State Tracking

A human-like chess engine should mimic the style, errors, and consistency of a strong human player rather than maximize playing strength. We show that training from move sequences alone forces a model to learn two capabilities: state tracking, which reconstructs the board from move history, and decision quality, which selects good moves from that reconstructed state. These impose contradictory data requirements: low-rated games provide the diversity needed for tracking, while high-rated games provide the quality signal for decision learning. Removing low-rated data degrades performance. We formalize this tension as a dual-capability bottleneck, P <= min(T,Q), where overall performance is limited by the weaker capability. Guided by this view, we scale the model from 28M to 120M parameters to improve tracking, then introduce Elo-weighted training to improve decisions while preserving diversity. A 2 x 2 factorial ablation shows that scaling improves tracking, weighting improves decisions, and their combination is superadditive. Linear weighting works best, while overly aggressive weighting harms tracking despite lower validation loss. We also introduce a coverage-decay formula, t* = log(N/kcrit)/log b, as a reliability horizon for intra-game degeneration risk. Our final 120M-parameter model, without search, reached Lichess bullet 2570 over 253 rated games. On human move prediction it achieves 55.2% Top-1 accuracy, exceeding Maia-2 rapid and Maia-2 blitz. Unlike position-based methods, sequence input naturally encodes full game history, enabling history-dependent decisions that single-position models cannot exhibit.

Most automated electronic medical record (EMR) pipelines remain output-oriented: they transcribe, extract, and summarize after the consultation, but they do not explicitly model what is already known, what is still missing, which uncertainty matters most, or what question or recommendation should come next. We formulate doctor-patient dialogue as a proactive knowledge-inquiry problem under partial observability. The proposed framework combines stateful extraction, sequential belief updating, gap-aware state modeling, hybrid retrieval over objectified medical knowledge, and a POMDP-lite action planner. Instead of treating the EMR as the only target artifact, the framework treats documentation as the structured projection of an ongoing inquiry loop. To make the formulation concrete, we report a controlled pilot evaluation on ten standardized multi-turn dialogues together with a 300-query retrieval benchmark aggregated across dialogues. On this pilot protocol, the full framework reaches 83.3% coverage, 80.0% risk recall, 81.4% structural completeness, and lower redundancy than the chunk-only and template-heavy interactive baselines. These pilot results do not establish clinical generalization; rather, they suggest that proactive inquiry may be methodologically interesting under tightly controlled conditions and can be viewed as a conceptually appealing formulation worth further investigation for dialogue-based EMR generation. This work should be read as a pilot concept demonstration under a controlled simulated setting rather than as evidence of clinical deployment readiness. No implication of clinical deployment readiness, clinical safety, or real-world clinical utility should be inferred from this pilot protocol.

Scaling inference-time compute has emerged as an important driver of LLM performance, making inference efficiency a central focus of model design alongside model quality. While the current Transformer-based models deliver strong model quality, their quadratic compute and linear memory make inference expensive. This has spurred the development of sub-quadratic models with reduced linear compute and constant memory requirements. However, many recent linear models trade off model quality and capability for algorithmic efficiency, failing on tasks such as state tracking. Moreover, their theoretically linear inference remains hardware-inefficient in practice. Guided by an inference-first perspective, we introduce three core methodological improvements inspired by the state space model (SSM) viewpoint of linear models. We combine: (1) a more expressive recurrence derived from SSM discretization, (2) a complex-valued state update rule that enables richer state tracking, and (3) a multi-input, multi-output (MIMO) formulation for better model performance without increasing decode latency. Together with architectural refinements, our Mamba-3 model achieves significant gains across retrieval, state-tracking, and downstream language modeling tasks. At the 1.5B scale, Mamba-3 improves average downstream accuracy by 0.6 percentage points compared to the next best model (Gated DeltaNet), with Mamba-3's MIMO variant further improving accuracy by another 1.2 points for a total 1.8 point gain. Across state-size experiments, Mamba-3 achieves comparable perplexity to Mamba-2 despite using half of its predecessor's state size. Our evaluations demonstrate Mamba-3's ability to advance the performance-efficiency Pareto frontier.

Video understanding requires models to continuously track and update world state during playback. Although existing benchmarks have advanced video understanding evaluation across multiple dimensions, they provide limited visibility into how models maintain world state over time. We propose SVCBench, a Streaming Video Counting Benchmark that repositions counting as a minimal, controlled probe for diagnosing models' world-state maintenance capability. We decompose this capability into object counting and event counting, forming 8 fine-grained subcategories. Object counting covers tracking currently visible objects and cumulative unique identities, while event counting covers detecting instantaneous actions and tracking complete activity cycles. SVCBench contains 406 videos with frame-by-frame annotations of 10,071 event occurrences and object state changes, yielding 1,000 streaming QA pairs with 4,576 query points distributed along video timelines. By observing state maintenance trajectories through streaming multi-point queries, we design three complementary metrics to diagnose numerical precision, trajectory consistency, and temporal awareness. Evaluations of mainstream video-language models show that current models still exhibit significant deficiencies in spatial-temporal state maintenance, with especially poor performance on periodic event counting. SVCBench provides a diagnostic framework for measuring and improving state maintenance in video understanding systems. Our code and data are available at https://buaa-colalab.github.io/SVCBench.

The performance of task-oriented dialogue models is strongly tied to how well they track dialogue states, which records and updates user information across multi-turn interactions. However, current multi-domain DST encounters two key challenges: the difficulty of effectively modeling dialogue history and the limited availability of annotated data, both of which hinder model performance. To tackle the aforementioned problems, we develop a dynamic knowledge fusion framework applicable to multi-domain DST. The model operates in two stages: first, an encoder-only network trained with contrastive learning encodes dialogue history and candidate slots, selecting relevant slots based on correlation scores; second, dynamic knowledge fusion leverages the structured information of selected slots as contextual prompts to enhance the accuracy and consistency of dialogue state tracking. This design enables more accurate integration of dialogue context and domain knowledge. Results obtained from multi-domain dialogue benchmarks indicate that our method notably improves both tracking accuracy and generalization, validating its capability in handling complex dialogue scenarios.

Visual entity tracking is an innate cognitive ability in humans, yet it remains a critical bottleneck for Vision-Language Models (VLMs). This deficit is often obscured in existing video benchmarks by visual shortcuts. We introduce VET-Bench, a synthetic diagnostic testbed featuring visually identical objects that necessitate tracking exclusively through spatiotemporal continuity. Our experiments reveal that current state-of-the-art VLMs perform at or near chance level on VET-Bench, exposing a fundamental limitation: an over-reliance on static frame-level features and a failure to maintain entity representations over time. We provide a theoretical analysis drawing connections to the state-tracking problem, proving that fixed-depth transformer-based VLMs are fundamentally limited in tracking indistinguishable objects without intermediate supervision due to expressivity constraints. To address this, we propose Spatiotemporal Grounded Chain-of-Thought (SGCoT): generating object trajectories as explicit intermediate states. Leveraging Molmo2's object tracking ability, we elicit SGCoT reasoning by fine-tuning on synthesized text-only data for alignment. Our method achieves state-of-the-art accuracy exceeding 90% on VET-Bench, demonstrating that VLMs can reliably solve the video shell-game task end-to-end without external tools. Our code and data are available at https://vetbench.github.io .

State-Space Models (SSMs) have recently been shown to achieve strong empirical performance on a variety of long-range sequence modeling tasks while remaining efficient and highly-parallelizable. However, the theoretical understanding of their expressive power remains limited. In this work, we study the expressivity of input-Dependent Complex-valued Diagonal (DCD) SSMs on sequential state-tracking tasks. We show that single-layer DCD SSMs cannot express state-tracking of any non-Abelian group at finite precision. More generally, we show that $k$-layer DCD SSMs can express state-tracking of a group if and only if that group has a subnormal series of length $k$, with Abelian factors. That is, we identify the precise expressivity range of $k$-layer DCD SSMs within the solvable groups. Empirically, we find that multi-layer models often fail to learn state-tracking for non-Abelian groups, highlighting a gap between expressivity and learnability.

Despite the remarkable practical success of transformer-based language models, recent work has raised concerns about their ability to perform state tracking. In particular, a growing body of literature has shown this limitation primarily through failures in out-of-distribution (OOD) generalization, such as length extrapolation. In this work, we shift attention to the in-distribution implications of these limitations. We conduct a large-scale experimental study of the data efficiency of transformers and recurrent neural networks (RNNs) across multiple supervision regimes. We find that the amount of training data required by transformers grows much more rapidly with state-space size and sequence length than for RNNs. Furthermore, we analyze the extent to which learned state-tracking mechanisms are shared across different sequence lengths. We show that transformers exhibit negligible or even detrimental weight sharing across lengths, indicating that they learn length-specific solutions in isolation. In contrast, recurrent models exhibit effective amortized learning by sharing weights across lengths, allowing data from one sequence length to improve performance on others. Together, these results demonstrate that state tracking remains a fundamental challenge for transformers, even when training and evaluation distributions match.

Over the last years, state-tracking tasks, particularly permutation composition, have become a testbed to understand the limits of sequence models architectures like Transformers and RNNs (linear and non-linear). However, these are often sequence-to-sequence tasks: learning to map actions (permutations) to states, which is incompatible with the next-token prediction setting commonly used to train language models. We address this gap by converting permutation composition into code via REPL traces that interleave state-reveals through prints and variable transformations. We show that linear RNNs capable of state-tracking excel also in this setting, while Transformers still fail. Motivated by this representation, we investigate why tracking states in code is generally difficult: actions are not always fully observable. We frame this as tracking the state of a probabilistic finite-state automaton with deterministic state reveals and show that linear RNNs can be worse than non-linear RNNs at tracking states in this setup.