Recent advancements in Mixed Integer Optimization (MIO) algorithms, paired with hardware enhancements, have led to significant speedups in resolving MIO problems. These strategies have been utilized for optimal subset selection, specifically for choosing $k$ features out of $p$ in linear regression given $n$ observations. In this paper, we broaden this method to facilitate cluster-aware regression, where selection aims to choose $\lambda$ out of $K$ clusters in a linear mixed effects (LMM) model with $n_k$ observations for each cluster. Through comprehensive testing on a multitude of synthetic and real datasets, we exhibit that our method efficiently solves problems within minutes. Through numerical experiments, we also show that the MIO approach outperforms both Gaussian- and Laplace-distributed LMMs in terms of generating sparse solutions with high predictive power. Traditional LMMs typically assume that clustering effects are independent of individual features. However, we introduce an innovative algorithm that evaluates cluster effects for new data points, thereby increasing the robustness and precision of this model. The inferential and predictive efficacy of this approach is further illustrated through its application in student scoring and protein expression.
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Biological nervous systems constitute important sources of inspiration towards computers that are faster, cheaper, and more energy efficient. Neuromorphic disciplines view the brain as a coevolved system, simultaneously optimizing the hardware and the algorithms running on it. There are clear efficiency gains when bringing the computations into a physical substrate, but we presently lack theories to guide efficient implementations. Here, we present a principled computational model for neuromorphic systems in terms of spatio-temporal receptive fields, based on affine Gaussian kernels over space and leaky-integrator and leaky integrate-and-fire models over time. Our theory is provably covariant to spatial affine and temporal scaling transformations, and with close similarities to the visual processing in mammalian brains. We use these spatio-temporal receptive fields as a prior in an event-based vision task, and show that this improves the training of spiking networks, which otherwise is known as problematic for event-based vision. This work combines efforts within scale-space theory and computational neuroscience to identify theoretically well-founded ways to process spatio-temporal signals in neuromorphic systems. Our contributions are immediately relevant for signal processing and event-based vision, and can be extended to other processing tasks over space and time, such as memory and control.
The rapid advancement in artificial intelligence (AI), particularly through deep neural networks, has catalyzed significant progress in fields such as vision and text processing. Nonetheless, the pursuit of AI systems that exhibit human-like reasoning and interpretability continues to pose a substantial challenge. The Neural-Symbolic paradigm, which integrates the deep learning prowess of neural networks with the reasoning capabilities of symbolic systems, presents a promising pathway toward developing more transparent and comprehensible AI systems. Within this paradigm, the Knowledge Graph (KG) emerges as a crucial element, offering a structured and dynamic method for representing knowledge through interconnected entities and relationships, predominantly utilizing the triple (subject, predicate, object). This paper explores recent advancements in neural-symbolic integration based on KG, elucidating how KG underpins this integration across three key categories: enhancing the reasoning and interpretability of neural networks through the incorporation of symbolic knowledge (Symbol for Neural), refining the completeness and accuracy of symbolic systems via neural network methodologies (Neural for Symbol), and facilitating their combined application in Hybrid Neural-Symbolic Integration. It highlights current trends and proposes directions for future research in the domain of Neural-Symbolic AI.
The unique solvability and error analysis of the original Lagrange multiplier approach proposed in [8] for gradient flows is studied in this paper. We identify a necessary and sufficient condition that must be satisfied for the nonlinear algebraic equation arising from the original Lagrange multiplier approach to admit a unique solution in the neighborhood of its exact solution, and propose a modified Lagrange multiplier approach so that the computation can continue even if the aforementioned condition is not satisfied. Using Cahn-Hilliard equation as an example, we prove rigorously the unique solvability and establish optimal error estimates of a second-order Lagrange multiplier scheme assuming this condition and that the time step is sufficient small. We also present numerical results to demonstrate that the modified Lagrange multiplier approach is much more robust and can use much larger time step than the original Lagrange multiplier approach.
The evaluation of text-generative vision-language models is a challenging yet crucial endeavor. By addressing the limitations of existing Visual Question Answering (VQA) benchmarks and proposing innovative evaluation methodologies, our research seeks to advance our understanding of these models' capabilities. We propose a novel VQA benchmark based on well-known visual classification datasets which allows a granular evaluation of text-generative vision-language models and their comparison with discriminative vision-language models. To improve the assessment of coarse answers on fine-grained classification tasks, we suggest using the semantic hierarchy of the label space to ask automatically generated follow-up questions about the ground-truth category. Finally, we compare traditional NLP and LLM-based metrics for the problem of evaluating model predictions given ground-truth answers. We perform a human evaluation study upon which we base our decision on the final metric. We apply our benchmark to a suite of vision-language models and show a detailed comparison of their abilities on object, action, and attribute classification. Our contributions aim to lay the foundation for more precise and meaningful assessments, facilitating targeted progress in the exciting field of vision-language modeling.
Training data memorization in language models impacts model capability (generalization) and safety (privacy risk). This paper focuses on analyzing prompts' impact on detecting the memorization of 6 masked language model-based named entity recognition models. Specifically, we employ a diverse set of 400 automatically generated prompts, and a pairwise dataset where each pair consists of one person's name from the training set and another name out of the set. A prompt completed with a person's name serves as input for getting the model's confidence in predicting this name. Finally, the prompt performance of detecting model memorization is quantified by the percentage of name pairs for which the model has higher confidence for the name from the training set. We show that the performance of different prompts varies by as much as 16 percentage points on the same model, and prompt engineering further increases the gap. Moreover, our experiments demonstrate that prompt performance is model-dependent but does generalize across different name sets. A comprehensive analysis indicates how prompt performance is influenced by prompt properties, contained tokens, and the model's self-attention weights on the prompt.
We propose an algorithm to construct optimal exact designs (EDs). Most of the work in the optimal regression design literature focuses on the approximate design (AD) paradigm due to its desired properties, including the optimality verification conditions derived by Kiefer (1959, 1974). ADs may have unbalanced weights, and practitioners may have difficulty implementing them with a designated run size $n$. Some EDs are constructed using rounding methods to get an integer number of runs at each support point of an AD, but this approach may not yield optimal results. To construct EDs, one may need to perform new combinatorial constructions for each $n$, and there is no unified approach to construct them. Therefore, we develop a systematic way to construct EDs for any given $n$. Our method can transform ADs into EDs while retaining high statistical efficiency in two steps. The first step involves constructing an AD by utilizing the convex nature of many design criteria. The second step employs a simulated annealing algorithm to search for the ED stochastically. Through several applications, we demonstrate the utility of our method for various design problems. Additionally, we show that the design efficiency approaches unity as the number of design points increases.
We consider the computation of statistical moments to operator equations with stochastic data. We remark that application of PINNs -- referred to as TPINNs -- allows to solve the induced tensor operator equations under minimal changes of existing PINNs code, and enabling handling of non-linear and time-dependent operators. We propose two types of architectures, referred to as vanilla and multi-output TPINNs, and investigate their benefits and limitations. Exhaustive numerical experiments are performed; demonstrating applicability and performance; raising a variety of new promising research avenues.
A change point detection (CPD) framework assisted by a predictive machine learning model called "Predict and Compare" is introduced and characterised in relation to other state-of-the-art online CPD routines which it outperforms in terms of false positive rate and out-of-control average run length. The method's focus is on improving standard methods from sequential analysis such as the CUSUM rule in terms of these quality measures. This is achieved by replacing typically used trend estimation functionals such as the running mean with more sophisticated predictive models (Predict step), and comparing their prognosis with actual data (Compare step). The two models used in the Predict step are the ARIMA model and the LSTM recursive neural network. However, the framework is formulated in general terms, so as to allow the use of other prediction or comparison methods than those tested here. The power of the method is demonstrated in a tribological case study in which change points separating the run-in, steady-state, and divergent wear phases are detected in the regime of very few false positives.
Out-of-distribution (OOD) detection, crucial for reliable pattern classification, discerns whether a sample originates outside the training distribution. This paper concentrates on the high-dimensional features output by the final convolutional layer, which contain rich image features. Our key idea is to project these high-dimensional features into two specific feature subspaces, leveraging the dimensionality reduction capacity of the network's linear layers, trained with Predefined Evenly-Distribution Class Centroids (PEDCC)-Loss. This involves calculating the cosines of three projection angles and the norm values of features, thereby identifying distinctive information for in-distribution (ID) and OOD data, which assists in OOD detection. Building upon this, we have modified the batch normalization (BN) and ReLU layer preceding the fully connected layer, diminishing their impact on the output feature distributions and thereby widening the distribution gap between ID and OOD data features. Our method requires only the training of the classification network model, eschewing any need for input pre-processing or specific OOD data pre-tuning. Extensive experiments on several benchmark datasets demonstrates that our approach delivers state-of-the-art performance. Our code is available at //github.com/Hewell0/ProjOOD.
In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.
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