#01Nov 9, 2026
stat.ML
From Granger causality to causal structure in dynamical systems
Víctor Elvira
The idea of testing whether the past of one signal improves the prediction of another can be traced back to Wiener. It was Granger who formalized the concept. Granger causality has become one of the most widely used tools to infer directed interactions between the components of a system. The name however can be misleading: it detects predictive relations among the measured signals, not causal relations among the mechanisms that generate them. This article starts by reviewing recent advances in observation-space Granger analysis. It then follows a path to directed structure in latent dynamical models, and asks under which conditions that structure can be read causally.
#02Nov 9, 2026
cs.LG
What the Loss Curve Misses: FP4 Pretraining Slows the Acquisition of Rare Facts
Chang Lu, Mengjiao Zhang
Low-precision pretraining is usually judged by validation loss. We ask whether matching loss also means learning rare facts as efficiently. We train transformers from scratch with emulated 4-bit matrix multiplications on synthetic biographies with controlled exposure counts, on their own and mixed into web text. NVFP4 needs 1.32$\times$ and 1.52$\times$ as many exposures as BF16 to match its recall while validation loss differs by only 0.5% and 2%, and 1.26$\times$ and 1.30$\times$ when both models are evaluated with BF16 matrix multiplications. Under our primary readout, the exposure cost is about 1.2$\times$ at matched loss. Zero-mean gradient noise reproduces the cost of quantizing only the backward pass, which barely moves the loss. In a controlled experiment at twice the NVFP4 error, noise fed only to Adam's second-moment estimate acts like a lower learning rate and its cost fades, whereas noise in the update lowers its signal-to-noise ratio and carries about two thirds of the cost through the end of training. Raising the learning rate to offset the smaller average step does not recover the cost, either for this noise or for NVFP4. Gradient statistics of BF16 checkpoints rank the costs of formats, partial quantizations and noise controls without fitting (Spearman 0.96). We suggest measuring rare-fact acquisition alongside loss when evaluating low-precision recipes.
#03Nov 9, 2026
cs.LG
Inversion-Free High-Dimensional Counterfactual Inference
Saketh Vishnubhatla, Pingchuan Ma, Shu Wan and 4 more
Counterfactual inference is the task of answering hypothetical "what-if" queries about a unit, given an observational dataset, modeling assumptions, and a causal graph. This enables a modeler to reason about hypothetical scenarios that cannot otherwise be answered without assumptions or a causal graph. The simpler case involves a causal graph with scalar 1-D variables that denote different attributes in the data-generation process. While the literature is clear in the 1-D case, extending this to settings with high-dimensional nodes (e.g., images) remains challenging. Conventionally, in the literature, methods recover the latent state from the factual image (inversion), generate counterfactual attributes from the graph, and render the counterfactual image from the latent state using the updated attributes. In our work, we investigate the necessity of the inversion step in computing high-dimensional counterfactuals. We first discuss moving from the scalar 1-D case to the higher-dimensional case. Secondly, we discuss the relevance of the inversion step and evaluate an inversion-free counterpart repurposed from the image-editing literature. Finally, on image datasets such as CelebA and ADNI, we benchmark our approach using two measures: namely, effectiveness and identity preservation. While effectiveness is a measure of how faithfully the counterfactual attribute is rendered, identity preservation measures whether the same unit (image) is being rendered, both of which are crucial for high-dimensional counterfactual inference. We present the tradeoffs of using inversion-based and inversion-free approaches in our work.
#04Nov 9, 2026
cs.LG
Anchor Behavior, Not Parameters: Rehearsal-Free Continual Learning with a Single Shared Prompt
Duy-Cuong Bui, Trung-Anh Dang, Vincent Nguyen and 2 more
Prompt-based continual learning adapts a frozen pre-trained vision transformer by tuning a small set of prompt tokens. Recently, one-prompt methods which share one single prompt across all tasks make this paradigm maximally parameter efficient. The open question is how a shared prompt can keep the knowledge of old classes while being updated for new ones. Existing methods protect old knowledge in parameter space, where they freeze task-specific prompts, expand new components, or sparsely gate which tokens receive gradients. However, this method sacrifices plasticity, yet the drift it still permits in shared tokens can corrupt the prompt's function on past classes. What must be preserved is the prompt's behavior. We propose TEA-Prompt, which couples (i) a token evaluation module that assigns each prompt token a continuous, input-conditional relevance score injected into the attention logits, softly specializing tokens across tasks without discarding any of them, and (ii) an attention-behavior anchoring loss that constrains each token's attention output around class-specific query regions using only compact Gaussian query statistics without stored old images, weighted by the token's past relevance. Anchoring the attention value allows the parameters to continue updating freely, as long as their interaction remains unchanged. TEA-Prompt achieves state-of-the-art accuracy with markedly lower forgetting on CIFAR-100, ImageNet-R, and CUB-200 with only 0.38M parameters. Code is publicy available at https://github.com/cuonga1cvp/TEA-Prompt.git
#05Nov 9, 2026
cs.CV
What kills $v$-prediction? A Patch-wise PCA Perspective on Pixel-Space Flow Matching
Tianze Luo, Haofeng Huang, Yuan Yao
Latent Diffusion Models dominate generative modeling but face two-stage training complexity and the inherent reconstruction limits of pre-trained autoencoders. Pixel-space Flow Matching offers a simplified end-to-end alternative yet often encounters training difficulties when using the standard $v$-prediction objective. Recent research attributes this difficulty to the off-manifold nature of noised targets, motivating a shift toward $x$-prediction. In this paper, we investigate this explanation through patch-wise Principal Component Analysis (PCA) and identify a bandwidth bottleneck. The velocity in minor components is largely determined by the raw noisy input, requiring deep backbones to preserve information that competes with principal-component modeling. Through controlled experiments and representation analysis, we further examine why $x$-prediction remains effective: its parameterization provides a raw-input bypass, while its learned input representation can spontaneously concentrate on principal directions. Under low-rank observations, our analysis of the induced flow characterizes $x$-prediction as an implicit conditional-mean decoder, reconstructing discarded components from the retained information. These observations motivate the Raw-injected Transformer (RiT), which combines a lightweight raw-conditioned decoder with an output-side shortcut to separate semantic modeling from raw-state propagation. Our method restores effective $v$-prediction and achieves competitive performance on ImageNet $256\times256$, providing a perspective on the interaction between prediction objectives and architectural bandwidth.