Can Language Models Remember What Happened?

Author: Denis Avetisyan

A new study investigates how well large language models track changing information across extended interactions.

Across the LinearWorld task—a multi-agent environment with five individuals—querying based on state dependencies consistently outperformed random querying, demonstrating the value of informed exploration in complex systems despite inherent challenges in maintaining accuracy as depth increases.

Researchers assess the state tracking capabilities of transformer-based language models, finding performance limitations related to task complexity and model scale.

Despite advances in reasoning, Large Language Models (LLMs) still struggle with tasks demanding consistent internal state management. This paper, ‘Exploring State Tracking Capabilities of Large Language Models’, investigates how effectively LLMs can maintain and update information across sequential interactions using a dedicated benchmark of state tracking tasks. Our results demonstrate that while recent LLMs like GPT-4 and Llama 3 exhibit promising state tracking abilities, particularly with Chain of Thought prompting, performance degrades with increasing task complexity and is notably limited in older model generations. Can we develop more robust architectures or training strategies to enable LLMs to reliably track state over extended, dynamic scenarios?

The Illusion of State: Tracking in a World of Noise

Many practical challenges, from robotic navigation and financial forecasting to natural language understanding, fundamentally require state tracking – the ability to build and maintain a precise, internal model of a system’s evolving condition. This isn’t merely about recording a series of events, but rather constructing a coherent representation that captures the relevant history and allows for accurate predictions about the future. Consider a self-driving car, for instance; it must continuously track the positions of other vehicles, pedestrian movements, traffic signals, and even anticipate potential hazards – all while updating its internal “state” multiple times per second. Effectively performing this task demands a system’s capacity to integrate new information with existing knowledge, filter out irrelevant details, and prioritize the most critical elements, ultimately enabling informed decision-making in dynamic and often unpredictable environments.

Many conventional approaches to state tracking falter when confronted with intricate, extended sequences of events. Smaller models, in particular, experience a significant decline in performance as the length of these sequences increases, a phenomenon stemming from their limited capacity to retain and process information over time. This inability to effectively capture the evolving condition of a system—to maintain a coherent understanding of ‘what happened when’—creates a bottleneck in tasks requiring nuanced temporal reasoning. The core challenge isn’t simply processing more data, but rather preserving the context of earlier events while integrating new information, a demand that quickly overwhelms the capabilities of less-parameterized architectures.

A core challenge in many dynamic systems lies in maintaining an accurate understanding of their evolving condition – a task hindered by the limitations of traditional state tracking methods. These approaches often struggle to effectively capture and update information across extended sequences of events, leading to performance degradation as complexity increases. However, recent advancements in large language models, specifically Transformer-based architectures like Llama3 70B and GPT-4, offer a promising solution. Their capacity to process and retain information over significantly longer contexts allows these models to better approximate the true state of a system, even as it undergoes continuous change, representing a substantial leap towards robust and reliable state tracking in complex environments.

In the LinearWorld task, state-dependent query systems using the 'swap' update type demonstrate higher accuracy at varying depths compared to those employing the 'integer' update type. — In the LinearWorld task, state-dependent query systems using the ‘swap’ update type demonstrate higher accuracy at varying depths compared to those employing the ‘integer’ update type.

Benchmarking the Ephemeral: Tasks to Probe State Tracking

To objectively assess a model’s ability to maintain state tracking, we utilize a defined set of tasks – the Lights Task, LinearWorld Task, and HandSwap Task – each constructed to present distinct challenges in monitoring evolving system states. These tasks are not simply qualitative assessments; they are designed for quantitative measurement, allowing us to isolate and evaluate the performance of state tracking mechanisms independently of other capabilities. The methodology involves presenting the model with input reflecting changes within these tasks and then evaluating its responses to determine the accuracy and consistency of its internal state representation. This approach provides a standardized and reproducible method for benchmarking state tracking across different model architectures and sizes.

The evaluation suite includes the Lights Task, which assesses tracking of discrete state changes in a grid world; the LinearWorld Task, measuring recall of object positions along a linear trajectory; and the HandSwap Task, designed to test tracking of object locations after a simulated hand-swap manipulation. Each task presents a distinct challenge to state tracking capabilities: Lights focuses on boolean state recall, LinearWorld on continuous position memory, and HandSwap on maintaining identity through a visual transformation. These tasks are designed to isolate the ability to track changes within a system, providing granular insights into model performance beyond overall task completion rates.

State tracking performance is evaluated by comparing responses to state-dependent queries – which directly assess the model’s ability to recall changes in a defined system – against random queries serving as a control. Analysis reveals that mid-sized language models exhibit a significant performance disparity between these query types, indicating a limited capacity for maintaining and utilizing state information. However, larger models, such as GPT-4, demonstrate comparable performance on both state-dependent and random queries, suggesting a reduced reliance on explicit state tracking and potentially leveraging alternative mechanisms for information retention and retrieval.

A single update step transitions the initial task configuration (top) to a new state (bottom), though the depicted Lights configuration is incomplete and fully detailed in section 4.2.

The Algebra of Forgetting: Complexity and State Representation

Algebraic Formal Language Theory provides a rigorous mathematical foundation for analyzing state tracking by modeling states as elements within algebraic structures – typically, finite state automata or more complex systems defined by grammars and associated algebras. This allows computational complexity to be determined through the analysis of the language generated by these structures, focusing on metrics like state space size, transition complexity, and the length of sequences required to reach specific states. By formally defining state representations and state transitions as algebraic operations, researchers can apply theorems from language theory – such as those concerning decidability, ambiguity, and the Chomsky hierarchy – to establish upper and lower bounds on the computational resources needed for state management. This approach contrasts with purely empirical analysis and enables precise characterization of scalability limitations in stateful systems, particularly concerning memory usage and processing time as the number of possible states grows.

Group theory demonstrates limitations in state representation through the analysis of state spaces as mathematical groups, where the number of possible states can grow exponentially with the number of variables or parameters defining the system. This growth arises because each new variable introduces a multiplicative factor to the size of the state space; for n variables each with k possible values, the state space can reach $k^n$ states. Consequently, tracking and updating these states requires computational resources that scale exponentially with the system’s dimensionality, presenting a fundamental challenge for complex systems and necessitating the development of state abstraction or approximation techniques.

As task complexity escalates, the volume of state information requiring tracking and updating grows disproportionately. This growth is not merely linear; the inherent limitations identified through Group Theory suggest the potential for exponential increases in computational demands. Consequently, efficient state management becomes critical to maintain feasible processing times and resource utilization. Techniques such as state abstraction, selective state tracking, and optimized data structures are essential to mitigate the impact of increasing state space size on overall system performance. Failure to address these challenges can lead to computational bottlenecks and ultimately, system failure as the state space becomes intractable.

Models vary significantly in the complexity of mathematical expressions they generate and in the accuracy of evaluating those expressions when paired with chain-of-thought reasoning.

The Fixed Window: Constraints and Current Architectures

The Transformer architecture, despite its demonstrated capabilities in numerous applications, inherently processes information within a fixed input window. This constraint poses a challenge when dealing with sequences where relevant information is separated by long distances. Unlike recurrent neural networks which, in theory, can maintain information across arbitrary sequence lengths, Transformers must compress all necessary context within this window. Consequently, tracking dependencies that span beyond this fixed size becomes problematic, requiring either truncation of vital information or complex strategies to approximate long-range interactions. This limitation impacts performance in tasks like analyzing lengthy documents, understanding extended dialogues, or processing time-series data where past events significantly influence the present, necessitating architectural innovations to effectively capture these long-range dependencies.

The limitation of a fixed input window within Transformer architectures presents a substantial challenge for tasks demanding multi-hop reasoning. These tasks, characterized by the need to synthesize information across numerous sequential steps, require the model to effectively retain and integrate data from distant points in the input sequence. As the number of reasoning steps increases, the model’s ability to accurately track dependencies weakens, leading to performance degradation. Unlike processing immediate context, multi-hop reasoning compels the model to build a coherent understanding from fragmented information spread across a longer sequence, a process severely hampered by the constraints of a limited input window and the difficulty of propagating crucial details over many layers without significant information loss.

Efforts to equip Transformer models with the capacity for complex state tracking reveal a challenging relationship between scale and performance. While smaller models struggle to maintain accuracy as the required reasoning depth—or number of update steps—increases, exhibiting a precipitous decline in performance, larger models such as Llama3 70B and GPT-4 demonstrate considerably more resilience. These substantial architectures not only sustain higher accuracy at greater depths but, remarkably, often achieve near-perfect performance even with relatively shallow reasoning chains. This suggests that simply increasing model size can partially mitigate the limitations imposed by fixed input windows, though the computational cost associated with these larger models represents a significant hurdle and indicates diminishing returns beyond a certain scale.

Across diverse robotic tasks, average accuracy generally decreases with increasing depth, though Llama3 70B and GPT-4—employing Chain of Thought reasoning—consistently outperform other systems.

Beyond the Turn: Dialogue and the Future of State

Effective conversational AI hinges on a process called dialogue state tracking, a continuous assessment of each interaction’s evolving context. This isn’t simply remembering past turns; it requires the system to infer user goals, identify relevant entities, and maintain a coherent representation of the discussion’s current state. As a conversation unfolds, the system must dynamically update this ‘state’ based on new information, resolving ambiguities and anticipating future needs. Without precise state tracking, conversational AI struggles to provide relevant responses, leading to frustrating and disjointed interactions; a robust system, however, enables nuanced understanding and paves the way for genuinely engaging and helpful dialogue.

Advancements in dialogue systems are intrinsically linked to progress in general state tracking. As a system’s ability to accurately monitor and update the evolving context of a conversation improves, so too does its capacity to generate relevant and coherent responses. This heightened awareness allows for more natural turn-taking, reduces the incidence of repetitive or nonsensical exchanges, and ultimately fosters a more engaging user experience. Sophisticated state tracking moves beyond simply recognizing keywords; it involves understanding user intent, tracking entities, and remembering previous interactions – all crucial elements for building truly intelligent conversational agents capable of maintaining context over extended dialogues and adapting to nuanced user behavior. The result is a move away from rigid, pre-programmed responses and towards fluid, dynamic interactions that more closely mimic human conversation.

The development of genuinely intelligent systems hinges on a comprehensive grasp of state tracking – the ability to monitor and update contextual understanding throughout an interaction. Recent research demonstrates that consistently improving this capability directly unlocks more effective reasoning and action in complex, dynamic environments. A particularly promising technique, Chain of Thought prompting, consistently elevates the accuracy of state tracking across various models; this improvement is especially notable in larger models, suggesting a capacity for increasingly sophisticated contextual awareness as computational scale increases. This suggests that by refining the system’s ability to ‘think through’ the implications of each conversational turn, a more nuanced and effective response can be generated, laying the groundwork for truly intelligent interactions.

The pursuit of elegant state tracking within these Large Language Models feels… familiar. This paper demonstrates that even the most sophisticated Transformer architecture struggles with maintaining consistent state as task complexity increases – a predictable outcome. It’s a reminder that while models may appear to reason sequentially, that reasoning is fragile. As Carl Friedrich Gauss observed, “If I have to wait for inspiration, it never comes.” Similarly, expecting these LLMs to flawlessly maintain state across extended interactions is a waiting game. The deeper the task, the more likely the elegant theory will crumble under the weight of production realities, revealing the limitations inherent in any attempt to perfectly model complex systems. The performance dependency on model size only confirms this—throwing more parameters at the problem delays the inevitable, not prevents it.

The Road Ahead

The observed correlation between model scale and state tracking ability is, predictably, not a solution. It’s a postponement. The tendency to equate parameter count with genuine understanding has been a recurring theme in this field. One anticipates a near future saturated with ever-larger models exhibiting marginally improved performance on increasingly contrived benchmarks – a familiar trajectory. The underlying fragility, the susceptibility to subtle shifts in task complexity, will remain.

The focus will inevitably shift towards architectural innovations promising more ‘efficient’ state management. Claims of ‘infinite scalability’ should be met with a practiced skepticism; the problem isn’t usually scale, but rather the fundamental limitations of attempting sequential computation within a fundamentally parallel architecture. Any purported breakthrough will, without fail, introduce new forms of technical debt, manifesting as opaque failure modes in production environments.

Ultimately, the interesting questions aren’t about whether these models can track state, but rather how much effort is required to coerce them into doing so. And, more importantly, what simpler, less theoretically elegant approach might achieve comparable results with a fraction of the computational cost. The pursuit of elegance often obscures the virtues of pragmatism.

Original article: https://arxiv.org/pdf/2511.10457.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/