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This study introduces a decentralized approach to secure wireless communication using a cryptographic secret key generation algorithm among distributed nodes. The system model employs Gaussian prime numbers, ensuring the collaborative generation of a secret key. Pre-processing and post-processing functions enable to generate a secret key across the network. An error model evaluates aspects like thermal noise power and channel estimation errors, while simulations assess the success rate to factorize the norm of the secret key. It is observed that path loss-induced large scale fading emerges as a critical component impacting information and power loss. The robustness of the proposed model under fading channel conditions is evaluated with a success rate. Additionally, it is also observed that the tolerance value set in the factorization algorithms has a significant impact on the success rate. Furthermore, the success rate is compared in two scenarios, one with 2 users and another with 3 users, to provide a comprehensive evaluation of the system performance.

We study principal components regression (PCR) in an asymptotic high-dimensional regression setting, where the number of data points is proportional to the dimension. We derive exact limiting formulas for the estimation and prediction risks, which depend in a complicated manner on the eigenvalues of the population covariance, the alignment between the population PCs and the true signal, and the number of selected PCs. A key challenge in the high-dimensional setting stems from the fact that the sample covariance is an inconsistent estimate of its population counterpart, so that sample PCs may fail to fully capture potential latent low-dimensional structure in the data. We demonstrate this point through several case studies, including that of a spiked covariance model. To calculate the asymptotic prediction risk, we leverage tools from random matrix theory which to our knowledge have not seen much use to date in the statistics literature: multi-resolvent traces and their associated eigenvector overlap measures.

The study evaluates the efficacy of Conversational Artificial Intelligence (CAI) in rectifying cognitive biases and recognizing affect in human-AI interactions, which is crucial for digital mental health interventions. Cognitive biases (systematic deviations from normative thinking) affect mental health, intensifying conditions like depression and anxiety. Therapeutic chatbots can make cognitive-behavioral therapy (CBT) more accessible and affordable, offering scalable and immediate support. The research employs a structured methodology with clinical-based virtual case scenarios simulating typical user-bot interactions. Performance and affect recognition were assessed across two categories of cognitive biases: theory of mind biases (anthropomorphization of AI, overtrust in AI, attribution to AI) and autonomy biases (illusion of control, fundamental attribution error, just-world hypothesis). A qualitative feedback mechanism was used with an ordinal scale to quantify responses based on accuracy, therapeutic quality, and adherence to CBT principles. Therapeutic bots (Wysa, Youper) and general-use LLMs (GTP 3.5, GTP 4, Gemini Pro) were evaluated through scripted interactions, double-reviewed by cognitive scientists and a clinical psychologist. Statistical analysis showed therapeutic bots were consistently outperformed by non-therapeutic bots in bias rectification and in 4 out of 6 biases in affect recognition. The data suggests that non-therapeutic chatbots are more effective in addressing some cognitive biases.

In this study, we attempt to model intuition and incorporate this formalism to improve the performance of the Convolutional Neural Networks. Despite decades of research, ambiguities persist on principles of intuition. Experimental psychology reveals many types of intuition, which depend on state of the human mind. We focus on visual intuition, useful for completing missing information during visual cognitive tasks. First, we set up a scenario to gradually decrease the amount of visual information in the images of a dataset to examine its impact on CNN accuracy. Then, we represent a model for visual intuition using Gestalt theory. The theory claims that humans derive a set of templates according to their subconscious experiences. When the brain decides that there is missing information in a scene, such as occlusion, it instantaneously completes the information by replacing the missing parts with the most similar ones. Based upon Gestalt theory, we model the visual intuition, in two layers. Details of these layers are provided throughout the paper. We use the MNIST data set to test the suggested intuition model for completing the missing information. Experiments show that the augmented CNN architecture provides higher performances compared to the classic models when using incomplete images.

In the realm of self-supervised learning (SSL), masked image modeling (MIM) has gained popularity alongside contrastive learning methods. MIM involves reconstructing masked regions of input images using their unmasked portions. A notable subset of MIM methodologies employs discrete tokens as the reconstruction target, but the theoretical underpinnings of this choice remain underexplored. In this paper, we explore the role of these discrete tokens, aiming to unravel their benefits and limitations. Building upon the connection between MIM and contrastive learning, we provide a comprehensive theoretical understanding on how discrete tokenization affects the model's generalization capabilities. Furthermore, we propose a novel metric named TCAS, which is specifically designed to assess the effectiveness of discrete tokens within the MIM framework. Inspired by this metric, we contribute an innovative tokenizer design and propose a corresponding MIM method named ClusterMIM. It demonstrates superior performance on a variety of benchmark datasets and ViT backbones. Code is available at //github.com/PKU-ML/ClusterMIM.

Human cognition exhibits systematic compositionality, the algebraic ability to generate infinite novel combinations from finite learned components, which is the key to understanding and reasoning about complex logic. In this work, we investigate the compositionality of large language models (LLMs) in mathematical reasoning. Specifically, we construct a new dataset \textsc{MathTrap}\footnotemark[3] by introducing carefully designed logical traps into the problem descriptions of MATH and GSM8k. Since problems with logical flaws are quite rare in the real world, these represent ``unseen'' cases to LLMs. Solving these requires the models to systematically compose (1) the mathematical knowledge involved in the original problems with (2) knowledge related to the introduced traps. Our experiments show that while LLMs possess both components of requisite knowledge, they do not \textbf{spontaneously} combine them to handle these novel cases. We explore several methods to mitigate this deficiency, such as natural language prompts, few-shot demonstrations, and fine-tuning. We find that LLMs' performance can be \textbf{passively} improved through the above external intervention. Overall, systematic compositionality remains an open challenge for large language models.

The development of a satisfying and rigorous mathematical understanding of the performance of neural networks is a major challenge in artificial intelligence. Against this background, we study the expressive power of neural networks through the example of the classical NP-hard Knapsack Problem. Our main contribution is a class of recurrent neural networks (RNNs) with rectified linear units that are iteratively applied to each item of a Knapsack instance and thereby compute optimal or provably good solution values. We show that an RNN of depth four and width depending quadratically on the profit of an optimum Knapsack solution is sufficient to find optimum Knapsack solutions. We also prove the following tradeoff between the size of an RNN and the quality of the computed Knapsack solution: for Knapsack instances consisting of $n$ items, an RNN of depth five and width $w$ computes a solution of value at least $1-\mathcal{O}(n^2/\sqrt{w})$ times the optimum solution value. Our results build upon a classical dynamic programming formulation of the Knapsack Problem as well as a careful rounding of profit values that are also at the core of the well-known fully polynomial-time approximation scheme for the Knapsack Problem. A carefully conducted computational study qualitatively supports our theoretical size bounds. Finally, we point out that our results can be generalized to many other combinatorial optimization problems that admit dynamic programming solution methods, such as various Shortest Path Problems, the Longest Common Subsequence Problem, and the Traveling Salesperson Problem.

The emergence of Large Language Models (LLMs) has demonstrated promising progress in solving logical reasoning tasks effectively. Several recent approaches have proposed to change the role of the LLM from the reasoner into a translator between natural language statements and symbolic representations which are then sent to external symbolic solvers to resolve. This paradigm has established the current state-of-the-art result in logical reasoning (i.e., deductive reasoning). However, it remains unclear whether the variance in performance of these approaches stems from the methodologies employed or the specific symbolic solvers utilized. There is a lack of consistent comparison between symbolic solvers and how they influence the overall reported performance. This is important, as each symbolic solver also has its own input symbolic language, presenting varying degrees of challenge in the translation process. To address this gap, we perform experiments on 3 deductive reasoning benchmarks with LLMs augmented with widely used symbolic solvers: Z3, Pyke, and Prover9. The tool-executable rates of symbolic translation generated by different LLMs exhibit a near 50% performance variation. This highlights a significant difference in performance rooted in very basic choices of tools. The almost linear correlation between the executable rate of translations and the accuracy of the outcomes from Prover9 highlight a strong alignment between LLMs ability to translate into Prover9 symbolic language, and the correctness of those translations.

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of comparable size? Furthermore, from among all solutions that fit the training data, how does GD find one that generalizes well (when such a well-generalizing solution exists)? We argue that the answer to both questions lies in the interaction of the gradients of different examples during training. Intuitively, if the per-example gradients are well-aligned, that is, if they are coherent, then one may expect GD to be (algorithmically) stable, and hence generalize well. We formalize this argument with an easy to compute and interpretable metric for coherence, and show that the metric takes on very different values on real and random datasets for several common vision networks. The theory also explains a number of other phenomena in deep learning, such as why some examples are reliably learned earlier than others, why early stopping works, and why it is possible to learn from noisy labels. Moreover, since the theory provides a causal explanation of how GD finds a well-generalizing solution when one exists, it motivates a class of simple modifications to GD that attenuate memorization and improve generalization. Generalization in deep learning is an extremely broad phenomenon, and therefore, it requires an equally general explanation. We conclude with a survey of alternative lines of attack on this problem, and argue that the proposed approach is the most viable one on this basis.

We study the problem of incorporating prior knowledge into a deep Transformer-based model,i.e.,Bidirectional Encoder Representations from Transformers (BERT), to enhance its performance on semantic textual matching tasks. By probing and analyzing what BERT has already known when solving this task, we obtain better understanding of what task-specific knowledge BERT needs the most and where it is most needed. The analysis further motivates us to take a different approach than most existing works. Instead of using prior knowledge to create a new training task for fine-tuning BERT, we directly inject knowledge into BERT's multi-head attention mechanism. This leads us to a simple yet effective approach that enjoys fast training stage as it saves the model from training on additional data or tasks other than the main task. Extensive experiments demonstrate that the proposed knowledge-enhanced BERT is able to consistently improve semantic textual matching performance over the original BERT model, and the performance benefit is most salient when training data is scarce.