Formal theories of arithmetic have traditionally been based on either classical or intuitionistic logic, leading to the development of Peano and Heyting arithmetic, respectively. We propose to use $\mu$MALL as a formal theory of arithmetic based on linear logic. This formal system is presented as a sequent calculus proof system that extends the standard proof system for multiplicative-additive linear logic (MALL) with the addition of the logical connectives universal and existential quantifiers (first-order quantifiers), term equality and non-equality, and the least and greatest fixed point operators. We first demonstrate how functions defined using $\mu$MALL relational specifications can be computed using a simple proof search algorithm. By incorporating weakening and contraction into $\mu$MALL, we obtain $\mu$LK+, a natural candidate for a classical sequent calculus for arithmetic. While important proof theory results are still lacking for $\mu$LK+ (including cut-elimination and the completeness of focusing), we prove that $\mu$LK+ is consistent and that it contains Peano arithmetic. We also prove some conservativity results regarding $\mu$LK+ over $\mu$MALL.
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Predicting future dynamics is crucial for applications like autonomous driving and robotics, where understanding the environment is key. Existing pixel-level methods are computationally expensive and often focus on irrelevant details. To address these challenges, we introduce $\texttt{DINO-Foresight}$, a novel framework that operates in the semantic feature space of pretrained Vision Foundation Models (VFMs). Our approach trains a masked feature transformer in a self-supervised manner to predict the evolution of VFM features over time. By forecasting these features, we can apply off-the-shelf, task-specific heads for various scene understanding tasks. In this framework, VFM features are treated as a latent space, to which different heads attach to perform specific tasks for future-frame analysis. Extensive experiments show that our framework outperforms existing methods, demonstrating its robustness and scalability. Additionally, we highlight how intermediate transformer representations in $\texttt{DINO-Foresight}$ improve downstream task performance, offering a promising path for the self-supervised enhancement of VFM features. We provide the implementation code at //github.com/Sta8is/DINO-Foresight .
A probabilistic framework to study the dependence structure induced by deterministic discrete-time state-space systems between input and output processes is introduced. General sufficient conditions are formulated under which output processes exist and are unique once an input process has been fixed, a property that in the deterministic state-space literature is known as the echo state property. When those conditions are satisfied, the given state-space system becomes a generative model for probabilistic dependences between two sequence spaces. Moreover, those conditions guarantee that the output depends continuously on the input when using the Wasserstein metric. The output processes whose existence is proved are shown to be causal in a specific sense and to generalize those studied in purely deterministic situations. The results in this paper constitute a significant stochastic generalization of sufficient conditions for the deterministic echo state property to hold, in the sense that the stochastic echo state property can be satisfied under contractivity conditions that are strictly weaker than those in deterministic situations. This means that state-space systems can induce a purely probabilistic dependence structure between input and output sequence spaces even when there is no functional relation between those two spaces.
A convergent numerical method for $\alpha$-dissipative solutions of the Hunter-Saxton equation is derived. The method is based on applying a tailor-made projection operator to the initial data, and then solving exactly using the generalized method of characteristics. The projection step is the only step that introduces any approximation error. It is therefore crucial that its design ensures not only a good approximation of the initial data, but also that errors due to the energy dissipation at later times remain small. Furthermore, it is shown that the main quantity of interest, the wave profile, converges in $L^{\infty}$ for all $t \geq 0$, while a subsequence of the energy density converges weakly for almost every time.
We study the problem of drawing samples from a logconcave distribution truncated on a polytope, motivated by computational challenges in Bayesian statistical models with indicator variables, such as probit regression. Building on interior point methods and the Dikin walk for sampling from uniform distributions, we analyze the mixing time of regularized Dikin walks. Our contributions are threefold. First, for a logconcave and log-smooth distribution with condition number $\kappa$, truncated on a polytope in $\mathbb{R}^n$ defined with $m$ linear constraints, we prove that the soft-threshold Dikin walk mixes in $\widetilde{O}((m+\kappa)n)$ iterations from a warm initialization. It improves upon prior work which required the polytope to be bounded and involved a bound dependent on the radius of the bounded region. Moreover, we introduce the regularized Dikin walk using Lewis weights for approximating the John ellipsoid. We show that it mixes in $\widetilde{O}((n^{2.5}+\kappa n)$. Second, we extend the mixing time guarantees mentioned above to weakly log-concave distributions truncated on polytopes, provided that they have a finite covariance matrix. Third, going beyond worst-case mixing time analysis, we demonstrate that soft-threshold Dikin walk can mix significantly faster when only a limited number of constraints intersect the high-probability mass of the distribution, improving the $\widetilde{O}((m+\kappa)n)$ upper bound to $\widetilde{O}(m + \kappa n)$. Additionally, per-iteration complexity of regularized Dikin walk and ways to generate a warm initialization are discussed to facilitate practical implementation.
Language model approaches have recently been integrated into binary analysis tasks, such as function similarity detection and function signature recovery. These models typically employ a two-stage training process: pre-training via Masked Language Modeling (MLM) on machine code and fine-tuning for specific tasks. While MLM helps to understand binary code structures, it ignores essential code characteristics, including control and data flow, which negatively affect model generalization. Recent work leverages domain-specific features (e.g., control flow graphs and dynamic execution traces) in transformer-based approaches to improve binary code semantic understanding. However, this approach involves complex feature engineering, a cumbersome and time-consuming process that can introduce predictive uncertainty when dealing with stripped or obfuscated code, leading to a performance drop. In this paper, we introduce ProTST, a novel transformer-based methodology for binary code embedding. ProTST employs a hierarchical training process based on a unique tree-like structure, where knowledge progressively flows from fundamental tasks at the root to more specialized tasks at the leaves. This progressive teacher-student paradigm allows the model to build upon previously learned knowledge, resulting in high-quality embeddings that can be effectively leveraged for diverse downstream binary analysis tasks. The effectiveness of ProTST is evaluated in seven binary analysis tasks, and the results show that ProTST yields an average validation score (F1, MRR, and Recall@1) improvement of 14.8% compared to traditional two-stage training and an average validation score of 10.7% compared to multimodal two-stage frameworks.
Efficient algorithms for solving the Smallest Enclosing Sphere (SES) problem, such as Welzl's algorithm, often fail to handle degenerate subsets of points in 3D space. Degeneracies and ill-posed configurations present significant challenges, leading to failures in convergence, inaccuracies or increased computational cost in such cases. Existing improvements to these algorithms, while addressing some of these issues, are either computationally expensive or only partially effective. In this paper, we propose a hybrid algorithm designed to mitigate degeneracy while maintaining an overall computational complexity of $O(N)$. By combining robust preprocessing steps with efficient core computations, our approach avoids the pitfalls of degeneracy without sacrificing scalability. The proposed method is validated through theoretical analysis and experimental results, demonstrating its efficacy in addressing degenerate configurations and achieving high efficiency in practice.
Methods of computational quantum chemistry provide accurate approximations of molecular properties crucial for computer-aided drug discovery and other areas of chemical science. However, high computational complexity limits the scalability of their applications. Neural network potentials (NNPs) are a promising alternative to quantum chemistry methods, but they require large and diverse datasets for training. This work presents a new dataset and benchmark called $\nabla^2$DFT that is based on the nablaDFT. It contains twice as much molecular structures, three times more conformations, new data types and tasks, and state-of-the-art models. The dataset includes energies, forces, 17 molecular properties, Hamiltonian and overlap matrices, and a wavefunction object. All calculations were performed at the DFT level ($\omega$B97X-D/def2-SVP) for each conformation. Moreover, $\nabla^2$DFT is the first dataset that contains relaxation trajectories for a substantial number of drug-like molecules. We also introduce a novel benchmark for evaluating NNPs in molecular property prediction, Hamiltonian prediction, and conformational optimization tasks. Finally, we propose an extendable framework for training NNPs and implement 10 models within it.
User interactions in recommender systems are inherently complex, often involving behaviors that go beyond simple acceptance or rejection. One particularly common behavior is hesitation, where users deliberate over recommended items, signaling uncertainty. Our large-scale surveys, with 6,644 and 3,864 responses respectively, confirm that hesitation is not only widespread but also has a profound impact on user experiences. When users spend additional time engaging with content they are ultimately uninterested in, this can lead to negative emotions, a phenomenon we term as tolerance. The surveys reveal that such tolerance behaviors often arise after hesitation and can erode trust, satisfaction, and long-term loyalty to the platform. For instance, a click might reflect a need for more information rather than genuine interest, and prolonged exposure to unsuitable content amplifies frustration. This misalignment between user intent and system interpretation introduces noise into recommendation training, resulting in suggestions that increase uncertainty and disengagement. To address these issues, we identified signals indicative of tolerance behavior and analyzed datasets from both e-commerce and short-video platforms. The analysis shows a strong correlation between increased tolerance behavior and decreased user activity. We integrated these insights into the training process of a recommender system for a major short-video platform. Results from four independent online A/B experiments demonstrated significant improvements in user retention, achieved with minimal additional computational costs. These findings underscore the importance of recognizing hesitation as a ubiquitous user behavior and addressing tolerance to enhance satisfaction, build trust, and sustain long-term engagement in recommender systems.
Accurately measuring the geometry and spatially-varying reflectance of real-world objects is a complex task due to their intricate shapes formed by concave features, hollow engravings and diverse surfaces, resulting in inter-reflection and occlusion when photographed. Moreover, issues like lens flare and overexposure can arise from interference from secondary reflections and limitations of hardware even in professional studios. In this paper, we propose a novel approach using polarized reflectance field capture and a comprehensive statistical analysis algorithm to obtain highly accurate surface normals (within 0.1mm/px) and spatially-varying reflectance data, including albedo, specular separation, roughness, and anisotropy parameters for realistic rendering and analysis. Our algorithm removes image artifacts via analytical modeling and further employs both an initial step and an optimization step computed on the whole image collection to further enhance the precision of per-pixel surface reflectance and normal measurement. We showcase the captured shapes and reflectance of diverse objects with a wide material range, spanning from highly diffuse to highly glossy - a challenge unaddressed by prior techniques. Our approach enhances downstream applications by offering precise measurements for realistic rendering and provides a valuable training dataset for emerging research in inverse rendering. We will release the polarized reflectance fields of several captured objects with this work.
As data-privacy requirements are becoming increasingly stringent and statistical models based on sensitive data are being deployed and used more routinely, protecting data-privacy becomes pivotal. Partial Least Squares (PLS) regression is the premier tool for building such models in analytical chemistry, yet it does not inherently provide privacy guarantees, leaving sensitive (training) data vulnerable to privacy attacks. To address this gap, we propose an $(\epsilon, \delta)$-differentially private PLS (edPLS) algorithm, which integrates well-studied and theoretically motivated Gaussian noise-adding mechanisms into the PLS algorithm to ensure the privacy of the data underlying the model. Our approach involves adding carefully calibrated Gaussian noise to the outputs of four key functions in the PLS algorithm: the weights, scores, $X$-loadings, and $Y$-loadings. The noise variance is determined based on the global sensitivity of each function, ensuring that the privacy loss is controlled according to the $(\epsilon, \delta)$-differential privacy framework. Specifically, we derive the sensitivity bounds for each function and use these bounds to calibrate the noise added to the model components. Experimental results demonstrate that edPLS effectively renders privacy attacks, aimed at recovering unique sources of variability in the training data, ineffective. Application of edPLS to the NIR corn benchmark dataset shows that the root mean squared error of prediction (RMSEP) remains competitive even at strong privacy levels (i.e., $\epsilon=1$), given proper pre-processing of the corresponding spectra. These findings highlight the practical utility of edPLS in creating privacy-preserving multivariate calibrations and for the analysis of their privacy-utility trade-offs.
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