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In proof-theoretic semantics, meaning is based on inference. It may seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provability in a `base' of atomic rules. Base-extension semantics for classical and intuitionistic propositional logic have been explored by several authors. In this paper, we develop base-extension semantics for the classical propositional modal systems K, KT , K4, and S4, with $\square$ as the primary modal operator. We establish appropriate soundness and completeness theorems and establish the duality between $\square$ and a natural presentation of $\lozenge$. We also show that our semantics is in its current form not complete with respect to euclidean modal logics. Our formulation makes essential use of relational structures on bases.

We propose a new mapping tool for supervised and unsupervised analysis of multivariate binary data with multiple items, questions, or response variables. The mapping assumes an underlying proximity response function, where participants can have multiple reasons to disagree or say ``no'' to a question. The probability to endorse, or to agree with an item depends on an item specific parameter and the distance in a joint space between a point representing the item and a point representing the participant. The item specific parameter defines a circle in the joint space around the location of the item such that for participants positioned within the circle the probability is larger than 0.5. For map estimation, we develop and test an MM-algorithm in which the negative likelihood function is majorized with a weighted least squares function. The weighted least squares function can be minimized with standard algorithms for multidimensional unfolding, except that negative working dissimilarities may occur in the iterative process. To illustrate the new mapping, two empirical data sets are analyzed. The mappings are interpreted in detail and the unsupervised map is compared to a visualization based on correspondence analysis. In a Monte Carlo study, we test the performance of the algorithm in terms of recovery of population parameters and conclude that this recovery is adequate. A second Monte Carlo study investigates the predictive performance of the new mapping compared to a similar mapping with a monotone response function.

This paper addresses the challenge of optimizing meta-parameters (i.e., hyperparameters) in machine learning algorithms, a critical factor influencing training efficiency and model performance. Moving away from the computationally expensive traditional meta-parameter search methods, we introduce MetaOptimize framework that dynamically adjusts meta-parameters, particularly step sizes (also known as learning rates), during training. More specifically, MetaOptimize can wrap around any first-order optimization algorithm, tuning step sizes on the fly to minimize a specific form of regret that accounts for long-term effect of step sizes on training, through a discounted sum of future losses. We also introduce low complexity variants of MetaOptimize that, in conjunction with its adaptability to multiple optimization algorithms, demonstrate performance competitive to those of best hand-crafted learning rate schedules across various machine learning applications.

We introduce NeuralVDB, which improves on an existing industry standard for efficient storage of sparse volumetric data, denoted VDB [Museth 2013], by leveraging recent advancements in machine learning. Our novel hybrid data structure can reduce the memory footprints of VDB volumes by orders of magnitude, while maintaining its flexibility and only incurring small (user-controlled) compression errors. Specifically, NeuralVDB replaces the lower nodes of a shallow and wide VDB tree structure with multiple hierarchical neural networks that separately encode topology and value information by means of neural classifiers and regressors respectively. This approach is proven to maximize the compression ratio while maintaining the spatial adaptivity offered by the higher-level VDB data structure. For sparse signed distance fields and density volumes, we have observed compression ratios on the order of 10x to more than 100x from already compressed VDB inputs, with little to no visual artifacts. Furthermore, NeuralVDB is shown to offer more effective compression performance compared to other neural representations such as Neural Geometric Level of Detail [Takikawa et al. 2021], Variable Bitrate Neural Fields [Takikawa et al. 2022a], and Instant Neural Graphics Primitives [M\"uller et al. 2022]. Finally, we demonstrate how warm-starting from previous frames can accelerate training, i.e., compression, of animated volumes as well as improve temporal coherency of model inference, i.e., decompression.

Multi-sequence magnetic resonance imaging (MRI) has found wide applications in both modern clinical studies and deep learning research. However, in clinical practice, it frequently occurs that one or more of the MRI sequences are missing due to different image acquisition protocols or contrast agent contraindications of patients, limiting the utilization of deep learning models trained on multi-sequence data. One promising approach is to leverage generative models to synthesize the missing sequences, which can serve as a surrogate acquisition. State-of-the-art methods tackling this problem are based on convolutional neural networks (CNN) which usually suffer from spectral biases, resulting in poor reconstruction of high-frequency fine details. In this paper, we propose Conditional Neural fields with Shift modulation (CoNeS), a model that takes voxel coordinates as input and learns a representation of the target images for multi-sequence MRI translation. The proposed model uses a multi-layer perceptron (MLP) instead of a CNN as the decoder for pixel-to-pixel mapping. Hence, each target image is represented as a neural field that is conditioned on the source image via shift modulation with a learned latent code. Experiments on BraTS 2018 and an in-house clinical dataset of vestibular schwannoma patients showed that the proposed method outperformed state-of-the-art methods for multi-sequence MRI translation both visually and quantitatively. Moreover, we conducted spectral analysis, showing that CoNeS was able to overcome the spectral bias issue common in conventional CNN models. To further evaluate the usage of synthesized images in clinical downstream tasks, we tested a segmentation network using the synthesized images at inference.

Randomness supports many critical functions in the field of machine learning (ML) including optimisation, data selection, privacy, and security. ML systems outsource the task of generating or harvesting randomness to the compiler, the cloud service provider or elsewhere in the toolchain. Yet there is a long history of attackers exploiting poor randomness, or even creating it -- as when the NSA put backdoors in random number generators to break cryptography. In this paper we consider whether attackers can compromise an ML system using only the randomness on which they commonly rely. We focus our effort on Randomised Smoothing, a popular approach to train certifiably robust models, and to certify specific input datapoints of an arbitrary model. We choose Randomised Smoothing since it is used for both security and safety -- to counteract adversarial examples and quantify uncertainty respectively. Under the hood, it relies on sampling Gaussian noise to explore the volume around a data point to certify that a model is not vulnerable to adversarial examples. We demonstrate an entirely novel attack, where an attacker backdoors the supplied randomness to falsely certify either an overestimate or an underestimate of robustness for up to 81 times. We demonstrate that such attacks are possible, that they require very small changes to randomness to succeed, and that they are hard to detect. As an example, we hide an attack in the random number generator and show that the randomness tests suggested by NIST fail to detect it. We advocate updating the NIST guidelines on random number testing to make them more appropriate for safety-critical and security-critical machine-learning applications.

TestGen automatically generates unit tests, carved from serialized observations of complex objects, observed during app execution. We describe the development and deployment of TestGen at Meta. In particular, we focus on the scalability challenges overcome during development in order to deploy observation-based test carving at scale in industry. So far, TestGen has landed 518 tests into production, which have been executed 9,617,349 times in continuous integration, finding 5,702 faults. Meta is currently in the process of more widespread deployment. Our evaluation reveals that, when carving its observations from 4,361 reliable end-to-end tests, TestGen was able to generate tests for at least 86\% of the classes covered by end-to-end tests. Testing on 16 Kotlin Instagram app-launch-blocking tasks demonstrated that the TestGen tests would have trapped 13 of these before they became launch blocking.

Self-attention, the core mechanism of transformers, distinguishes them from traditional neural networks and drives their outstanding performance. Towards developing the fundamental optimization principles of self-attention, we investigate the implicit bias of gradient descent (GD) in training a self-attention layer with fixed linear decoder in binary classification. Drawing inspiration from the study of GD in linear logistic regression over separable data, recent work demonstrates that as the number of iterations $t$ approaches infinity, the key-query matrix $W_t$ converges locally (with respect to the initialization direction) to a hard-margin SVM solution $W_{mm}$. Our work enhances this result in four aspects. Firstly, we identify non-trivial data settings for which convergence is provably global, thus shedding light on the optimization landscape. Secondly, we provide the first finite-time convergence rate for $W_t$ to $W_{mm}$, along with quantifying the rate of sparsification in the attention map. Thirdly, through an analysis of normalized GD and Polyak step-size, we demonstrate analytically that adaptive step-size rules can accelerate the convergence of self-attention. Additionally, we remove the restriction of prior work on a fixed linear decoder. Our results reinforce the implicit-bias perspective of self-attention and strengthen its connections to implicit-bias in linear logistic regression, despite the intricate non-convex nature of the former.

We introduce an online mathematical framework for survival analysis, allowing real time adaptation to dynamic environments and censored data. This framework enables the estimation of event time distributions through an optimal second order online convex optimization algorithm-Online Newton Step (ONS). This approach, previously unexplored, presents substantial advantages, including explicit algorithms with non-asymptotic convergence guarantees. Moreover, we analyze the selection of ONS hyperparameters, which depends on the exp-concavity property and has a significant influence on the regret bound. We propose a stochastic approach that guarantees logarithmic stochastic regret for ONS. Additionally, we introduce an adaptive aggregation method that ensures robustness in hyperparameter selection while maintaining fast regret bounds. The findings of this paper can extend beyond the survival analysis field, and are relevant for any case characterized by poor exp-concavity and unstable ONS. Finally, these assertions are illustrated by simulation experiments.

Deep learning constitutes a recent, modern technique for image processing and data analysis, with promising results and large potential. As deep learning has been successfully applied in various domains, it has recently entered also the domain of agriculture. In this paper, we perform a survey of 40 research efforts that employ deep learning techniques, applied to various agricultural and food production challenges. We examine the particular agricultural problems under study, the specific models and frameworks employed, the sources, nature and pre-processing of data used, and the overall performance achieved according to the metrics used at each work under study. Moreover, we study comparisons of deep learning with other existing popular techniques, in respect to differences in classification or regression performance. Our findings indicate that deep learning provides high accuracy, outperforming existing commonly used image processing techniques.