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The Euler characteristic transform (ECT) is an integral transform used widely in topological data analysis. Previous efforts by Curry et al. and Ghrist et al. have independently shown that the ECT is injective on all compact definable sets. In this work, we first study the injectivity of the ECT on definable sets that are not necessarily compact and prove a complete classification of constructible functions that the Euler characteristic transform is not injective on. We then introduce the quadric Euler characteristic transform (QECT) as a natural generalization of the ECT by detecting definable shapes with quadric hypersurfaces rather than hyperplanes. We also discuss some criteria for the injectivity of QECT.

Hidden Markov models (HMM) have been widely used by scientists to model stochastic systems: the underlying process is a discrete Markov chain and the observations are noisy realizations of the underlying process. Determining the number of hidden states for an HMM is a model selection problem, which is yet to be satisfactorily solved, especially for the popular Gaussian HMM with heterogeneous covariance. In this paper, we propose a consistent method for determining the number of hidden states of HMM based on the marginal likelihood, which is obtained by integrating out both the parameters and hidden states. Moreover, we show that the model selection problem of HMM includes the order selection problem of finite mixture models as a special case. We give rigorous proof of the consistency of the proposed marginal likelihood method and provide an efficient computation method for practical implementation. We numerically compare the proposed method with the Bayesian information criterion (BIC), demonstrating the effectiveness of the proposed marginal likelihood method.

In the era of generative artificial intelligence (AI), the fusion of large language models (LLMs) offers unprecedented opportunities for innovation in the field of modern education. We embark on an exploration of prompted LLMs within the context of educational and assessment applications to uncover their potential. Through a series of carefully crafted research questions, we investigate the effectiveness of prompt-based techniques in generating open-ended questions from school-level textbooks, assess their efficiency in generating open-ended questions from undergraduate-level technical textbooks, and explore the feasibility of employing a chain-of-thought inspired multi-stage prompting approach for language-agnostic multiple-choice question (MCQ) generation. Additionally, we evaluate the ability of prompted LLMs for language learning, exemplified through a case study in the low-resource Indian language Bengali, to explain Bengali grammatical errors. We also evaluate the potential of prompted LLMs to assess human resource (HR) spoken interview transcripts. By juxtaposing the capabilities of LLMs with those of human experts across various educational tasks and domains, our aim is to shed light on the potential and limitations of LLMs in reshaping educational practices.

Large Language Models (LLMs) have demonstrated exceptional proficiency in language-related tasks. However, their deployment presents significant challenges due to their substantial memory and storage requirements. To address this challenge, weight-only quantization has emerged as a promising solution. Previous research has indicated that fine-tuning through up and down rounding can enhance performance. In this study, we introduce SignRound, a method that utilizes signed gradient descent (SignSGD) to optimize rounding values and weight clipping within just 200 steps, combining the strengths of both Quantization-Aware Training (QAT) and Post-Training Quantization (PTQ). SignRound achieves outstanding results compared to recent methods across 2 to 4 bits, while maintaining low tuning costs and without introducing any additional inference overhead. For instance, SignRound led to absolute average accuracy improvements ranging from 6.91\% to 33.22\% at 2 bits. Furthermore, it demonstrates robust generalization to various recent models and achieves near-lossless quantization in most scenarios at 4 bits. The source code is publicly available at \url{//github.com/intel/auto-round}.

We introduce and characterize the operational diversity order (ODO) in fading channels, as a proxy to the classical notion of diversity order at any arbitrary operational signal-to-noise ratio (SNR). Thanks to this definition, relevant insights are brought up in a number of cases: (i) We quantify that in line-of-sight scenarios an increased diversity order is attainable compared to that achieved asymptotically; (ii) this effect is attenuated, but still visible, in the presence of an additional dominant specular component; (iii) we confirm that the decay slope in Rayleigh product channels increases very slowly and never fully achieves unitary slope for finite values of SNR.

Large language models (LLMs) have become crucial for many generative downstream tasks, leading to an inevitable trend and significant challenge to deploy them efficiently on resource-constrained devices. Structured pruning is a widely used method to address this challenge. However, when dealing with the complex structure of the multiple decoder layers, general methods often employ common estimation approaches for pruning. These approaches lead to a decline in accuracy for specific downstream tasks. In this paper, we introduce a simple yet efficient method that adaptively models the importance of each substructure. Meanwhile, it can adaptively fuse coarse-grained and finegrained estimations based on the results from complex and multilayer structures. All aspects of our design seamlessly integrate into the endto-end pruning framework. Our experimental results, compared with state-of-the-art methods on mainstream datasets, demonstrate average accuracy improvements of 1.1%, 1.02%, 2.0%, and 1.2% for LLaMa-7B,Vicuna-7B, Baichuan-7B, and Bloom-7b1, respectively.

Strong data processing inequalities (SDPI) are an important object of study in Information Theory and have been well studied for $f$-divergences. Universal upper and lower bounds have been provided along with several applications, connecting them to impossibility (converse) results, concentration of measure, hypercontractivity, and so on. In this paper, we study R\'enyi divergence and the corresponding SDPI constant whose behavior seems to deviate from that of ordinary $\Phi$-divergences. In particular, one can find examples showing that the universal upper bound relating its SDPI constant to the one of Total Variation does not hold in general. In this work, we prove, however, that the universal lower bound involving the SDPI constant of the Chi-square divergence does indeed hold. Furthermore, we also provide a characterization of the distribution that achieves the supremum when $\alpha$ is equal to $2$ and consequently compute the SDPI constant for R\'enyi divergence of the general binary channel.

Integrated Speech and Large Language Models (SLMs) that can follow speech instructions and generate relevant text responses have gained popularity lately. However, the safety and robustness of these models remains largely unclear. In this work, we investigate the potential vulnerabilities of such instruction-following speech-language models to adversarial attacks and jailbreaking. Specifically, we design algorithms that can generate adversarial examples to jailbreak SLMs in both white-box and black-box attack settings without human involvement. Additionally, we propose countermeasures to thwart such jailbreaking attacks. Our models, trained on dialog data with speech instructions, achieve state-of-the-art performance on spoken question-answering task, scoring over 80% on both safety and helpfulness metrics. Despite safety guardrails, experiments on jailbreaking demonstrate the vulnerability of SLMs to adversarial perturbations and transfer attacks, with average attack success rates of 90% and 10% respectively when evaluated on a dataset of carefully designed harmful questions spanning 12 different toxic categories. However, we demonstrate that our proposed countermeasures reduce the attack success significantly.

Massively multilingual neural machine translation (MMNMT) has been proven to enhance the translation quality of low-resource languages. In this paper, we empirically investigate the translation robustness of Indonesian-Chinese translation in the face of various naturally occurring noise. To assess this, we create a robustness evaluation benchmark dataset for Indonesian-Chinese translation. This dataset is automatically translated into Chinese using four NLLB-200 models of different sizes. We conduct both automatic and human evaluations. Our in-depth analysis reveal the correlations between translation error types and the types of noise present, how these correlations change across different model sizes, and the relationships between automatic evaluation indicators and human evaluation indicators. The dataset is publicly available at //github.com/tjunlp-lab/ID-ZH-MTRobustEval.

Large language models (LLMs) have shown exceptional proficiency in natural language processing but often fall short of generating creative and original responses to open-ended questions. To enhance LLM creativity, our key insight is to emulate the human process of inducing collective creativity through engaging discussions with participants from diverse backgrounds and perspectives. To this end, we propose LLM Discussion, a three-phase discussion framework that facilitates vigorous and diverging idea exchanges and ensures convergence to creative answers. Moreover, we adopt a role-playing technique by assigning distinct roles to LLMs to combat the homogeneity of LLMs. We evaluate the efficacy of the proposed framework with the Alternative Uses Test, Similarities Test, Instances Test, and Scientific Creativity Test through both LLM evaluation and human study. Our proposed framework outperforms single-LLM approaches and existing multi-LLM frameworks across various creativity metrics.