#01Nov 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.
#02Nov 9, 2026
cs.CR
DeepChronos: Temporal Neuro-Symbolic Reasoning for Multi-Step Attack Detection
Sofia Burkow, Andrea Agiollo, Enkeleda Bardhi and 3 more
Modern cyber threats commonly unfold as multi-step attacks comprising temporally and causally related phases. Current defenses commonly follow a detect first and correlate later paradigm. Intrusion detection systems classify events independently, while downstream systems reconstruct attack progression from the resulting alerts or audit records. In this context, learning-based detectors learn attack-step dependencies implicitly as statistical regularities in the data and cannot guarantee that their predictions follow the real attack progression. Conversely, correlation systems represent attack relationships explicitly, but apply this knowledge only after the underlying attack observations have been detected. We present DEEPCHRONOS, a neuro-symbolic network intrusion detection system that shifts the paradigm from detect first and correlate later to detection through logical progression. DEEPCHRONOS combines learned flow-level evidence with explicit attack-phase rules, temporal prerequisites, and previously inferred phases, allowing the evolving attack history to inform and constrain each detection decision. Evaluations on DARPA 2000 and AIT-LDS V2 show that DEEPCHRONOS improves macro F1 over purely neural baselines by up to 11.3%, eliminates causal violations under strict temporal constraints, and maintains millisecond-scale inference latency. These results demonstrate that integrating explicit attack progression knowledge into detection produces more accurate and temporally coherent multi-step attack predictions.
#03Nov 9, 2026
cs.LG
Clique Constraints for Exact Causal Structure Learning
Xiaoyu He, Pavel Rytíř, Petr Ryšavý and 1 more
Exact score-based causal structure learning supports explicit structural constraints and optimisation certificates, but its branch-and-cut search can be computationally demanding. We augment exact causal structure learning methods with an upper bound on the maximum clique size of the learned undirected skeleton, enforced at integer candidates through lazy cycle and clique constraints. On static linear-Gaussian Erdős-Rényi and scale-free DAGs, we evaluate callback order, alternative clique-cut policies, incumbent repair, fractional separation, and Big-M bounds. We report causal-recovery metrics jointly with optimality gaps, primal and dual bounds, node throughput, MIPSOL events, and callback cost. Two variants receive particular attention: B3 selects the most violated minimal (k+1)-clique inequality at each callback, whereas C3 repairs an infeasible integer candidate by deleting violating edges and refitting affected regression columns using QR-based least squares. The results do not indicate that clique constraints uniformly accelerate optimisation. However, their benefit depends on graph density, sample size, and cut-management policy, while large collections of correlated constraints can reduce node throughput. Tighter valid Big-M bounds reduced the fixed-budget optimality gap in most tested settings, without necessarily changing SHD or F1 at a fixed time limit. These findings characterize the computational trade-offs of clique-constrained exact causal learning, and identify selective separation and incumbent repair as promising directions.
#04Nov 9, 2026
cs.LG
Where Does Alignment Emerge and What Does It Mean? A Closer Look at the Platonic Representation Hypothesis
Julia Herbst, Simon Roschmann, Quentin Bouniot and 1 more
The Platonic Representation Hypothesis (PRH) suggests that neural networks are converging toward similar representation spaces. As language models become more capable, their representations are aligning with those of vision models. However, recent work has questioned whether this trend continues to hold for newer language models. Moreover, it has been shown that representation similarity metrics can be confounded by model depth and width, requiring appropriate baselines for interpretation. In this work, we first investigate where alignment emerges between unimodal models across model layers and representation dimensions. Next, we find that the PRH capability-alignment trend persists for newer models as long as the captions are sufficiently clean and informative. Finally, we contextualize cross-modal alignment, introducing unimodal and multimodal baselines on various datasets. Our results show that the cross-modal representational alignment of unimodal models can surpass that of explicitly aligned vision-language models, but remains substantially behind the alignment observed for models of the same modality. Code is available at https://github.com/ExplainableML/prh-closer-look.
#05Nov 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.