What Really Controls Temporal Reasoning in Large Language Models: Tokenisation or Representation of Time?

Tool use, such as web search, has become a standard capability even in freely available large language models (LLMs). However, existing benchmarks evaluate temporal reasoning mainly in static, non-tool-using settings, which poorly reflect how LLMs perform temporal reasoning in practice. We introduce Time Puzzles, a constraint-based date inference task for evaluating iterative temporal reasoning with tools. Each puzzle combines factual temporal anchors with (cross-cultural) calendar relations and may admit one or multiple valid dates. The puzzles are algorithmically generated, enabling controlled and continual evaluation. Across 13 LLMs, even the best model (GPT-5) achieves only 55.3% accuracy without tools, despite using easily searchable facts. While web search improves performance, models perform substantially better when constraints are rewritten with explicit dates, removing the need for factual lookup. These results reveal a gap in reliable tool use for iterative temporal reasoning.

Understanding a narrative means knowing how every event relates in time to every other, yet large language models (LLMs) are mostly tested on isolated event pairs or coarse labels. We ask five LLMs to reconstruct the complete network of Allen's 13 interval relations for 360 English narratives whose events are placed relative to one another rather than by dates, and evaluate the outputs under a pre-registered protocol for agreement with our gold annotations, converse consistency and logical satisfiability. End to end, the best model clearly beats trivial baselines on macro-F1, our primary metric, yet under our pre-registered parser no model matches the accuracy of always answering "before", which the skewed labels inflate. Most of that accuracy gap is a parsing artifact: formatting errors in large matrices cost whole rows, and a post hoc parser that recovers the determined cells of malformed rows raises coverage from 0.60 to 0.84 and closes the gap to the baseline for the best model. On the cells they do answer, models recover precedence and containment but rarely overlap, and they fail most on flashbacks, where both the narration and the event list present the later event first. Logical consistency varies widely yet says little about agreement with gold: enforcing it raises accuracy mainly by filling empty cells, and is beaten there by the trivial control of guessing the majority label. Reliable structured output and robust handling of relative time are prerequisites for temporal reasoning over whole narratives.

Time series analysis has recently been coupled with Large Language Models (LLMs) to leverage their reasoning and world knowledge capabilities, yet gains remain limited. We attribute this to a fundamental mismatch between existing task formulations and LLM strengths: most settings reduce time series understanding to curve-fitting systems, focusing on low-level prediction while ignoring the semantic, contextual, and reasoning-intensive nature of real-world temporal decision-making.To address these limitations, we introduce TSCognition, a multimodal benchmark for multi-dimensional time series reasoning. It collects real-world time series and textual information from 15 public sources and constructs approximately 41K QA samples around five cognitive reasoning tasks: Decoding, Grounding, Inferring, Extrapolating, and Acting. Building on this, we further propose TSAlign, a unified framework that encodes time series into compact patch-level representations and aligns them with semantic directions in the LLM embedding space via gated residual injection and multivariate fusion.Experiments show that TSAlign outperforms existing LLM, VLM, and time series QA baselines on TSCognition and the publicly available TimerBed benchmark while substantially reducing computational cost.Code is available at: https://github.com/EIT-NLP/CognitiveTSR