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Deep Learning · Theory

Ronen Basri, David Jacobs

In many popular transformer architectures, an output projection matrix linearly maps lower-dimensional embeddings into a higher-dimensional space of logits. It has been shown that this leads to a softmax bottleneck that prevents the production of arbitrary probability distributions. It has been argued that this limits large language models (LLMs) in their ability to express next token probabilities that perfectly align with the statistics of natural language. We focus on the ability of such models to produce accurate probabilities for just the top-$m$ tokens. We provide theoretical bounds that show that even a randomly initialized projection matrix can successfully do this for rather large values of $m$, supported by empirical results on both random and trained matrices. This raises questions about whether the softmax bottleneck significantly limits the capabilities of LLMs. We also derive bounds on the maximum number of probabilities that any trained output projection matrix can specify.

Applications · Neuroscience, Cognitive Science

Hwa Hui Tew, Junn Yong Loo, Leong Yu, Julia Lau, Ding Fan, Hernando Ombao, Raphaël Phan, Chee Tan, Chee-Ming Ting

Functional Magnetic Resonance Imaging (fMRI) provides non-invasive access to dynamic brain activity by measuring blood oxygen level-dependent (BOLD) signals over time. However, the resource-intensive nature of fMRI acquisition limits the availability of high-fidelity samples required for data-driven brain analysis models. While modern generative models can synthesize fMRI data, they often remain challenging in replicating their inherent non-stationarity, intricate spatiotemporal dynamics, and physiological variations of raw BOLD signals. To address these challenges, we propose Dual-Spectral Flow Matching (DSFM), a novel fMRI generative framework that cascades dual frequency representation of BOLD signals with spectral flow matching. Specifically, our framework first converts BOLD signals into a wavelet decomposition map via a discrete wavelet transform (DWT) to capture globalized transient and multi-scale variations, and projects into the discrete cosine transform (DCT) space across brain regions and time to exploit localized energy compaction of low-frequency dominant BOLD coefficients. Subsequently, a spectral flow matching model is trained to generate class-conditioned cosine-frequency representation. The generated samples are reconstructed through inverse DCT and inverse DWT operations to recover physiologically plausible time-domain BOLD signals. This dual-transform approach imposes structured frequency priors and preserves key physiological brain dynamics. Ultimately, we demonstrate the efficacy of our approach through improved downstream fMRI-based brain network classification.

General Machine Learning · Transfer, Multitask and Meta-learning

Thinh On, Hengzhi Pei, Leonard Lausen, George Karypis

Knowledge distillation has become a crucial technique to transfer the capacities of large language models (LLMs) to smaller, more efficient models for practical deployment. While recent work exploits rich information from intermediate states of the teacher model for more effective knowledge transfer, imperfect knowledge from the teacher can also mislead student learning, restricting the student’s generalization capacity. In this work, we propose a two-stage distillation framework that is effective for diverse knowledge distillation scenarios. In the first stage, we pretrain projectors to extract and compress teacher knowledge into a low-dimensional vector space via self-reconstruction. In the second stage, we perform distillation with a hybrid objective that combines learning from the compressed teacher representations with standard supervised fine-tuning on ground-truth data. Our key innovation is residual learning for LLM distillation, where the student learns to make predictions based on the differential between its representations and projected states from the teacher. This approach encourages the student to further improve its representations beyond potentially erroneous teacher knowledge. For Mixture-of-Experts (MoE) teacher models, we further fuse the experts’ outputs using a self-attention mechanism for better utilizing the teacher knowledge. Moreover, to support the cross-tokenizer distillation setting, where the teacher and student models have different vocabularies, we adopt a cross-model attention mechanism that eliminates the need for explicit token alignment rules. Experimental results show the superior performance of our proposed framework under both same- and cross-tokenizer settings, demonstrating the effectiveness in preserving teacher knowledge and improving student generalization capability.

Optimization · Large Scale, Parallel and Distributed

Mostapha Essoullami, El Houcine Bergou, Aritra Dutta

Distributed learning has achieved remarkable success in training deep neural networks (DNNs) on large datasets, but the communication bottleneck limits its scalability. Various compression techniques have been proposed to alleviate this limitation; however, they either use fixed parameters throughout training or rely on complex and computationally intensive methods to adapt compression parameters. Instead of the hard-to-tune hyperparameters required by adaptive compressors, this paper investigates the impact of two fundamental factors in DNN training—the layer size of the networks and their training phases—to design a simple yet efficient dynamic scheduler for any compressor, guiding the selection of compression parameters. We present a **L**ightweight **E**fficient **G**r**A**dient **C**ompression strategy**Y** or LEGACY, which, in theory, can work with any compression technique to produce a simple dynamic counterpart. We benchmark LEGACY on distributed and federated training, involving seven different DNN architectures, ranging from ResNet, Transformer-XL, to GPT-2, across large and challenging datasets, including ImageNet, WikiText-103, and OpenWebText. On ImageNet-1K, with an equivalent average data volume, LEGACY's dynamic compression strategies improve the Top-1 accuracy of ResNet-50 by 7-11% compared to uniform Top-0.1% compression, while on WikiText-103, the layer-based dynamic strategy reduces the perplexity of Transformer-XL by ~26% relative to the same baseline. In addition, we evaluate LEGACY under constrained and federated settings, and demonstrate that it scales effectively to a 100-worker configuration while maintaining strong accuracy under aggressive compression. We publish anonymized code at: https://github.com/LEGACY-compression/LEGACY.

Deep Learning · Attention Mechanisms

Xiaoran Liu, Yuerong Song, Zhigeng Liu, Zengfeng Huang, Qipeng Guo, Zhaoxiang Liu, Shiguo Lian, Ziwei He, Xipeng Qiu

Rotary Position Embeddings (RoPE) have become a standard for encoding sequence order in Large Language Models (LLMs) by applying rotations to query and key vectors in the complex plane. Standard implementations, however, utilize only the real component of the complex-valued dot product for attention score calculation. This simplification discards the imaginary component, which contains valuable phase information, leading to a potential loss of relational details crucial for modeling long-context dependencies. In this paper, we propose an extension that re-incorporates this discarded imaginary component. Our method leverages the full complex-valued representation to create a dual-component attention score. We theoretically and empirically demonstrate that this approach enhances the modeling of long-context dependencies by preserving more positional information. Furthermore, evaluations on a suite of long-context language modeling benchmarks show that our method consistently improves performance over the standard RoPE, with the benefits becoming more significant as context length increases. The code is available at https://github.com/OpenMOSS/rope_pp.

General Machine Learning · Representation Learning

Kewen Xia, Xiaodong Yue, WeiZhipeng, Yaxin Peng, Zihao Li, Jianxiang Zhu, Jie Shi, PeilinXu

Real-world out-of-distribution (OOD) data exhibit broad, continually evolving distributions, rendering reliance solely on in-distribution (ID) data insufficient for robust detection. Consequently, methods leveraging auxiliary Outlier Exposure (OE) data have emerged, substantially enhancing generalization by jointly fine-tuning models on ID and large-scale OE data. However, many existing approaches primarily enforce orthogonality between ID and OE features while pushing OE predictions toward near-uniform, low-confidence scores, thus overlooking the controllability of representation geometry. We propose Vast Predefined Classifiers (VPC), which constructs a pre-specified Orthogonal Equiangular Feature Space (OEFS) to explicitly separate ID and OOD representations while capturing the rich variability of OOD features. We employ evidential priors to align ID features with their class-specific Equiangular Basic Vectors (EBVs), thereby preserving ID performance. In parallel, a new VEBV loss encourages OE features to explore the subspace spanned by Vast EBVs (VEBVs), enabling a rich characterization of diverse OOD patterns. This dual optimization, coupled with the prescribed geometric representation space, promotes optimal orthogonality between ID and OOD representations. Furthermore, we introduce the VPC Score, a discriminative metric based on the L2 activation intensity of features over the predefined classifiers. Extensive experiments across diverse OOD settings and training paradigms on benchmarks including CIFAR-10/100 and the ImageNet-1k, demonstrate strong and robust performance, validating VPC's effectiveness. Code is available at https://github.com/eightnight2049/VPC.

Xidong Wang, Guo shuqi, YUE SHEN, Junying Chen, Jian Wang, Jinjie Gu, Ping Zhang, Lei Liu, Wang Benyou

The reliability of medical LLM evaluation is critically undermined by data contamination and knowledge obsolescence, leading to inflated scores on static benchmarks. To address these challenges, we introduce LiveClin, a live benchmark designed for the approximating real-world clinical practice. Built from contemporary, peer-reviewed case reports and updated biannually, LiveClin ensures clinical currency and resists data contamination. Using a verified AI–human workflow involving 239 physicians, we transform authentic patient cases into complex, multimodal evaluation scenarios that span the entire clinical pathway. The benchmark currently comprises 1,407 case reports and 6,605 questions. Our evaluation of 26 models on LiveClin reveals the profound difficulty of these real-world scenarios, with the top-performing model achieving a Case Accuracy of just 35.7\%. In benchmarking against human experts, Chief Physicians achieved the highest accuracy, followed closely by Attending Physicians, with both surpassing most models. LiveClin thus provides a continuously evolving, clinically grounded framework to guide the development of medical LLMs towards closing this gap and achieving greater reliability and real-world utility. Our data and code are publicly available at https://github.com/AQ-MedAI/LiveClin.

Applications · Robotics

Chen Li, Zhantao Yang, Han Zhang, Fangyi Chen, Chenchen Zhu, Anudeepsekhar Bolimera, Marios Savvides

Vision–Language–Action (VLA) models show promise in embodied reasoning, yet remain far from true generalists—they often require task-specific fine-tuning, incur high compute costs, and generalize poorly to unseen tasks. We propose MetaVLA, a unified, backbone-agnostic post-training framework for efficient and scalable alignment. MetaVLA introduces Context-Aware Meta Co-Training, which consolidates diverse target tasks into a single fine-tuning stage while leveraging structurally diverse auxiliary tasks to improve in-domain generalization. Unlike naive multi-task SFT, MetaVLA integrates a lightweight meta-learning mechanism—derived from Attentive Neural Processes—to enable rapid adaptation from diverse contexts with minimal architectural change or inference overhead. On the LIBERO benchmark, MetaVLA with six auxiliary tasks outperforms OpenVLA by up to 8.0\% on long-horizon tasks, reduces training steps from 240K to 75K, and cuts GPU time by 76%. These results show that scalable, low-resource post-training is achievable—paving the way toward general-purpose embodied agents. Code will be available.

Theory · Domain Adaptation and Transfer Learning

Wei Chen, Xingyu Guo, Shuang Li, Zhao Zhang, Yan Zhong, Fuzhen Zhuang, deqing wang

Graph Domain Adaptation (GDA) transfers knowledge from labeled source graphs to unlabeled target graphs but is challenged by complex, multi-faceted distributional shifts. Existing methods attempt to reduce distributional shifts by aligning manually selected graph elements (e.g., node attributes or structural statistics), which typically require manually designed graph filters to extract relevant features before alignment. However, such approaches are inflexible: they rely on scenario-specific heuristics, and struggle when dominant discrepancies vary across transfer scenarios. To address these limitations, we propose \textbf{ADAlign}, an Adaptive Distribution Alignment framework for GDA. Unlike heuristic methods, ADAlign requires no manual specification of alignment criteria. It automatically identifies the most relevant discrepancies in each transfer and aligns them jointly, capturing the interplay between attributes, structures, and their dependencies. This makes ADAlign flexible, scenario-aware, and robust to diverse and dynamically evolving shifts. To enable this adaptivity, we introduce the Neural Spectral Discrepancy (NSD), a theoretically principled parametric distance that provides a unified view of cross-graph shifts. NSD leverages neural characteristic function in the spectral domain to encode feature-structure dependencies of all orders, while a learnable frequency sampler adaptively emphasizes the most informative spectral components for each task via minimax paradigm. Extensive experiments on 10 datasets and 16 transfer tasks show that ADAlign not only outperforms state-of-the-art baselines but also achieves efficiency gains with lower memory usage and faster training.

Theory · Everything Else

Juni Schindler, Mauricio Barahona

Datasets often possess an intrinsic multiscale structure with meaningful descriptions at different levels of coarseness. Such datasets are naturally described as multi-resolution clusterings, i.e., not necessarily hierarchical sequences of partitions across scales. To analyse and compare such sequences, we use tools from topological data analysis and define the Multiscale Clustering Bifiltration (MCbiF), a 2-parameter filtration of abstract simplicial complexes that encodes cluster intersection patterns across scales. The MCbiF is a complete invariant of (non-hierarchical) sequences of partitions and can be interpreted as a higher-order extension of Sankey diagrams, which reduce to dendrograms for hierarchical sequences. We show that the multiparameter persistent homology (MPH) of the MCbiF yields a finitely presented and block decomposable module, and its stable Hilbert functions characterise the topological autocorrelation of the sequence of partitions. In particular, at dimension zero, the MPH captures violations of the refinement order of partitions, whereas at dimension one, the MPH captures higher-order inconsistencies between clusters across scales. We then demonstrate through experiments the use of MCbiF Hilbert functions as interpretable topological feature maps for downstream machine learning tasks, and show that MCbiF feature maps outperform both baseline features and representation learning methods on regression and classification tasks for non-hierarchical sequences of partitions. We also showcase an application of MCbiF to real-world data of non-hierarchical wild mice social grouping patterns across time.

Computer Vision · Image and Video Generation

Xin Luo, Jiahao Wang, Chenyuan Wu, Shitao Xiao, Xiyan Jiang, Defu Lian, Jiajun Zhang, Dong Liu, Zheng Liu

Instruction-guided image editing has achieved remarkable progress, yet current models still face challenges with complex instructions and often require multiple samples to produce a desired result. Reinforcement Learning (RL) offers a promising solution, but its adoption in image editing has been severely hindered by the lack of a high-fidelity, efficient reward signal. In this work, we present a comprehensive methodology to overcome this barrier, centered on the development of a state-of-the-art, specialized reward model. We first introduce $\textbf{EditReward-Bench}$, a comprehensive benchmark to systematically evaluate reward models on editing quality. Guided by this benchmark, we develop $\textbf{EditScore}$, an efficient model to evaluate the quality of instruction-guided editing. Through meticulous data curation and filtering, EditScore effectively matches the performance of learning proprietary VLMs. Furthermore, coupled with an effective self-ensemble strategy tailored for the generative nature of EditScore, our largest variant even surpasses GPT-5 in the benchmark. We then demonstrate that a high-fidelity reward model is the key to unlocking online RL for image editing. Our experiments show that, while even the largest open-source VLMs fail to provide an effective learning signal, EditScore enables efficient and robust policy optimization. Applying our framework to a strong base model, OmniGen2, results in a final model that shows a substantial and consistent performance uplift. Overall, this work provides the first systematic path from benchmarking to reward modeling to RL training in image editing, showing that a high-fidelity, domain-specialized reward model is the key to unlocking the full potential of RL in this domain. Our code, models, and benchmark will be released publicly.

Applications · Chemistry and Drug Discovery

Runhan Shi, Zhicheng Zhang, Letian Chen, Gufeng Yu, Yang Yang

Chirality is a fundamental molecular property that governs stereospecific behavior in chemistry and biology. Capturing chirality in machine learning models remains challenging due to the geometric complexity of stereochemical relationships and the limitations of traditional molecular representations that often lack explicit stereochemical encoding. Existing approaches to chiral molecular representation primarily focus on central chirality, relying on handcrafted stereochemical tags or limited 3D encodings, and thus fail to generalize to more complex forms, such as axial chirality. In this work, we introduce \textbf{ChiDeK} (\textbf{Chi}ral \textbf{De}terminant \textbf{K}ernels), a framework that systematically integrates stereogenic information into molecular representation learning. We propose the chiral determinant kernel to encode the SE(3)-invariant chirality matrix and employ cross-attention to integrate stereochemical information from local chiral centers into the global molecular representation. This design enables explicit modeling of chiral-related features within a unified architecture, capable of jointly encoding central and axial chirality. To support the evaluation of axial chirality, we construct a new benchmark for electronic circular dichroism (ECD) and optical rotation (OR) prediction. Across four tasks, including R/S configuration classification, enantiomer ranking, ECD spectrum prediction, and OR prediction, ChiDeK achieves substantial improvements over state-of-the-art baselines, most notably yielding over 7\% higher accuracy on axially chiral tasks on average.

Applications · Robotics

Yixin Zhang, Yunhao Luo, Utkarsh Mishra, Woo Shin, Yongxin Chen, Danfei Xu

Diffusion models excel at short-horizon robot planning, yet scaling them to long-horizon tasks remains challenging due to computational constraints and limited training data. Existing compositional approaches stitch together short segments by separately denoising each component and averaging overlapping regions. However, this suffers from instability as the factorization assumption breaks down in noisy data space, leading to inconsistent global plans. We propose that the key to stable compositional generation lies in enforcing boundary agreement on the estimated clean data (Tweedie estimates) rather than on noisy intermediate states. Our method formulates long-horizon planning as inference over a chain-structured factor graph of overlapping video chunks, where pretrained short-horizon video diffusion models provide local priors. At inference time, we enforce boundary agreement through a novel combination of synchronous and asynchronous message passing that operates on Tweedie estimates, producing globally consistent guidance without requiring additional training. Our training-free framework demonstrates significant improvements over existing baselines, effectively generalizing to unseen start-goal combinations that were not present in the original training data. Project website: https://comp-visual-planning.github.io/

Social Aspects · Accountability, Transparency and Interpretability

Luke Guerdan, Justin Whitehouse, Kimberly Truong, Ken Holstein, Steven Wu

As Generative AI (GenAI) systems see growing adoption, a key concern involves the external validity of evaluations, or the extent to which they generalize from lab-based to real-world deployment conditions. Threats to the external validity of GenAI evaluations arise when the source sample of human raters and system outputs used to obtain a system quality estimate differs from the target distribution at deployment time. In this work, we propose a doubly-robust estimation framework designed to address this evaluation sampling bias. Key to our approach is the use of synthetic "persona" ratings -- produced by prompting an LLM evaluator (i.e., an LLM-as-a-judge) to behave as a human rater with specific sociodemographic characteristics. Our doubly-robust framework combines these informative yet imperfect persona ratings with human ratings obtained under evaluation sampling bias to produce statistically valid system quality estimates. In particular, we show that our approach yields valid system quality estimates when either: (i) a model trained to predict human ratings using persona ratings and source data observed under sampling bias, or (ii) a reweighting model that corrects for sampling bias is of sufficient quality. We validate our framework theoretically and via a novel Persona Simulation Framework (PSF) designed to systematically manipulate persona quality and the degree of evaluation sampling bias present in source data. Our work provides a principled foundation for combining imperfect persona ratings with human ratings observed under sampling bias to obtain valid system quality estimates.

Deep Learning · Robustness

Desong Zhang, Jia Hu, Geyong Min

Spiking Neural Networks (SNNs) process information via discrete spikes, enabling them to operate at remarkably low energy levels. However, our experimental observations reveal a striking vulnerability when SNNs are trained using the mainstream method—direct encoding combined with backpropagation through time (BPTT): even a single backward pass on data drawn from a slightly different distribution can lead to catastrophic network collapse. We refer to this phenomenon as the heterogeneous training vulnerability of SNNs. Our theoretical analysis attributes this vulnerability to the repeated inputs inherent in direct encoding and the gradient accumulation characteristic of BPTT, which together produce an exceptional large Hessian spectral radius. To address this challenge, we develop a hyperparameter-free method called Dominant Singular Deflation (DSD). By orthogonally projecting the dominant singular components of gradients, DSD effectively reduces the Hessian spectral radius, thereby preventing SNNs from settling into sharp minima. Extensive experiments demonstrate that DSD not only mitigates the vulnerability of SNNs under heterogeneous training, but also significantly enhances overall robustness compared to key baselines, providing strong support for safer SNNs.

Optimization · Learning for Optimization

Panagiotis D. Grontas, Antonio Terpin, Efe Balta, Raffaello D'Andrea, John Lygeros

We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $\Pi$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem for backpropagation. We deploy $\Pi$net as a feasible-by-design optimization proxy for parametric constrained optimization problems and obtain modest-accuracy solutions faster than traditional solvers when solving a single problem, and significantly faster for a batch of problems. We surpass state-of-the-art learning approaches by orders of magnitude in terms of training time, solution quality, and robustness to hyperparameter tuning, while maintaining similar inference times. Finally, we tackle multi-vehicle motion planning with non-convex trajectory preferences and provide $\Pi$net as a GPU-ready package implemented in JAX.

Applications · Time Series

Zhengyu Li, Xiangfei Qiu, Yuhan Zhu, Xingjian Wu, Jilin Hu, Guo, Bin Yang

Exogenous variables offer valuable supplementary information for predicting future endogenous variables. Forecasting with exogenous variables needs to consider both past-to-future dependencies (i.e., temporal correlations) and the influence of exogenous variables on endogenous variables (i.e., channel correlations). This is pivotal when future exogenous variables are available, because they may directly affect the future endogenous variables. Many methods have been proposed for time series forecasting with exogenous variables, focusing on modeling temporal and channel correlations. However, most of them use a two-step strategy, modeling temporal and channel correlations separately, which limits their ability to capture joint correlations across time and channels. Furthermore, in real-world scenarios, recorded time series are frequently affected by various forms of noises, underscoring the critical importance of robustness in such correlations modeling. To address these limitations, we propose GCGNet, a Graph-Consistent Generative Network for time series forecasting with exogenous variables. Specifically, GCGNet first employs a Variational Generator to produce coarse predictions. A Graph Structure Aligner then further guides it by evaluating the consistency between the generated and true correlations, where the correlations are represented as graphs, and are robust to noises. Finally, a Graph Refiner is proposed to refine the predictions to prevent degeneration and improve accuracy. Extensive experiments on 12 real-world datasets demonstrate that GCGNet outperforms state-of-the-art baselines.

Computer Vision · 3D Rendering & Reconstruction

Sheng-Chi Hsu, Ting-Yu Yen, Shih-Hsuan Hung, Hung-Kuo Chu

Gaussian Splatting has emerged as a powerful representation for high-quality, real-time 3D scene rendering. While recent works extend Gaussians with learnable textures to enrich visual appearance, existing approaches allocate a fixed square texture per primitive, leading to inefficient memory usage and limited adaptability to scene variability. In this paper, we introduce adaptive anisotropic textured Gaussians (A$^2$TG), a novel representation that generalizes textured Gaussians by equipping each primitive with an anisotropic texture. Our method employs a gradient-guided adaptive rule to jointly determine texture resolution and aspect ratio, enabling non-uniform, detail-aware allocation that aligns with the anisotropic nature of Gaussian splats. This design significantly improves texture efficiency, reducing memory consumption while enhancing image quality. Experiments on multiple benchmark datasets demonstrate that A$^2$TG consistently outperforms fixed-texture Gaussian Splatting methods, achieving comparable rendering fidelity with substantially lower memory requirements.

Applications · Physics

Alessandro Trenta, Andrea Cossu, Davide Bacciu

Real-world phenomena typically involve multiple, interwoven dynamics that can be elegantly captured by systems of Partial Differential Equations (PDEs). However, accurately solving such systems remains a challenge. In this paper, we introduce ComPhy (CP), a novel modular framework designed to leverage the inherent physical structure of the problem to solve systems of PDEs. CP assigns each PDE to a dedicated learning module, each capable of incorporating state-of-the-art methodologies such as Physics-Informed Neural Networks or Neural Conservation Laws. Crucially, CP introduces an end-to-end alignment mechanism, explicitly designed around the physical interplay of shared variables, enabling knowledge transfer between modules, and promoting solutions that are the result of the collective effort of all modules. CP is the first approach specifically designed to tackle systems of PDEs, and our results show that it outperforms state-of-the-art approaches where a single model is trained on all PDEs at once.

Applications · Time Series

Yuanzhao Zhang, William Gilpin

Recent time-series foundation models exhibit strong abilities to predict physical systems. These abilities include zero-shot forecasting, in which a model forecasts future states of a system given only a short trajectory as context, without knowledge of the underlying physics. Here, we show that foundation models often forecast through a simple parroting strategy, and when they are not parroting they exhibit some shared failure modes such as converging to the mean. As a result, a naive context parroting model that copies directly from the context scores higher than leading time-series foundation models on predicting a diverse range of dynamical systems, including low-dimensional chaos, turbulence, coupled oscillators, and electrocardiograms, at a tiny fraction of the computational cost. We draw a parallel between context parroting and induction heads, which explains recent works showing that large language models can often be repurposed for time series forecasting. Our dynamical systems perspective also ties the scaling between forecast accuracy and context length to the fractal dimension of the underlying chaotic attractor, providing insight into previously observed in-context neural scaling laws. By revealing the performance gaps and failure modes of current time-series foundation models, context parroting can guide the design of future foundation models and help identify in-context learning strategies beyond parroting.