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

We propose TimePre, a simple framework that unifies the efficiency of Multilayer Perceptron (MLP)-based models with the distributional flexibility of Multiple Choice Learning (MCL) for Probabilistic Time-Series Forecasting (PTSF). Stabilized Instance Normalization (SIN), the core of TimePre, is a normalization layer that explicitly addresses the trade-off among accuracy, efficiency, and stability. SIN stabilizes the hybrid architecture by correcting channel-wise statistical shifts, thereby resolving the catastrophic hypothesis collapse. Extensive experiments on six benchmark datasets demonstrate that TimePre achieves state-of-the-art (SOTA) accuracy on key probabilistic metrics. Critically, TimePre achieves inference speeds that are orders of magnitude faster than sampling-based models, and is more stable than prior MCL approaches.

Long-term time series forecasting (LTSF) underpins critical applications from energy management to weather prediction, yet achieving reliable multi-step-ahead accuracy remains challenging. Existing LTSF approaches, dominated by MLP- and Transformer-based architectures, either rely on simple linear mappings or introduce increasingly complex hand-crafted inductive biases, raising the question of whether a more expressive and principled nonlinear core could offer a better alternative. Therefore, we investigate whether Kolmogorov-Arnold Networks (KANs), a recently proposed model featuring adaptive basis functions capable of granular modulation of nonlinearities, can improve LTSF performance, and under which design choices they are most effective. Specifically, we propose KANMixer, a minimal KAN-centered architecture consisting of a multi-scale pooling frontend, a KAN-based temporal mixing backbone, and prediction heads. By avoiding heavy auxiliary modules, KANMixer enables a clear assessment of KAN components in LTSF. Across 28 benchmark-horizon settings against nine baselines, KANMixer achieves the best MSE in 16 settings and the best MAE in 11. Furthermore, extensive ablations on three representative datasets show that KAN effectiveness depends strongly on the choice of edge function; B-spline bases outperform Fourier and Wavelet alternatives; the prediction head contributes most to the gains; moderate depth is preferred over deeper unstable stacks; and decomposition priors help MLP but harm KAN. Beyond practical guidance for integrating KAN into LTSF, these results reveal an underexplored dependency between structural priors and backbone nonlinearity: design choices that benefit MLP can degrade KAN.