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In this paper, we introduce a novel analysis of neural networks based on geometric (Clifford) algebra and convex optimization. We show that optimal weights of deep ReLU neural networks are given by the wedge product of training samples when trained with standard regularized loss. Furthermore, the training problem reduces to convex optimization over wedge product features, which encode the geometric structure of the training dataset. This structure is given in terms of signed volumes of triangles and parallelotopes generated by data vectors. The convex problem finds a small subset of samples via $\ell_1$ regularization to discover only relevant wedge product features. Our analysis provides a novel perspective on the inner workings of deep neural networks and sheds light on the role of the hidden layers.

In this paper, we introduce an improved approach of speculative decoding aimed at enhancing the efficiency of serving large language models. Our method capitalizes on the strengths of two established techniques: the classic two-model speculative decoding approach, and the more recent single-model approach, Medusa. Drawing inspiration from Medusa, our approach adopts a single-model strategy for speculative decoding. However, our method distinguishes itself by employing a single, lightweight draft head with a recurrent dependency design, akin in essence to the small, draft model uses in classic speculative decoding, but without the complexities of the full transformer architecture. And because of the recurrent dependency, we can use beam search to swiftly filter out undesired candidates with the draft head. The outcome is a method that combines the simplicity of single-model design and avoids the need to create a data-dependent tree attention structure only for inference in Medusa. We empirically demonstrate the effectiveness of the proposed method on several popular open source language models, along with a comprehensive analysis of the trade-offs involved in adopting this approach.

In this paper, we consider the physical layer security of an RIS-assisted multiple-antenna communication system with randomly located eavesdroppers. The exact distributions of the received signal-to-noise-ratios (SNRs) at the legitimate user and the eavesdroppers located according to a Poisson point process (PPP) are derived, and a closed-form expression for the secrecy outage probability (SOP) is obtained. It is revealed that the secrecy performance is mainly affected by the number of RIS reflecting elements, and the impact of the transmit antennas and transmit power at the base station is marginal. In addition, when the locations of the randomly located eavesdroppers are unknown, deploying the RIS closer to the legitimate user rather than to the base station is shown to be more efficient. We also perform an analytical study demonstrating that the secrecy diversity order depends on the path loss exponent of the RIS-to-ground links. Finally, numerical simulations are conducted to verify the accuracy of these theoretical observations.

The aim of this paper is to evaluate whether large language models trained on multi-choice question data can be used to discriminate between medical subjects. This is an important and challenging task for automatic question answering. To achieve this goal, we train deep neural networks for multi-class classification of questions into the inferred medical subjects. Using our Multi-Question (MQ) Sequence-BERT method, we outperform the state-of-the-art results on the MedMCQA dataset with an accuracy of 0.68 and 0.60 on their development and test sets, respectively. In this sense, we show the capability of AI and LLMs in particular for multi-classification tasks in the Healthcare domain.

In this paper we discuss a first attempt to build a language learning game for brazilian indigenous languages and the challenges around it. We present a design for the tool with gamification aspects. Then we describe a process to automatically generate language exercises and questions from a dependency treebank and a lexical database for Tupian languages. We discuss the limitations of our prototype highlighting ethical and practical implementation concerns. Finally, we conclude that new data gathering processes should be established in partnership with indigenous communities and oriented for educational purposes.

In this paper, we present a new antithetic multilevel Monte Carlo (MLMC) method for the estimation of expectations with respect to laws of diffusion processes that can be elliptic or hypo-elliptic. In particular, we consider the case where one has to resort to time discretization of the diffusion and numerical simulation of such schemes. Motivated by recent developments, we introduce a new MLMC estimator of expectations, which does not require simulation of intractable L\'evy areas but has a weak error of order 2 and achieves the optimal computational complexity. We then show how this approach can be used in the context of the filtering problem associated to partially observed diffusions with discrete time observations. We illustrate with numerical simulations that our new approaches provide efficiency gains for several problems relative to some existing methods.

In this paper, we introduce a novel approach to centroidal state estimation, which plays a crucial role in predictive model-based control strategies for dynamic legged locomotion. Our approach uses the Koopman operator theory to transform the robot's complex nonlinear dynamics into a linear system, by employing dynamic mode decomposition and deep learning for model construction. We evaluate both models on their linearization accuracy and capability to capture both fast and slow dynamic system responses. We then select the most suitable model for estimation purposes, and integrate it within a moving horizon estimator. This estimator is formulated as a convex quadratic program, to facilitate robust, real-time centroidal state estimation. Through extensive simulation experiments on a quadruped robot executing various dynamic gaits, our data-driven framework outperforms conventional filtering techniques based on nonlinear dynamics. Our estimator addresses challenges posed by force/torque measurement noise in highly dynamic motions and accurately recovers the centroidal states, demonstrating the adaptability and effectiveness of the Koopman-based linear representation for complex locomotive behaviors. Importantly, our model based on dynamic mode decomposition, trained with two locomotion patterns (trot and jump), successfully estimates the centroidal states for a different motion (bound) without retraining.

In this paper we define a class of polynomial functors suited for constructing coalgebras representing processes in which uncertainty plays an important role. In these polynomial functors we include upper and lower probability measures, finitely additive probability measures, plausibilty measures (and their duals, belief functions), and possibility measures. We give axioms and inference rules for the associated system of coalgebraic modal logic, and construct the canonical coalgebras to prove a completeness result.

In this paper, we first identify activation shift, a simple but remarkable phenomenon in a neural network in which the preactivation value of a neuron has non-zero mean that depends on the angle between the weight vector of the neuron and the mean of the activation vector in the previous layer. We then propose linearly constrained weights (LCW) to reduce the activation shift in both fully connected and convolutional layers. The impact of reducing the activation shift in a neural network is studied from the perspective of how the variance of variables in the network changes through layer operations in both forward and backward chains. We also discuss its relationship to the vanishing gradient problem. Experimental results show that LCW enables a deep feedforward network with sigmoid activation functions to be trained efficiently by resolving the vanishing gradient problem. Moreover, combined with batch normalization, LCW improves generalization performance of both feedforward and convolutional networks.

In this paper, we propose the joint learning attention and recurrent neural network (RNN) models for multi-label classification. While approaches based on the use of either model exist (e.g., for the task of image captioning), training such existing network architectures typically require pre-defined label sequences. For multi-label classification, it would be desirable to have a robust inference process, so that the prediction error would not propagate and thus affect the performance. Our proposed model uniquely integrates attention and Long Short Term Memory (LSTM) models, which not only addresses the above problem but also allows one to identify visual objects of interests with varying sizes without the prior knowledge of particular label ordering. More importantly, label co-occurrence information can be jointly exploited by our LSTM model. Finally, by advancing the technique of beam search, prediction of multiple labels can be efficiently achieved by our proposed network model.