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Density Functional Theory (DFT) is used extensively in the computation of electronic properties of matter, with various applications. Approximating the exchange-correlation (XC) functional is the key to the Kohn-Sham DFT approach, the basis of most DFT calculations. The choice of this density functional approximation (DFA) depends crucially on the particular system under study, which has resulted in the development of hundreds of DFAs. Though the exact density functional is not known, researchers have discovered analytical properties of this exact functional. Furthermore, these exact conditions are used when designing DFAs. We present XCVerifier, the first approach for verifying whether a DFA implementation satisfies the DFT exact conditions. XCVerifier was evaluated on five DFAs from the popular Libxc library and seven exact conditions from recent work. XCVerifier was able to verify or find violations for a majority of the DFA/condition pairs, demonstrating the feasibility of using formal methods to verify DFA implementations.

The cylindrical algebraic covering method was originally proposed to decide the satisfiability of a set of non-linear real arithmetic constraints. We reformulate and extend the cylindrical algebraic covering method to allow for checking the truth of arbitrary non-linear arithmetic formulas, adding support for both quantifiers and Boolean structure. Furthermore, we also propose a variant to perform quantifier elimination on such formulas. After introducing the algorithm, we elaborate on various extensions, optimizations and heuristics. Finally, we present an experimental evaluation of our implementation and provide a comparison with state-of-the-art SMT solvers and quantifier elimination tools.

Large Language Models (LLMs) have demonstrated unparalleled effectiveness in various NLP tasks, and integrating LLMs with automatic speech recognition (ASR) is becoming a mainstream paradigm. Building upon this momentum, our research delves into an in-depth examination of this paradigm on a large open-source Chinese dataset. Specifically, our research aims to evaluate the impact of various configurations of speech encoders, LLMs, and projector modules in the context of the speech foundation encoder-LLM ASR paradigm. Furthermore, we introduce a three-stage training approach, expressly developed to enhance the model's ability to align auditory and textual information. The implementation of this approach, alongside the strategic integration of ASR components, enabled us to achieve the SOTA performance on the AISHELL-1, Test_Net, and Test_Meeting test sets. Our analysis presents an empirical foundation for future research in LLM-based ASR systems and offers insights into optimizing performance using Chinese datasets. We will publicly release all scripts used for data preparation, training, inference, and scoring, as well as pre-trained models and training logs to promote reproducible research.

Unlabeled sensing is the problem of solving a linear system of equations, where the right-hand-side vector is known only up to a permutation. In this work, we study fields of rational functions related to symmetric polynomials and their images under a linear projection of the variables; as a consequence, we establish that the solution to an n-dimensional unlabeled sensing problem with generic data can be obtained as the unique solution to a system of n + 1 polynomial equations of degrees 1, 2, . . . , n + 1 in n unknowns. Besides the new theoretical insights, this development offers the potential for scaling up algebraic unlabeled sensing algorithms.

Deriving a priority vector from a pairwise comparison matrix (PCM) is a crucial step in the Analytical Hierarchy Process (AHP). Although there exists a priority vector that satisfies the conditions of order preservation (COP), the priority vectors obtained through existing prioritization methods frequently violate these conditions, resulting in numerous COP violations. To address this issue, this paper introduces a novel procedure to manage COP violations in AHP. Firstly, we prove that the index-exchangeability condition is both a necessary and sufficient condition for determining whether a priority vector satisfies COP. This enables the direct detection of COP violations, relying solely on the pairwise comparison preferences of decision-makers, rather than the prioritization methods utilized. Subsequently, we propose the Minimal Number of Violations and Deviations Method (MNVDM) model, which aims to derive a priority vector with the minimal number of COP violations. In particular, the MNVDM can obtain a violation-free priority vector when the PCM meets the index exchangeability conditions. Furthermore, an optimization model based on minimizing information loss is designed to ensure the COP by revising the preferences when the index-exchangeability conditions are violated. Finally, the feasibility and efficiency of the proposed models are validated through numerical examples and Monte Carlo simulation experiments. Our implementation is available at: //github.com/Tommytutu/COP.

Artificial Intelligence (AI) research often aims to develop models that generalize reliably across complex datasets, yet this remains challenging in fields where data is scarce, intricate, or inaccessible. This paper introduces a novel approach leveraging three generative models of varying complexity to synthesize one of the most demanding structured datasets: Malicious Network Traffic. Our approach transforms numerical data into text, reframing data generation as a language modeling task, which enhances data regularization and significantly improves generalization and the quality of the synthetic data. Extensive statistical analyses demonstrate that our method surpasses state-of-the-art generative models in producing high-fidelity synthetic data. Additionally, we conduct a comprehensive study on synthetic data applications, effectiveness, and evaluation strategies, offering valuable insights into its role across various domains. Our code and pre-trained models are openly accessible at //github.com/Moe-Zbeeb/Exploring-the-landscape-for-generative-models-for-specialized-data-generation, enabling further exploration and application of our methodology. Index Terms: Data synthesis, machine learning, traffic generation, privacy-preserving data, generative models.

Modern optimizers such as AdamW, equipped with momentum and adaptive learning rate, are designed to escape local minima and explore the vast parameter space. This exploration is beneficial for finding good loss basins when training from scratch. It is not necessarily ideal when resuming from a powerful foundation model because it can lead to large deviations from the pre-trained initialization and, consequently, worse robustness and generalization. At the same time, strong regularization on all parameters can lead to under-fitting. We hypothesize that selectively regularizing the parameter space is the key to fitting and retraining the pre-trained knowledge. This paper proposes a new weight decay technique, Selective Projection Decay (SPD), that selectively imposes a strong penalty on certain layers while allowing others to change freely. Intuitively, SPD expands and contracts the parameter search space for layers with consistent and inconsistent loss reduction, respectively. Experimentally, when equipped with SPD, Adam consistently provides better in-distribution generalization and out-of-distribution robustness performance on multiple popular vision and language benchmarks. Code available at~\url{//github.com/GT-RIPL/Selective-Projection-Decay.git}

Tiny Machine Learning (TinyML) has become a growing field in on-device processing for Internet of Things (IoT) applications, capitalizing on AI algorithms that are optimized for their low complexity and energy efficiency. These algorithms are designed to minimize power and memory footprints, making them ideal for the constraints of IoT devices. Within this domain, Spiking Neural Networks (SNNs) stand out as a cutting-edge solution for TinyML, owning to their event-driven processing paradigm which offers an efficient method of handling dataflow. This paper presents a novel SNN architecture based on the 1st Order Leaky Integrate-and-Fire (LIF) neuron model to efficiently deploy vision-based ML algorithms on TinyML systems. A hardware-friendly LIF design is also proposed, and implemented on a Xilinx Artix-7 FPGA. To evaluate the proposed model, a collision avoidance dataset is considered as a case study. The proposed SNN model is compared to the state-of-the-art works and Binarized Convolutional Neural Network (BCNN) as a baseline. The results show the proposed approach is 86% more energy efficient than the baseline.

Human perception is inherently multimodal. We integrate, for instance, visual, proprioceptive and tactile information into one experience. Hence, multimodal learning is of importance for building robotic systems that aim at robustly interacting with the real world. One potential model that has been proposed for multimodal integration is the multimodal variational autoencoder. A variational autoencoder (VAE) consists of two networks, an encoder that maps the data to a stochastic latent space and a decoder that reconstruct this data from an element of this latent space. The multimodal VAE integrates inputs from different modalities at two points in time in the latent space and can thereby be used as a controller for a robotic agent. Here we use this architecture and introduce information-theoretic measures in order to analyze how important the integration of the different modalities are for the reconstruction of the input data. Therefore we calculate two different types of measures, the first type is called single modality error and assesses how important the information from a single modality is for the reconstruction of this modality or all modalities. Secondly, the measures named loss of precision calculate the impact that missing information from only one modality has on the reconstruction of this modality or the whole vector. The VAE is trained via the evidence lower bound, which can be written as a sum of two different terms, namely the reconstruction and the latent loss. The impact of the latent loss can be weighted via an additional variable, which has been introduced to combat posterior collapse. Here we train networks with four different weighting schedules and analyze them with respect to their capabilities for multimodal integration.

We introduce group crosscoders, an extension of crosscoders that systematically discover and analyse symmetrical features in neural networks. While neural networks often develop equivariant representations without explicit architectural constraints, understanding these emergent symmetries has traditionally relied on manual analysis. Group crosscoders automate this process by performing dictionary learning across transformed versions of inputs under a symmetry group. Applied to InceptionV1's mixed3b layer using the dihedral group $\mathrm{D}_{32}$, our method reveals several key insights: First, it naturally clusters features into interpretable families that correspond to previously hypothesised feature types, providing more precise separation than standard sparse autoencoders. Second, our transform block analysis enables the automatic characterisation of feature symmetries, revealing how different geometric features (such as curves versus lines) exhibit distinct patterns of invariance and equivariance. These results demonstrate that group crosscoders can provide systematic insights into how neural networks represent symmetry, offering a promising new tool for mechanistic interpretability.