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Long chain-of-thought (CoT) traces are widely used as supervision for reasoning-oriented LLM SFT, yet answer-correct traces can still lead to markedly different fine-tuning outcomes. We study post-conclusion continuation in answer-correct long-CoT data: a continuation where the answer appears sufficiently supported, but the trace continues with additional reasoning that remains in the supervised target. To test its training effect, we use a delete-only editor to construct answer-preserving suffix removal and compare CoT-based SFT on the original and processed traces. We observe improved SFT outcomes after removing the editor-identified post-conclusion continuation, suggesting that this continuation is harmful to training in our setting. We therefore refer to this empirically supported phenomenon as harmful continuation. Beyond this intervention, we further characterize the removed post-conclusion continuation through uncertainty and hidden-state progress. We observe persistent local uncertainty together with weakened terminal-directional progress, forming an uncertainty--geometry mismatch. Finally, we instantiate Harmful Continuation Cut (HCC), a lightweight boundary proxy that app

Multistable dynamical systems are ever-prevalent, used to model for example ecosystems, power grids, climate elements, neurons, and more. When perturbed, such systems may ``tip'' from one state of operation to another, often with abrupt, irreversible, and high-impact consequences in each context. Traditionally, these systems are analysed via bifurcation diagrams, the result of a process we refer to as \emph{local continuation}, as it only captures the linear (local) system response to infinitesimal perturbations. Local continuation requires substantial expertise, constant interventions, and may yield inaccurate assessment of the system's response to large perturbations that is crucial for tipping analysis. To address some inherent challenges of local continuation and to provide fundamentally new information during a continuation, this paper introduces \emph{global continuation} as a complement suitable for the study of multistability, critical transitions and real-world-oriented applications. Global continuation finds and continues in parallel (practically) all system attractors and their response to finite perturbations by synthesising information from the whole state space, while

Continuous-variable quantum thermodynamics in the Gaussian regime provides a promising framework for investigating the energetic role of quantum correlations, particularly in optical systems. In this work, we introduce an entropy-free criterion for entanglement detection in bipartite Gaussian states, rooted in a distinct thermodynamic quantity: ergotropy--the maximum extractable work via unitary operations. By defining the relative ergotropic gap, which quantifies the disparity between global and local ergotropy, we derive two independent analytical bounds that distinguish entangled from separable states. These bounds coincide for a broad class of quantum states, making the criterion both necessary and sufficient in such cases. Unlike entropy-based measures, our ergotropic approach captures fundamentally different aspects of quantum correlations and entanglement, particularly in mixed continuous-variable systems. We also extend our analysis beyond the Gaussian regime to certain non-Gaussian states and observe that Gaussian ergotropy continues to reflect thermodynamic signatures in entangled states, albeit with some limitations. These findings establish a direct operational link bet

In this note we show that the support of a locally $k$-uniform measure in $\mathbb R^{n+1}$ satisfies a kind of unique continuation property. As a consequence, we show that locally uniformly distributed measures satisfy a weaker unique continuation property. This continues work of Kirchheim and Preiss (Math. Scand. 2002) and David, Kenig and Toro (Comm. Pure Appl. Math. 2001) and lends additional evidence to the conjecture proposed by Kowalski and Preiss (J. Reine Angew. Math. 1987) that each connected component of the support of a locally $n$-uniform measure in $\mathbb R^{n+1}$ is contained in the zero set of a quadratic polynomial.

Software vulnerabilities are constantly being reported and exploited in software products, causing significant impacts on society. In recent years, the main approach to vulnerability detection, fuzzing, has been integrated into the continuous integration process to run in short and frequent cycles. This continuous fuzzing allows for fast identification and remediation of vulnerabilities during the development process. Despite adoption by thousands of projects, however, it is unclear how continuous fuzzing contributes to vulnerability detection. This study aims to elucidate the role of continuous fuzzing in vulnerability detection. Specifically, we investigate the coverage and the total number of fuzzing sessions when fuzzing bugs are discovered. We collect issue reports, coverage reports, and fuzzing logs from OSS-Fuzz, an online service provided by Google that performs fuzzing during continuous integration. Through an empirical study of a total of approximately 1.12 million fuzzing sessions from 878 projects participating in OSS-Fuzz, we reveal that (i) a substantial number of fuzzing bugs exist prior to the integration of continuous fuzzing, leading to a high detection rate in th

Deep representation learning methods struggle with continual learning, suffering from both catastrophic forgetting of useful units and loss of plasticity, often due to rigid and unuseful units. While many methods address these two issues separately, only a few currently deal with both simultaneously. In this paper, we introduce Utility-based Perturbed Gradient Descent (UPGD) as a novel approach for the continual learning of representations. UPGD combines gradient updates with perturbations, where it applies smaller modifications to more useful units, protecting them from forgetting, and larger modifications to less useful units, rejuvenating their plasticity. We use a challenging streaming learning setup where continual learning problems have hundreds of non-stationarities and unknown task boundaries. We show that many existing methods suffer from at least one of the issues, predominantly manifested by their decreasing accuracy over tasks. On the other hand, UPGD continues to improve performance and surpasses or is competitive with all methods in all problems. Finally, in extended reinforcement learning experiments with PPO, we show that while Adam exhibits a performance drop after

Feedbacks between evolution and ecology are ubiquitous, with ecological interactions determining which mutants are successful, and these mutants in turn modifying community structure. We study the evolutionary dynamics of several ecological models with overlapping niches, including consumer resource and Lotka-Volterra models. Evolution is assumed slow and extinctions are permanent, with ecological dynamics reaching a stable fixed point between introductions of invaders or mutants. When new strains are slowly added to the community, the ecosystem converges, after an initial evolutionary transient, to a diverse eco-evolutionary steady state. In this "Red Queen" phase of continual evolution, the biodiversity continues to turn over without the invasion probability of new variants getting any smaller. For resource-mediated interactions, the Red Queen phase obtains for any amount of asymmetry in the interactions between strains, and is robust to "general fitness" differences in the intrinsic growth rates of strains. Via a dynamical mean field theory framework valid for high-dimensional phenotype space, we analytically characterize the Red Queen eco-evolutionary steady state in a particul

As robotics continues to advance, the need for adaptive and continuously-learning embodied agents increases, particularly in the realm of assistance robotics. Quick adaptability and long-term information retention are essential to operate in dynamic environments typical of humans' everyday lives. A lifelong learning paradigm is thus required, but it is scarcely addressed by current robotics literature. This study empirically investigates the impact of catastrophic forgetting and the effectiveness of knowledge transfer in neural networks trained continuously in an embodied setting. We focus on the task of visual odometry, which holds primary importance for embodied agents in enabling their self-localization. We experiment on the simple continual scenario of discrete transitions between indoor locations, akin to a robot navigating different apartments. In this regime, we observe initial satisfactory performance with high transferability between environments, followed by a specialization phase where the model prioritizes current environment-specific knowledge at the expense of generalization. Conventional regularization strategies and increased model capacity prove ineffective in miti

The continued fraction mapping maps a number in the interval $[0,1)$ to the sequence of its partial quotients. When restricted to the set of irrationals, which is a subspace of the Euclidean space $\mathbb{R}$, the continued fraction mapping is a homeomorphism onto the product space $\mathbb{N}^{\mathbb{N}}$, where $\mathbb{N}$ is a discrete space. In this short note, we examine the continuity of the continued fraction mapping, addressing both irrational and rational points of the unit interval.

We construct a monotone, continuous, but not absolutely continuous function whose minimal modulus of continuity is absolutely continuous. In particular, we establish that there is no equivalence between the absolute continuity of a function and the absolute continuity of its modulus of continuity, in contrast with a well-known property of Lipschitz functions.

As the application space of language models continues to evolve, a natural question to ask is how we can quickly adapt models to new tasks. We approach this classic question from a continual learning perspective, in which we aim to continue fine-tuning models trained on past tasks on new tasks, with the goal of "transferring" relevant knowledge. However, this strategy also runs the risk of doing more harm than good, i.e., negative transfer. In this paper, we construct a new benchmark of task sequences that target different possible transfer scenarios one might face, such as a sequence of tasks with high potential of positive transfer, high potential for negative transfer, no expected effect, or a mixture of each. An ideal learner should be able to maximally exploit information from all tasks that have any potential for positive transfer, while also avoiding the negative effects of any distracting tasks that may confuse it. We then propose a simple, yet effective, learner that satisfies many of our desiderata simply by leveraging a selective strategy for initializing new models from past task checkpoints. Still, limitations remain, and we hope this benchmark can help the community t

Despite the extensive investment and impressive recent progress at reasoning by similarity, deep learning continues to struggle with more complex forms of reasoning such as non-monotonic and commonsense reasoning. Non-monotonicity is a property of non-classical reasoning typically seen in commonsense reasoning, whereby a reasoning system is allowed (differently from classical logic) to jump to conclusions which may be retracted later, when new information becomes available. Neural-symbolic systems such as Logic Tensor Networks (LTN) have been shown to be effective at enabling deep neural networks to achieve reasoning capabilities. In this paper, we show that by combining a neural-symbolic system with methods from continual learning, LTN can obtain a higher level of accuracy when addressing non-monotonic reasoning tasks. Continual learning is added to LTNs by adopting a curriculum of learning from knowledge and data with recall. We call this process Continual Reasoning, a new methodology for the application of neural-symbolic systems to reasoning tasks. Continual Reasoning is applied to a prototypical non-monotonic reasoning problem as well as other reasoning examples. Experimentati

Keeping large foundation models up to date on latest data is inherently expensive. To avoid the prohibitive costs of constantly retraining, it is imperative to continually train these models. This problem is exacerbated by the lack of any large scale continual learning benchmarks or baselines. We introduce the first set of web-scale Time-Continual (TiC) benchmarks for training vision-language models: TiC-DataComp, TiC-YFCC, and TiC-Redcaps. TiC-DataComp, our largest dataset, contains over 12.7B timestamped image-text pairs spanning 9 years (2014-2022). We first use our benchmarks to curate various dynamic evaluations to measure temporal robustness of existing models. We show OpenAI's CLIP (trained on data up to 2020) loses $\approx 8\%$ zero-shot accuracy on our curated retrieval task from 2021-2022 compared with more recently trained models in OpenCLIP repository. We then study how to efficiently train models on time-continuous data. We demonstrate that a simple rehearsal-based approach that continues training from the last checkpoint and replays old data reduces compute by $2.5\times$ when compared to the standard practice of retraining from scratch. Code is available at https://

The Continuous software engineering is a collaborative software development environment which offers the continues development and deployment of quality software project within short time. The Continuous software engineering practices are not yet mature enough, and the software organizations hesitate to adopt it. This study aims: (1) to explore the Continuous software engineering challenges by conducting systematic literature review (SLR) and to get the insight of industry experts via questionnaire survey study; (2) to prioritize the investigated challenges using fuzzy analytical hierarchy process (FAHP). The study findings provides the set of critical challenges faced by the software organizations while adopting Continuous software engineering and a prioritization based taxonomy of the Continuous software engineering challenges. The application of FAHP is novel in this research area as it assists in addressing the vagueness of practitioners concerning the influencing factors of Continuous software engineering. We believe that the finding of this study will serve as a body of knowledge for real world practitioners and researchers to revise and develop the new strategies for the suc

A system having macroscopic patches in different topological phases have no well-defined global topological invariant. To treat such a case, the quantities labeling different areas of the sample according to their topological state are used, dubbed local topological markers. Here we study their dynamics. We concentrate on two quantities, namely local Chern marker and on-site charge induced by an applied magnetic field. We demonstrate that the time-dependent local Chern marker is much more non-local object than equilibrium one. Surprisingly, in large samples driven out of equilibrium, it leads to a simple description of the local Chern marker's dynamics by a local continuity equation. Also, we argue that the connection between the local Chern marker and magnetic-field induced charge known in static holds out of equilibrium in some experimentally relevant systems as well. This gives a clear physical description of the marker's evolution and provides a simple recipe for experimental estimation of the topological marker's value.

Since experiencing domain shifts during test-time is inevitable in practice, test-time adaption (TTA) continues to adapt the model after deployment. Recently, the area of continual and gradual test-time adaptation (TTA) emerged. In contrast to standard TTA, continual TTA considers not only a single domain shift, but a sequence of shifts. Gradual TTA further exploits the property that some shifts evolve gradually over time. Since in both settings long test sequences are present, error accumulation needs to be addressed for methods relying on self-training. In this work, we propose and show that in the setting of TTA, the symmetric cross-entropy is better suited as a consistency loss for mean teachers compared to the commonly used cross-entropy. This is justified by our analysis with respect to the (symmetric) cross-entropy's gradient properties. To pull the test feature space closer to the source domain, where the pre-trained model is well posed, contrastive learning is leveraged. Since applications differ in their requirements, we address several settings, including having source data available and the more challenging source-free setting. We demonstrate the effectiveness of our pr