fixed-width attention, can significantly improve grammatical accuracy especially when training data is scarce. These constrained models also tend to show a stronger alignment with human processing metrics. The findings suggest that such constraints may serve as a beneficial inductive bias, guiding models towards more robust linguistic representations, especially in data-limited settings.

Algebraic reasoning remains one of the most informative stress tests for large language models, yet current benchmarks provide no mechanism for attributing failure to a specific cause. When a model fails an algebraic problem, a single accuracy score cannot reveal whether the expression was too deeply nested, the operator too uncommon, the intermediate state count too high, or the dependency chain too long. Prior work has studied individual failure modes in isolation, but no framework has varied each complexity factor independently under strict experimental control. No prior system has offered automatic generation and verification of problems of increasing complexity to track model progress over time. We introduce a nine-dimension algebraic complexity framework in which each factor is varied independently while all others are held fixed, with problem generation and verification handled by a parametric pipeline requiring no human annotation. Each dimension is grounded in a documented LLM failure mode and captures a structurally distinct aspect of algebraic difficulty, including expression nesting depth, simultaneous intermediate result count, sub-expression complexity, operator hardness, and dependent reasoning chain length. We evaluated seven instruction-tuned models spanning 8B to 235B parameters across all nine dimensions and find that working memory is the dominant scale-invariant bottleneck. Every model collapses between 20 and 30 parallel branches regardless of parameter count, pointing to a hard architectural constraint rather than a solvable capacity limitation. Our analysis further identifies a minimal yet diagnostically sufficient subset of five dimensions that together span the full space of documented algebraic failure modes, providing a complete complexity profile of a model's algebraic reasoning capacity.

Intelligent systems must maintain and manipulate task-relevant information online to adapt to dynamic environments. This capacity, known as working memory, is fundamental to human reasoning. Yet, human working memory is strikingly limited, maintaining only three to four items in a brain with billions of neurons. Surprisingly, large language models (LLMs), despite different substrates and direct access to prior context through attention, exhibit similar working memory limitations. Why should such different systems face analogous constraints? We propose that working memory limitations reflect a general trade-off of shared representations: representational compression and reuse support efficient learning and generalization, but also cause simultaneously active representations to interfere. We show a two-layer transformer trained on a working memory task can solve it perfectly, but diverse trained LLMs exhibit human-like limitations: performance declines with memory load, while retrieval is biased by recency and stimulus statistics. Mirroring humans, working memory performance in LLMs is also associated with broader model capability. Mechanistically, we show that LLMs encode multiple memories in entangled representations --- a condition we call in-context superposition --- and progressively suppress competing content while aligning the target with the readout. Moreover, a causal intervention that suppresses interfering information improves performance. Together, these findings suggest that working memory capacity reflects the ability to select task-relevant information under interference, a computational challenge shared by biological and artificial systems.

Existing large language models (LLMs) evaluations use fixed-difficulty benchmarks that cannot adapt as models improve, and rarely isolate specific cognitive processes. We introduce Working Memory Fidelity-Active Manipulation (WMF-AM), a probe of cumulative state tracking, the ability to maintain and update intermediate results across K sequential operations within a single query, without a scratchpad. Unlike multi-step agent benchmarks that stress task orchestration, WMF-AM isolates within-pass cumulative load by parameterizing depth K. The core probe uses arithmetic accumulation on 28 models from 12 families (0.5B to frontier); a matched non-arithmetic extension (permissions, schedules, inventories) confirms the design generalizes beyond arithmetic. Three construct-isolation ablations confirm that cumulative load, not arithmetic skill or entity tracking, drives difficulty. We release WMF-AM as a lightweight, recalibratable diagnostic for characterizing where models degrade under cumulative load. Code and data can be accessed at https://github.com/dengzhe-hou/WMF-AM

The ability to represent oneself and others as agents with knowledge, intentions, and belief states that guide their behavior - Theory of Mind - is a human universal that enables us to navigate - and manipulate - the social world. It is supported by our ability to form mental models of ourselves and others. Its ubiquity in human affairs entails that LLMs have seen innumerable examples of it in their training data and therefore may have learned to mimic it, but whether they have actually learned causal models that they can deploy in arbitrary settings is unclear. We therefore develop a novel experimental paradigm that requires that subjects form representations of the mental states of themselves and others and act on them strategically rather than merely describe them. We test a wide range of leading open and closed source LLMs released since 2024, as well as human subjects, on this paradigm. We find that 1) LLMs released before mid-2025 fail at all of our tasks, 2) more recent LLMs achieve human-level performance on modeling the cognitive states of others, and 3) even frontier LLMs fail at our self-modeling task - unless afforded a scratchpad in the form of a reasoning trace. We further demonstrate cognitive load effects on other-modeling tasks, offering suggestive evidence that LLMs are using something akin to limited-capacity working memory to hold these mental representations in mind during a single forward pass. Finally, we explore the mechanisms by which reasoning models succeed at the self- and other-modeling tasks, and show that they readily engage in strategic deception.

The validity of online behavioral research relies on study participants being human rather than machine. In the past, it was possible to detect machines by posing simple challenges that were easily solved by humans but not by machines. General-purpose agents based on large language models (LLMs) can now solve many of these challenges, threatening the validity of online behavioral research. Here we explore the idea of detecting humanness by using tasks that machines can solve too well to be human. Specifically, we probe for the existence of an established human cognitive constraint: limited working memory capacity. We show that cognitive modeling on a standard serial recall task can be used to distinguish online participants from LLMs even when the latter are specifically instructed to mimic human working memory constraints. Our results demonstrate that it is viable to use well-established cognitive phenomena to distinguish LLMs from humans.

Discrete diffusion language models (dLLMs) generate text by iteratively denoising a masked sequence. However, standard dLLMs condition each denoising step solely on the current hard-masked sequence, while intermediate continuous representations are discarded after sampling and remasking. We term this bottleneck the Information Island issue: continuous information remains isolated within individual denoising steps and fails to propagate across the trajectory. This bottleneck is especially harmful for reasoning, which requires intermediate reasoning state to be preserved and updated across many denoising steps. To address this limitation, we introduce MetaState, a lightweight recurrent augmentation that equips a frozen dLLM backbone with persistent, fixed-size working memory. MetaState comprises three modules with a shared time conditioner: a cross-attention Mixer that reads backbone activations into memory slots, a GRU-style Updater that integrates information across steps, and a cross-attention Injector that writes the updated memory back into the backbone. We train these modules with a dedicated $K$-step unrolling pipeline to learn multi-step dynamics. MetaState adds only ${\sim}0.6\%$ trainable parameters while keeping the backbone frozen, and consistently improves reasoning performance over frozen baselines on mathematical reasoning and code generation benchmarks, with an average gain of 4.5 percentage points across all evaluations.