We show that language models' activations linearly encode when information was learned during training. Our setup involves creating a model with a known training order by sequentially fine-tuning Llama-3.2-1B on six disjoint but otherwise similar datasets about named entities. We find that the average activations of test samples corresponding to the six training datasets encode the training order: when projected into a 2D subspace, these centroids are arranged exactly in the order of training and lie on a straight line. Further, we show that linear probes can accurately (~90%) distinguish "early" vs. "late" entities, generalizing to entities unseen during the probes' own training. The model can also be fine-tuned to explicitly report an unseen entity's training stage (~80% accuracy). Interestingly, the training-order encoding does not seem attributable to simple differences in activation magnitudes, losses, or model confidence. Our paper demonstrates that models are capable of differentiating information by its acquisition time, and carries significant implications for how they might manage conflicting data and respond to knowledge modifications.

Although contrastive and other representation-learning methods have long been explored in vision and NLP, their adoption in modern time series forecasters remains limited. We believe they hold strong promise for this domain. To unlock this potential, we explicitly align past and future representations, thereby bridging the distributional gap between input histories and future targets. To this end, we introduce TimeAlign, a lightweight, plug-and-play framework that establishes a new representation paradigm, distinct from contrastive learning, by aligning auxiliary features via a simple reconstruction task and feeding them back into any base forecaster. Extensive experiments across eight benchmarks verify its superior performance. Further studies indicate that the gains arise primarily from correcting frequency mismatches between historical inputs and future outputs. Additionally, we provide two theoretical justifications for how reconstruction improves forecasting generalization and how alignment increases the mutual information between learned representations and predicted targets. The code is available at https://github.com/TROUBADOUR000/TimeAlign.

We present LightVLA, a simple yet effective differentiable token pruning framework for vision-language-action (VLA) models. While VLA models have shown impressive capability in executing real-world robotic tasks, their deployment on resource-constrained platforms is often bottlenecked by the heavy attention-based computation over large sets of visual tokens. LightVLA addresses this challenge through adaptive, performance-driven pruning of visual tokens: It generates dynamic queries to evaluate visual token importance, and adopts Gumbel softmax to enable differentiable token selection. Through fine-tuning, LightVLA learns to preserve the most informative visual tokens while pruning tokens which do not contribute to task execution, thereby improving efficiency and performance simultaneously. Notably, LightVLA requires no heuristic magic numbers and introduces no additional trainable parameters, making it compatible with modern inference frameworks. Experimental results demonstrate that LightVLA outperforms different VLA models and existing token pruning methods across diverse tasks on the LIBERO benchmark, achieving higher success rates with substantially reduced computational overhead. Specifically, LightVLA reduces FLOPs and latency by 59.1% and 38.2% respectively, with a 2.6% improvement in task success rate. Meanwhile, we also investigate the learnable query-based token pruning method LightVLA* with additional trainable parameters, which also achieves satisfactory performance. Our work reveals that as VLA pursues optimal performance, LightVLA spontaneously learns to prune tokens from a performance-driven perspective. To the best of our knowledge, LightVLA is the first work to apply adaptive visual token pruning to VLA tasks with the collateral goals of efficiency and performance, marking a significant step toward more efficient, powerful and practical real-time robotic systems.

Dynamic nonlinear systems exhibit distortions arising from coupled static and dynamic effects. Their intertwined nature poses major challenges for data-driven modeling. This paper presents a theoretical framework grounded in structured decomposition, variance analysis, and task-centric complexity bounds. The framework employs a directional lower bound on interactions between measurable system components, extending orthogonality in inner product spaces to structurally asymmetric settings. This bound supports variance inequalities for decomposed systems. Key behavioral indicators are introduced along with a memory finiteness index. A rigorous power-based condition establishes a measurable link between finite memory in realizable systems and the First Law of Thermodynamics. This offers a more foundational perspective than classical bounds based on the Second Law. Building on this foundation, we formulate a `Behavioral Uncertainty Principle,' demonstrating that static and dynamic distortions cannot be minimized simultaneously. We identify that real-world systems seem to resist complete deterministic decomposition due to entangled static and dynamic effects. We also present two general-purpose theorems linking function variance to mean-squared Lipschitz continuity and learning complexity. This yields a model-agnostic, task-aware complexity metric, showing that lower-variance components are inherently easier to learn. These insights explain the empirical benefits of structured residual learning, including improved generalization, reduced parameter count, and lower training cost, as previously observed in power amplifier linearization experiments. The framework is broadly applicable and offers a scalable, theoretically grounded approach to modeling complex dynamic nonlinear systems.

Pathological images play an essential role in cancer prognosis, while survival analysis, which integrates computational techniques, can predict critical clinical events such as patient mortality or disease recurrence from whole-slide images (WSIs). Recent advancements in multiple instance learning have significantly improved the efficiency of survival analysis. However, existing methods often struggle to balance the modeling of long-range spatial relationships with local contextual dependencies and typically lack inherent interpretability, limiting their clinical utility. To address these challenges, we propose the Interpretable Pathology Graph-Transformer (IPGPhormer), a novel framework that captures the characteristics of the tumor microenvironment and models their spatial dependencies across the tissue. IPGPhormer uniquely provides interpretability at both tissue and cellular levels without requiring post-hoc manual annotations, enabling detailed analyses of individual WSIs and cross-cohort assessments. Comprehensive evaluations on four public benchmark datasets demonstrate that IPGPhormer outperforms state-of-the-art methods in both predictive accuracy and interpretability. In summary, our method, IPGPhormer, offers a promising tool for cancer prognosis assessment, paving the way for more reliable and interpretable decision-support systems in pathology. The code is publicly available at https://anonymous.4open.science/r/IPGPhormer-6EEB.

Since any ReLU network is piecewise affine, its hidden units can be characterized by their pullbacks through the active subnetwork, i.e., by their gradients (up to bias terms). However, gradients of deeper neurons are notoriously misaligned, which obscures the network's internal representations. We posit that models do align gradients with data, yet this is concealed by the intrinsic noise of the ReLU hard gating. We validate this intuition by applying soft gating in the backward pass only, reducing the local impact of weakly excited neurons. The resulting modified gradients, which we call "excitation pullbacks", exhibit striking perceptual alignment on a number of ImageNet-pretrained architectures, while the rudimentary pixel-space gradient ascent quickly produces easily interpretable input- and target-specific features. Inspired by these findings, we formulate the "path stability" hypothesis, claiming that the binary activation patterns largely stabilize during training and get encoded in the pre-activation distribution of the final model. When true, excitation pullbacks become aligned with the gradients of a kernel machine that mainly determines the network's decision. This provides a theoretical justification for the apparent faithfulness of the feature attributions based on excitation pullbacks, potentially even leading to mechanistic interpretability of deep models. Incidentally, we give a possible explanation for the effectiveness of Batch Normalization and Deep Features, together with a novel perspective on the network's internal memory and generalization properties. We release the code and an interactive app for easier exploration of the excitation pullbacks.

Counterfactual reasoning aims at answering contrary-to-fact questions like "Would have Alice recovered had she taken aspirin?" and corresponds to the most fine-grained layer of causation. Critically, while many counterfactual statements cannot be falsified--even by randomized experiments--they underpin fundamental concepts like individual-wise fairness. Therefore, providing models to formalize and implement counterfactual beliefs remains a fundamental scientific problem. In the Markovian setting of Pearl's causal framework, we propose an alternative approach to structural causal models to represent counterfactuals compatible with a given causal graphical model. More precisely, we introduce counterfactual models, also called canonical representations of structural causal models. They enable analysts to choose a counterfactual assumption via random-process probability distributions with preassigned marginals and characterize the counterfactual equivalence class of structural causal models. Using these representations, we present a normalization procedure to disentangle the (arbitrary and unfalsifiable) counterfactual choice from the (typically testable) interventional constraints. In contrast to structural causal models, this allows to implement many counterfactual assumptions while preserving interventional knowledge, and does not require any estimation step at the individual-counterfactual layer: only to make a choice. Finally, we illustrate the specific role of counterfactuals in causality and the benefits of our approach on theoretical and numerical examples.

Dimensionality reduction via linear sketching is a powerful and widely used technique, but it is known to be vulnerable to adversarial inputs. We study the black-box adversarial setting, where a fixed, hidden sketching matrix $A \in R^{k \times n}$ maps high-dimensional vectors $v \in R^n$ to lower-dimensional sketches $A v \in R^k$, and an adversary can query the system to obtain approximate $\ell_2$-norm estimates that are computed from the sketch. We present a universal, nonadaptive attack that, using $\tilde{O}(k^2)$ queries, either causes a failure in norm estimation or constructs an adversarial input on which the optimal estimator for the query distribution (used by the attack) fails. The attack is completely agnostic to the sketching matrix and to the estimator: it applies to any linear sketch and any query responder, including those that are randomized, adaptive, or tailored to the query distribution. Our lower bound construction tightly matches the known upper bounds of $\tildeΩ(k^2)$, achieved by specialized estimators for Johnson Lindenstrauss transforms and AMS sketches. Beyond sketching, our results uncover structural parallels to adversarial attacks in image classification, highlighting fundamental vulnerabilities of compressed representations.

We study the problem of releasing a differentially private (DP) synthetic graph $G'$ that well approximates the triangle-motif sizes of all cuts of any given graph $G$, where a motif in general refers to a frequently occurring subgraph within complex networks. Non-private versions of such graphs have found applications in diverse fields such as graph clustering, graph sparsification, and social network analysis. Specifically, we present the first $(\varepsilon,δ)$-DP mechanism that, given an input graph $G$ with $n$ vertices, $m$ edges and local sensitivity of triangles $\ell_{3}(G)$, generates a synthetic graph $G'$ in polynomial time, approximating the triangle-motif sizes of all cuts $(S,V\setminus S)$ of the input graph $G$ up to an additive error of $\tilde{O}(\sqrt{m\ell_{3}(G)}n/\varepsilon^{3/2})$. Additionally, we provide a lower bound of $Ω(\sqrt{mn}\ell_{3}(G)/\varepsilon)$ on the additive error for any DP algorithm that answers the triangle-motif size queries of all $(S,T)$-cut of $G$. Finally, our algorithm generalizes to weighted graphs, and our lower bound extends to any $K_h$-motif cut for any constant $h\geq 2$.

Abstract-- Understanding open-world semantics is critical for robotic planning and control, particularly in unstructured outdoor environments. Existing vision-language mapping approaches typically rely on object-centric segmentation priors, which often fail outdoors due to semantic ambiguities and indistinct class boundaries. We propose OT AS--an Open-vocabulary T oken Alignment method for outdoor Segmentation. OT AS addresses the limitations of open-vocabulary segmentation models by extracting semantic structure directly from the output tokens of pre-trained vision models. By clustering semantically similar structures across single and multiple views and grounding them in language, OT AS reconstructs a geometrically consistent feature field that supports open-vocabulary segmentation queries. Our method operates in a zero-shot manner, without scene-specific fine-tuning, and achieves real-time performance of up to 17 fps. On the Off-Road Freespace Detection dataset, OT AS yields a modest IoU improvement over fine-tuned and open-vocabulary 2D segmentation baselines. In 3D segmentation on T artanAir, it achieves up to a 151% relative IoU improvement compared to existing open-vocabulary mapping methods. Real-world reconstructions further demonstrate OT AS' applicability to robotic deployment. Understanding the open world through semantics is a key challenge for robotics. Vision-Language Models (VLMs), that ground vision in language, have recently been shown to effectively provide semantics for mapping to facilitate task planning and navigation [1], [2]. However, open-vocabulary semantic mapping methods [3], [4], [5] rely on segmentation priors from general-purpose models to reason about the environment.