Event-related potentials (ERP) are measurements of brain activity with wide applications in basic and clinical neuroscience, that are typically estimated using the average of many trials of electroencephalography signals (EEG) to sufficiently reduce noise and signal variability. We introduce EEG2ERP, a novel uncertainty-aware autoencoder approach that maps an arbitrary number of EEG trials to their associated ERP. To account for the ERP uncertainty we use bootstrapped training targets and introduce a separate variance decoder to model the uncertainty of the estimated ERP. We evaluate our approach in the challenging zero-shot scenario of generalizing to new subjects considering three different publicly available data sources; i) the comprehensive ERP CORE dataset that includes over 50,000 EEG trials across six ERP paradigms from 40 subjects, ii) the large P300 Speller BCI dataset, and iii) a neuroimaging dataset on face perception consisting of both EEG and magnetoen-cephalography (MEG) data. We consistently find that our method in the few trial regime provides substantially better ERP estimates than commonly used conventional and robust averaging procedures. EEG2ERP is the first deep learning approach to map EEG signals to their associated ERP, moving toward reducing the number of trials necessary for ERP research.

Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and mechanistic interpretability. Since the introduction of code-specific models, despite their successes in generating code in Lean4 and Isabelle, the task of generalized theorem proving still remains far from being fully solved and will be a benchmark for reasoning capability in LLMs. In this work, we introduce a framework that generates whole proofs in a formal language to be used within systems that utilize the power of built-in tactics and off-the-shelf automated theorem provers. Our framework includes 3 components: generating natural language statements of the code to be verified, an LLM that generates formal proofs for the given statement, and a module employing heuristics for building the final proof. To train the LLM, we employ a 2-stage fine-tuning process, where we first use SFT-based training to enable the model to generate syntactically correct Isabelle code and then RL-based training that encourages the model to generate proofs verified by a theorem prover. We validate our framework using the miniF2F-test benchmark and the Isabelle proof assistant and design a use case to verify the correctness of the A WS S3 bucket access policy code.

Prompting methods for language models, such as Chain-of-thought (CoT), present intuitive step-by-step processes for problem solving. These methodologies aim to equip models with a better understanding of the correct procedures for addressing a given task. Despite these advancements, CoT lacks the ability of reflection and error correction, potentially causing a model to perpetuate mistakes and errors. Therefore, inspired by the human ability for said tasks, we propose Error Reflection Prompting (ERP) to further enhance reasoning in language models. Building upon CoT, ERP is a method comprised of an incorrect answer, error recognition, and a correct answer. This process enables the model to recognize types of errors and the steps that lead to incorrect answers, allowing the model to better discern which steps to avoid and which to take. The model is able to generate the error outlines itself with automated ERP generation, allowing for error recognition and correction to be integrated into the reasoning chain and produce scalability and reliability in the process. The results demonstrate that ERP serves as a versatile supplement to conventional CoT, ultimately contributing to more robust and capable reasoning abilities along with increased interpretability in how models ultimately reach their errors.

The research presents a machine learning (ML) classifier designed to differentiate between schizophrenia patients and healthy controls by utilising features extracted from electroencephalogram (EEG) data, specifically focusing on event-related potentials (ERPs) and certain demographic variables. The dataset comprises data from 81 participants, encompassing 32 healthy controls and 49 schizophrenia patients, all sourced from an online dataset. After preprocessing the dataset, our ML model achieved an accuracy of 99.930%. This performance outperforms earlier research, including those that used deep learning methods. Additionally, an analysis was conducted to assess individual features' contribution to improving classification accuracy. This involved systematically excluding specific features from the original dataset one at a time, and another technique involved an iterative process of removing features based on their entropy scores incrementally. The impact of these removals on model performance was evaluated to identify the most informative features.

Text classifiers suffer from small perturbations, that if chosen adversarially, can dramatically change the output of the model. Verification methods can provide robustness certificates against such adversarial perturbations, by computing a sound lower bound on the robust accuracy. Nevertheless, existing verification methods incur in prohibitive costs and cannot practically handle Levenshtein distance constraints. We propose the first method for computing the Lipschitz constant of convolutional classifiers with respect to the Levenshtein distance. We use these Lipschitz constant estimates for training 1-Lipschitz classifiers. This enables computing the certified radius of a classifier in a single forward pass. Our method, LipsLev, is able to obtain $38.80$% and $13.93$% verified accuracy at distance $1$ and $2$ respectively in the AG-News dataset, while being $4$ orders of magnitude faster than existing approaches. We believe our work can open the door to more efficient verification in the text domain.

The objective of drug discovery is to identify chemical compounds that possess specific pharmaceutical properties toward a binding target. Existing large language models (LLMS) can achieve high token matching scores in terms of likelihood for molecule generation. However, relying solely on LLM decoding often results in the generation of molecules that are either invalid due to a single misused token, or suboptimal due to unbalanced exploration and exploitation as a consequence of the LLMs prior experience. Here we propose ERP, Entropy-Reinforced Planning for Transformer Decoding, which employs an entropy-reinforced planning algorithm to enhance the Transformer decoding process and strike a balance between exploitation and exploration. ERP aims to achieve improvements in multiple properties compared to direct sampling from the Transformer. We evaluated ERP on the SARS-CoV-2 virus (3CLPro) and human cancer cell target protein (RTCB) benchmarks and demonstrated that, in both benchmarks, ERP consistently outperforms the current state-of-the-art algorithm by 1-5 percent, and baselines by 5-10 percent, respectively. Moreover, such improvement is robust across Transformer models trained with different objectives. Finally, to further illustrate the capabilities of ERP, we tested our algorithm on three code generation benchmarks and outperformed the current state-of-the-art approach as well. Our code is publicly available at: https://github.com/xuefeng-cs/ERP.

The study of effective connectivity (EC) is essential in understanding how the brain integrates and responds to various sensory inputs. Model-driven estimation of EC is a powerful approach that requires estimating global and local parameters of a generative model of neural activity. Insights gathered through this process can be used in various applications, such as studying neurodevelopmental disorders. However, accurately determining EC through generative models remains a significant challenge due to the complexity of brain dynamics and the inherent noise in neural recordings, e.g., in electroencephalography (EEG). Current model-driven methods to study EC are computationally complex and cannot scale to all brain regions as required by whole-brain analyses. To facilitate EC assessment, an inference algorithm must exhibit reliable prediction of parameters in the presence of noise. Further, the relationship between the model parameters and the neural recordings must be learnable. To progress toward these objectives, we benchmarked the performance of a Bi-LSTM model for parameter inference from the Jansen-Rit neural mass model (JR-NMM) simulated EEG under various noise conditions. Additionally, our study explores how the JR-NMM reacts to changes in key biological parameters (i.e., sensitivity analysis) like synaptic gains and time constants, a crucial step in understanding the connection between neural mechanisms and observed brain activity. Our results indicate that we can predict the local JR-NMM parameters from EEG, supporting the feasibility of our deep-learning-based inference approach. In future work, we plan to extend this framework to estimate local and global parameters from real EEG in clinically relevant applications.

This paper presents a multiplayer Homicidal Chauffeur reach-avoid differential game, which involves Dubins-car pursuers and simple-motion evaders. The goal of the pursuers is to cooperatively protect a planar convex region from the evaders, who strive to reach the region. We propose a cooperative strategy for the pursuers based on subgames for multiple pursuers against one evader and optimal task allocation. We introduce pursuit enclosure functions (PEFs) and propose a new enclosure region pursuit (ERP) winning approach that supports forward analysis for the strategy synthesis in the subgames. We show that if a pursuit coalition is able to defend the region against an evader under the ERP winning, then no more than two pursuers in the coalition are necessarily needed. We also propose a steer-to-ERP approach to certify the ERP winning and synthesize the ERP winning strategy. To implement the strategy, we introduce a positional PEF and provide the necessary parameters, states, and strategies that ensure the ERP winning for both one pursuer and two pursuers against one evader. Additionally, we formulate a binary integer program using the subgame outcomes to maximize the captured evaders in the ERP winning for the pursuit task allocation. Finally, we propose a multiplayer receding-horizon strategy where the ERP winnings are checked in each horizon, the task is allocated, and the strategies of the pursuers are determined. Numerical examples are provided to illustrate the results.

In this study we focus on the diagnosis of Parkinson's Disease (PD) based on electroencephalogram (EEG) signals. We propose a new approach inspired by the functioning of the brain that uses the dynamics, frequency and temporal content of EEGs to extract new demarcating features of the disease. The method was evaluated on a publicly available dataset containing EEG signals recorded during a 3-oddball auditory task involving N = 50 subjects, of whom 25 suffer from PD. By extracting two features, and separating them with a straight line using a Linear Discriminant Analysis (LDA) classifier, we can separate the healthy from the unhealthy subjects with an accuracy of 90 % $(p < 0.03)$ using a single channel. By aggregating the information from three channels and making them vote, we obtain an accuracy of 94 %, a sensitivity of 96 % and a specificity of 92 %. The evaluation was carried out using a nested Leave-One-Out cross-validation procedure, thus preventing data leakage problems and giving a less biased evaluation. Several tests were carried out to assess the validity and robustness of our approach, including the test where we use only half the available data for training. Under this constraint, the model achieves an accuracy of 83.8 %.

ERP (Enterprise Resource Planning) is the brain of your organization's technology apparatus. The brain coordinates the activities of your body. It is responsible for telling the body what it should do. A well-planned Enterprise Resource Planning system is essential for any organization to function. But things will change over time. Digital transformation is an important driving force in today's business world. Businesses that want to make the most of Industry 4.0's technological advances will need them. Enterprise services that are efficient and error-free make it possible to use machine learning and artificial Intelligence technologies in real time and automate operations. This is a significant influence on digital transformation. One of the significant impacts of ML is the potential enhancement of Enterprise resource plan (ERP) applications.