Rank Collapse, Fixed Points, and the Renormalization Group Structure of MLP Residual Networks

The analogy between deep neural network forward passes and renormalization group (RG) flows has been repeatedly noted in the literature, but existing treatments remain qualitative: depth is described as a coarse-graining scale, attention is likened to a partition function, and representations are said to flow toward fixed points. No existing work has defined a measurable RG order parameter, tested it under controlled variation of the input distribution, or made quantitative predictions that are empirically verified. We study the simplest architecture for which the analogy is tractable: a pure MLP residual stack trained on masked token prediction over synthetic Markov chain sequences with known spectral properties. We report three findings. (i) The effective rank of the residual stream decreases monotonically with depth after training, consistent with progressive integration of irrelevant degrees of freedom. (ii) This rank collapse is selective: it occurs for chains with short correlation length approximately 1 but is absent for chains with long correlation length approximately 7, measured at the position level to control for mean-pooling artifacts. The network preserves exactly the degrees of freedom relevant to the prediction task, the content of the RG relevance criterion. (iii) Inter-layer kernel drift is concentrated at one or two specific transitions, with the remainder of the network near a fixed point, consistent with a discrete fixed-point plateau. Together these findings constitute the first quantitative, position-level evidence that MLP residual networks implement a selective coarse-graining procedure governed by the spectral structure of the input distribution.

Failed Reasoning Traces Tell You What Is Fixable (But Not by Reading Them)

When post-trained language models fail on reasoning problems, the common test-time-scaling response is to spend more compute on additional attempts, and the failed traces play no further role. We argue this discards a crucial signal; some failures come from unlucky sampling, where more rollouts help, while others are structural and resist resampling regardless of budget. We propose that failed traces encode recoverability structure: the inference-time signature of which test-time interventions can rescue a given failure. Three problem-level trajectory features, derived from the structure of available interventions, recover this structure from the distributional signature of failed rollouts, not their text. They cluster failures into stable regimes, characterize the failure topography of different post-training methods ($84.3{\pm}4.3\%$ accuracy, $+20\%$ over a majority-class baseline), and support a training-free routing rule that lifts rescue by $+12.2\%$ on the deployment-relevant Steerable-Hard subset (failures where retry is insufficient and a bounded intervention is reachable). The features and the routing rule transfer across two cross-family probes. The same three features thus convert failed traces from discarded data into a diagnostic object, supporting test-time routing and post-training analysis without training-time or weight-space access.

Unified Neural Scaling Laws

We present a functional form (that we refer to as a Unified Neural Scaling Law (UNSL)) that accurately models and extrapolates the scaling behaviors of deep neural networks as multiple dimensions all vary simultaneously (i.e. how the evaluation metric of interest varies as one simultaneously varies the number of model parameters, training dataset size, number of training steps, number of inference steps, amount of compute, and various hyperparameters) for various architectures and for each of various tasks within a varied set of upstream and downstream tasks. This set includes large-scale vision, language, math, and reinforcement learning. When compared to other functional forms for neural scaling, this functional form yields extrapolations of scaling behavior that are considerably more accurate on this set.

LLM Pretraining Shapes a Generalizable Manifold: Insights into Cross-Modal Transfer to Time Series

Can language-pretrained transformers become effective time-series forecasters, and why? In this paper, we show that cross-modal transfer arises because language pretraining preconditions time series training with a reusable manifold. A linear probe on frozen LLM states decodes realistic time-series trajectories without paired supervision, and retrieval in this projected space yields competitive forecasts, showing that structure and dynamics exist before finetuning. Pretrained initialization also improves optimization, producing coherent gradients and a highly anisotropic loss landscape unlike random initialization. Finetuning then acts as low-dimensional alignment, reusing existing directions rather than learning temporal primitives from scratch, as evidenced by low-rank updates, subspace alignment, and shared features for periodicity, trend, and repetition. Together, these results support a geometric account of LLM-to-time-series transfer: language pretraining builds the manifold, and finetuning projects numerical dynamics onto task-relevant directions.

Adaptive Batch Sizes Using Non-Euclidean Gradient Noise Scales for Stochastic Sign and Spectral Descent

To maximize hardware utilization, modern machine learning systems typically employ large constant or manually tuned batch size schedules, relying on heuristics that are brittle and costly to tune. Existing adaptive strategies based on gradient noise scale (GNS) offer a principled alternative. However, their assumption of SGD's Euclidean geometry creates a fundamental mismatch with popular optimizers based on generalized norms, such as signSGD / Signum ($\ell_\infty$) and stochastic spectral descent (specSGD) / Muon ($\mathcal{S}_\infty$). In this work, we derive gradient noise scales for signSGD and specSGD that naturally emerge from the geometry of their respective dual norms. To practically estimate these non-Euclidean metrics, we propose an efficient variance estimation procedure that leverages the local mini-batch gradients on different ranks in distributed data-parallel systems. Our experiments demonstrate that adaptive batch size strategies using non-Euclidean GNS enable us to match the validation loss of constant-batch baselines while reducing training steps by up to 66% for Signum and Muon on a 160 million parameter Llama model.

Image Tiling for High-Resolution Reasoning: Balancing Local Detail with Global Context

Reproducibility remains a cornerstone of scientific progress, yet complex multimodal models often lack transparent implementation details and accessible training infrastructure. In this work, we present a detailed reproduction and critical analysis of the Monkey Vision-Language Model (VLM) (Li et al. 2023b) published in CVPR24, a recent approach to high-resolution image understanding via image tiling. The original paper proposed splitting large images into tiles to recover fine-grained visual details while maintaining computational efficiency. Our study replicates this strategy using open checkpoints and reimplements the training pipeline. We confirm the key finding of the original Monkey VLM work, namely that tiling effectively recovers local details. We then extend this work further, by investigating the effect of the inclusion of the global context, which provide practical insights for future high-resolution multimodal modeling. However, we also report deviations in the results, with the magnitude of these effects depending heavily on task type and tile granularity.

Small Vocabularies, Big Gains: Pretraining and Tokenization in Time Series Models

Tokenization and transfer learning are two critical components in building state of the art time series foundation models for forecasting. In this work, we systematically study the effect of tokenizer design, specifically scaling and quantization strategies, on model performance, alongside the impact of pretraining versus random initialization. We show that tokenizer configuration primarily governs the representational capacity and stability of the model, while transfer learning influences optimization efficiency and alignment. Using a combination of empirical training experiments and theoretical analyses, we demonstrate that pretrained models consistently leverage well-designed tokenizers more effectively, particularly at smaller vocabulary sizes. Conversely, misaligned tokenization can diminish or even invert the benefits of pretraining. These findings highlight the importance of careful tokenization in time series modeling and suggest that combining small, efficient vocabularies with pretrained weights is especially advantageous in multi-modal forecasting settings, where the overall vocabulary must be shared across modalities. Our results provide concrete guidance for designing tokenizers and leveraging transfer learning in discrete representation learning for continuous signals.

CAVE: Detecting and Explaining Commonsense Anomalies in Visual Environments

Humans can naturally identify, reason about, and explain anomalies in their environment. In computer vision, this long-standing challenge remains limited to industrial defects or unrealistic, synthetically generated anomalies, failing to capture the richness and unpredictability of real-world anomalies. In this work, we introduce CAVE, the first benchmark of real-world visual anomalies. CAVE supports three open-ended tasks: anomaly description, explanation, and justification; with fine-grained annotations for visual grounding and categorizing anomalies based on their visual manifestations, their complexity, severity, and commonness. These annotations draw inspiration from cognitive science research on how humans identify and resolve anomalies, providing a comprehensive framework for evaluating Vision-Language Models (VLMs) in detecting and understanding anomalies. We show that state-of-the-art VLMs struggle with visual anomaly perception and commonsense reasoning, even with advanced prompting strategies. By offering a realistic and cognitively grounded benchmark, CAVE serves as a valuable resource for advancing research in anomaly detection and commonsense reasoning in VLMs.

Warming Up for Zeroth-Order Federated Pre-Training with Low Resource Clients

Federated learning enables collaborative model training across numerous edge devices without requiring participants to share data; however, memory and communication constraints on these edge devices may preclude their participation in training. We consider a setting in which a subset of edge devices are below a critical memory or communication threshold required to conduct model updates. Under typical federated optimization algorithms, these devices are excluded from training which renders their data inaccessible and increases system induced bias. We are inspired by MeZO, a zeroth-order method used for memory-efficient fine-tuning. The increased variance inherent to zeroth-order gradient approximations has relegated previous zeroth-order optimizers exclusively to the domain of fine tuning; a limitation we seek to correct. We devise a federated, memory-efficient zeroth-order optimizer, ZOWarmUp that permits zeroth-order training from a random initialization. ZOWarmUp leverages differing client capabilities and careful variance reduction techniques to facilitate participation of under-represented, low-resource clients in model training. Like other federated zeroth-order methods, ZOWarmUp eliminates the need for edge devices to transmit their full gradients to the server and instead relies on only a small set of random seeds, rendering the up-link communication cost negligible. We present experiments using various datasets and model architectures to show that ZOWarmUp is a robust algorithm that can can be applied under a wide variety of circumstances. For systems with a high proportion of edge devices that would otherwise be excluded from training, this algorithm provides access to a greater volume and diversity of data, thus improving training outcomes.

Beyond Naïve Prompting: Strategies for Improved Zero-shot Context-aided Forecasting with LLMs

Forecasting in real-world settings requires models to integrate not only historical data but also relevant contextual information, often available in textual form. While recent work has shown that large language models (LLMs) can be effective context-aided forecasters via na\"ive direct prompting, their full potential remains underexplored. We address this gap with 4 strategies, providing new insights into the zero-shot capabilities of LLMs in this setting. ReDP improves interpretability by eliciting explicit reasoning traces, allowing us to assess the model's reasoning over the context independently from its forecast accuracy. CorDP leverages LLMs solely to refine existing forecasts with context, enhancing their applicability in real-world forecasting pipelines. IC-DP proposes embedding historical examples of context-aided forecasting tasks in the prompt, substantially improving accuracy even for the largest models. Finally, RouteDP optimizes resource efficiency by using LLMs to estimate task difficulty, and routing the most challenging tasks to larger models. Evaluated on different kinds of context-aided forecasting tasks from the CiK benchmark, our strategies demonstrate distinct benefits over na\"ive prompting across LLMs of different sizes and families. These results open the door to further simple yet effective improvements in LLM-based context-aided forecasting.