In this work, we conduct a comparative study on two deep unfolding mechanisms to efficiently perform power control in the next generation wireless networks. The power control problem is formulated as energy efficiency over multiple interference links. The problem is nonconvex. We employ fractional programming transformation to design two solutions for the problem. The first solution is a numerical solution while the second solution is a closed-form solution. Based on the first solution, we design a semi-unfolding deep learning model where we combine the domain knowledge of the wireless communications and the recent advances in the data-driven deep learning. Moreover, on the highlights of the closed-form solution, fully deep unfolded deep learning model is designed in which we fully leveraged the expressive closed-form power control solution and deep learning advances. In the simulation results, we compare the performance of the proposed deep learning models and the iterative solutions in terms of accuracy and inference speed to show their suitability for the real-time application in next generation networks.
Handling possible infeasibility and providing an execution time certificate are two pressing requirements of real-time Model Predictive Control (MPC). To meet these two requirements simultaneously, this paper proposes an $\ell_1$-penalty soft-constrained MPC formulation that is globally feasible and solvable with an execution time certificate using our proposed algorithm. This paper proves for the first time that $\ell_1$-penalty soft-constrained MPC problems can be equivalently transformed into a box-constrained quadratic programming (Box-QP) and then our previous execution-time-certified algorithm \cite{wu2023direct} (only limited to Box-QP) can be applied. However, our previous Box-QP algorithm \cite{wu2023direct}, which provides a theoretical execution-time certificate, is conservative in its iteration analysis, thus sacrificing computation efficiency. To this end, this paper proposes a novel $LDL^\top$ decomposition for the first time, to accelerate the computation of Newton step at each iteration. The speedup of our $LDL^\top$ decomposition comes from two-fold: \textit{i)} exploitation of the fact that the number of inequality constraints is generally larger than the number of variables in condensed MPC formulations, \textit{ii)} vectorized and parallel implementation based on based on its vector-wise operations, instead of element-wise operations of previous decomposition methods. Numerical experiments demonstrate great speedups of the proposed $LDL^\top$ decomposition (even up to 1000-fold, compared to the standard Choleksky method), which thus helps our solver achieve comparable computation performance to the state-of-the-art solvers such as IPOPT and OSQP. Code is available at \url{https://github.com/liangwu2019/L1-penalty-QP}.
RGB-T tracking, a vital downstream task of object tracking, has made remarkable progress in recent years. Yet, it remains hindered by two major challenges: 1) the trade-off between performance and efficiency; 2) the scarcity of training data. To address the latter challenge, some recent methods employ prompts to fine-tune pre-trained RGB tracking models and leverage upstream knowledge in a parameter-efficient manner. However, these methods inadequately explore modality-independent patterns and disregard the dynamic reliability of different modalities in open scenarios. We propose M3PT, a novel RGB-T prompt tracking method that leverages middle fusion and multi-modal and multi-stage visual prompts to overcome these challenges. We pioneer the use of the adjustable middle fusion meta-framework for RGB-T tracking, which could help the tracker balance the performance with efficiency, to meet various demands of application. Furthermore, based on the meta-framework, we utilize multiple flexible prompt strategies to adapt the pre-trained model to comprehensive exploration of uni-modal patterns and improved modeling of fusion-modal features in diverse modality-priority scenarios, harnessing the potential of prompt learning in RGB-T tracking. Evaluating on 6 existing challenging benchmarks, our method surpasses previous state-of-the-art prompt fine-tuning methods while maintaining great competitiveness against excellent full-parameter fine-tuning methods, with only 0.34M fine-tuned parameters.
Energy-efficient spikformer has been proposed by integrating the biologically plausible spiking neural network (SNN) and artificial Transformer, whereby the Spiking Self-Attention (SSA) is used to achieve both higher accuracy and lower computational cost. However, it seems that self-attention is not always necessary, especially in sparse spike-form calculation manners. In this paper, we innovatively replace vanilla SSA (using dynamic bases calculating from Query and Key) with spike-form Fourier Transform, Wavelet Transform, and their combinations (using fixed triangular or wavelets bases), based on a key hypothesis that both of them use a set of basis functions for information transformation. Hence, the Fourier-or-Wavelet-based spikformer (FWformer) is proposed and verified in visual classification tasks, including both static image and event-based video datasets. The FWformer can achieve comparable or even higher accuracies ($0.4\%$-$1.5\%$), higher running speed ($9\%$-$51\%$ for training and $19\%$-$70\%$ for inference), reduced theoretical energy consumption ($20\%$-$25\%$), and reduced GPU memory usage ($4\%$-$26\%$), compared to the standard spikformer. Our result indicates the continuous refinement of new Transformers, that are inspired either by biological discovery (spike-form), or information theory (Fourier or Wavelet Transform), is promising.
Large language models (LLMs) often generate content that contains factual errors when responding to fact-seeking prompts on open-ended topics. To benchmark a model's long-form factuality in open domains, we first use GPT-4 to generate LongFact, a prompt set comprising thousands of questions spanning 38 topics. We then propose that LLM agents can be used as automated evaluators for long-form factuality through a method which we call Search-Augmented Factuality Evaluator (SAFE). SAFE utilizes an LLM to break down a long-form response into a set of individual facts and to evaluate the accuracy of each fact using a multi-step reasoning process comprising sending search queries to Google Search and determining whether a fact is supported by the search results. Furthermore, we propose extending F1 score as an aggregated metric for long-form factuality. To do so, we balance the percentage of supported facts in a response (precision) with the percentage of provided facts relative to a hyperparameter representing a user's preferred response length (recall). Empirically, we demonstrate that LLM agents can outperform crowdsourced human annotators - on a set of ~16k individual facts, SAFE agrees with crowdsourced human annotators 72% of the time, and on a random subset of 100 disagreement cases, SAFE wins 76% of the time. At the same time, SAFE is more than 20 times cheaper than human annotators. We also benchmark thirteen language models on LongFact across four model families (Gemini, GPT, Claude, and PaLM-2), finding that larger language models generally achieve better long-form factuality. LongFact, SAFE, and all experimental code are available at https://github.com/google-deepmind/long-form-factuality.
Despite their simplicity, linear models perform well at time series forecasting, even when pitted against deeper and more expensive models. A number of variations to the linear model have been proposed, often including some form of feature normalisation that improves model generalisation. In this paper we analyse the sets of functions expressible using these linear model architectures. In so doing we show that several popular variants of linear models for time series forecasting are equivalent and functionally indistinguishable from standard, unconstrained linear regression. We characterise the model classes for each linear variant. We demonstrate that each model can be reinterpreted as unconstrained linear regression over a suitably augmented feature set, and therefore admit closed-form solutions when using a mean-squared loss function. We provide experimental evidence that the models under inspection learn nearly identical solutions, and finally demonstrate that the simpler closed form solutions are superior forecasters across 72% of test settings.
This paper presents a novel sparse signal detection scheme designed for a correlated Markovian Bernoulli-Gaussian sparse signal model, which can equivalently be viewed as a block sparse signal model. Despite the inherent complexity of the model, our approach yields a closed-form detection criterion. Theoretical analyses of the proposed detector are provided, including the computation of false alarm probability and detection probability through closed-form formulas. Simulation results compellingly demonstrate the advantages of our proposed detector compared to an existing detector in the literature.
Long-form video understanding represents a significant challenge within computer vision, demanding a model capable of reasoning over long multi-modal sequences. Motivated by the human cognitive process for long-form video understanding, we emphasize interactive reasoning and planning over the ability to process lengthy visual inputs. We introduce a novel agent-based system, VideoAgent, that employs a large language model as a central agent to iteratively identify and compile crucial information to answer a question, with vision-language foundation models serving as tools to translate and retrieve visual information. Evaluated on the challenging EgoSchema and NExT-QA benchmarks, VideoAgent achieves 54.1% and 71.3% zero-shot accuracy with only 8.4 and 8.2 frames used on average. These results demonstrate superior effectiveness and efficiency of our method over the current state-of-the-art methods, highlighting the potential of agent-based approaches in advancing long-form video understanding.
We study the welfare effects of overreaction to information in the form of diagnostic expectations in markets with asymmetric information, and the effect of a simple intervention in the form of a tax or a subsidy. A large enough level of overreaction is always welfare-decreasing and can rationalize a tax on financial transactions. A small degree of overreaction to private information can both increase or decrease welfare. This is because there are two competing externalities: an information externality, due to the informational role of prices, and a pecuniary externality, due to the allocative role of prices. When the information externality prevails on the pecuniary externality, the loading on private information in agents' trades is too small compared to the welfare optimum: in this case, a small degree of overreaction is welfare-improving.
It has recently been conjectured that neural network solution sets reachable via stochastic gradient descent (SGD) are convex, considering permutation invariances (Entezari et al., 2022). This means that a linear path can connect two independent solutions with low loss, given the weights of one of the models are appropriately permuted. However, current methods to test this theory often require very wide networks to succeed. In this work, we conjecture that more generally, the SGD solution set is a "star domain" that contains a "star model" that is linearly connected to all the other solutions via paths with low loss values, modulo permutations. We propose the Starlight algorithm that finds a star model of a given learning task. We validate our claim by showing that this star model is linearly connected with other independently found solutions. As an additional benefit of our study, we demonstrate better uncertainty estimates on the Bayesian Model Averaging over the obtained star domain. Further, we demonstrate star models as potential substitutes for model ensembles. Our code is available at https://github.com/aktsonthalia/starlight.
We propose a unifying framework for the pricing of debt securities under general time-inhomogeneous short-rate diffusion processes. The pricing of bonds, bond options, callable/putable bonds, and convertible bonds (CBs) is covered. Using continuous-time Markov chain (CTMC) approximations, we obtain closed-form matrix expressions to approximate the price of bonds and bond options under general one-dimensional short-rate processes. A simple and efficient algorithm is also developed to price callable/putable debt. The availability of a closed-form expression for the price of zero-coupon bonds allows for the perfect fit of the approximated model to the current market term structure of interest rates, regardless of the complexity of the underlying diffusion process selected. We further consider the pricing of CBs under general bi-dimensional time-inhomogeneous diffusion processes to model equity and short-rate dynamics. Credit risk is also incorporated into the model using the approach of Tsiveriotis and Fernandes (1998). Based on a two-layer CTMC method, an efficient algorithm is developed to approximate the price of convertible bonds. When conversion is only allowed at maturity, a closed-form matrix expression is obtained. Numerical experiments show the accuracy and efficiency of the method across a wide range of model parameters and short-rate models.
Effective action abstraction is crucial in tackling challenges associated with large action spaces in Imperfect Information Extensive-Form Games (IIEFGs). However, due to the vast state space and computational complexity in IIEFGs, existing methods often rely on fixed abstractions, resulting in sub-optimal performance. In response, we introduce RL-CFR, a novel reinforcement learning (RL) approach for dynamic action abstraction. RL-CFR builds upon our innovative Markov Decision Process (MDP) formulation, with states corresponding to public information and actions represented as feature vectors indicating specific action abstractions. The reward is defined as the expected payoff difference between the selected and default action abstractions. RL-CFR constructs a game tree with RL-guided action abstractions and utilizes counterfactual regret minimization (CFR) for strategy derivation. Impressively, it can be trained from scratch, achieving higher expected payoff without increased CFR solving time. In experiments on Heads-up No-limit Texas Hold'em, RL-CFR outperforms ReBeL's replication and Slumbot, demonstrating significant win-rate margins of $64\pm 11$ and $84\pm 17$ mbb/hand, respectively.
This paper presents a comprehensive survey of research works on the topic of form understanding in the context of scanned documents. We delve into recent advancements and breakthroughs in the field, highlighting the significance of language models and transformers in solving this challenging task. Our research methodology involves an in-depth analysis of popular documents and forms of understanding of trends over the last decade, enabling us to offer valuable insights into the evolution of this domain. Focusing on cutting-edge models, we showcase how transformers have propelled the field forward, revolutionizing form-understanding techniques. Our exploration includes an extensive examination of state-of-the-art language models designed to effectively tackle the complexities of noisy scanned documents. Furthermore, we present an overview of the latest and most relevant datasets, which serve as essential benchmarks for evaluating the performance of selected models. By comparing and contrasting the capabilities of these models, we aim to provide researchers and practitioners with useful guidance in choosing the most suitable solutions for their specific form understanding tasks.
We consider a decision maker who is unaware of objects to be sampled and thus cannot form beliefs about the occurrence of particular objects. Ex ante she can form beliefs about the occurrence of novelty and the frequencies of yet to be known objects. Conditional on any sampled objects, she can also form beliefs about the next object being novel or being one of the previously sampled objects. We characterize behaviorally such beliefs under subjective expected utility. In doing so, we relate "reverse" Bayesianism, a central property in the literature on decision making under growing awareness, with exchangeable random partitions, the central property in the literature on the discovery of species problem and mutations in statistics, combinatorial probability theory, and population genetics. Partition exchangeable beliefs do not necessarily satisfy "reverse" Bayesianism. Yet, the most prominent models of exchangeable random partitions, the model by De Morgan (1838), the one parameter model of Ewens (1972), and the two parameter model of Pitman (1995) and Zabell (1997), do satisfy "reverse" Bayesianism. Our characterization allows us to interpret these models as subjective beliefs of a decision maker and to derive the parameters from choice behavior.
The design of feedback controllers is undergoing a paradigm shift from modelic (i.e., model-driven) control to datatic (i.e., data-driven) control. Canonical form of state space model is an important concept in modelic control systems, exemplified by Jordan form, controllable form and observable form, whose purpose is to facilitate system analysis and controller synthesis. In the realm of datatic control, there is a notable absence in the standardization of data-based system representation. This paper for the first time introduces the concept of canonical data form for the purpose of achieving more effective design of datatic controllers. In a control system, the data sample in canonical form consists of a transition component and an attribute component. The former encapsulates the plant dynamics at the sampling time independently, which is a tuple containing three elements: a state, an action and their corresponding next state. The latter describes one or some artificial characteristics of the current sample, whose calculation must be performed in an online manner. The attribute of each sample must adhere to two requirements: (1) causality, ensuring independence from any future samples; and (2) locality, allowing dependence on historical samples but constrained to a finite neighboring set. The purpose of adding attribute is to offer some kinds of benefits for controller design in terms of effectiveness and efficiency. To provide a more close-up illustration, we present two canonical data forms: temporal form and spatial form, and demonstrate their advantages in reducing instability and enhancing training efficiency in two datatic control systems.
Recent studies have investigated utilizing Knowledge Graphs (KGs) to enhance Quesetion Answering (QA) performance of Large Language Models (LLMs), yet structured KG verbalization remains challengin. Existing methods, such as triple-form or free-form textual conversion of triple-form facts, encounter several issues. These include reduced evidence density due to duplicated entities or relationships, and reduced evidence clarity due to an inability to emphasize crucial evidence. To address these issues, we propose EFSum, an Evidence-focused Fact Summarization framework for enhanced QA with knowledge-augmented LLMs. We optimize an open-source LLM as a fact summarizer through distillation and preference alignment. Our extensive experiments show that EFSum improves LLM's zero-shot QA performance, and it is possible to ensure both the helpfulness and faithfulness of the summary.
Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions (e.g., maximum likelihood estimation for Gaussian distribution), or by iterative numerical methods such as Newton-Raphson method when closed-form solution does not exist (e.g., for Beta distribution). In this paper we propose a transformer-based approach to parameter estimation. Compared with existing solutions, our approach does not require a closed-form solution or any mathematical derivations. It does not even require knowing the probability density function, which is needed by numerical methods. After the transformer model is trained, only a single inference is needed to estimate the parameters of the underlying distribution based on a sample of observations. In the empirical study we compared our approach with maximum likelihood estimation on commonly used distributions such as normal distribution, exponential distribution and beta distribution. It is shown that our approach achieves similar or better accuracy as measured by mean-square-errors.
Evaluating the factuality of long-form large language model (LLM)-generated text is an important challenge. Recently there has been a surge of interest in factuality evaluation for English, but little is known about the factuality evaluation of multilingual LLMs, specially when it comes to long-form generation. %This paper systematically evaluates multilingual LLMs' factual accuracy across languages and geographic regions. We introduce a simple pipeline for multilingual factuality evaluation, by applying FActScore (Min et al., 2023) for diverse languages. In addition to evaluating multilingual factual generation, we evaluate the factual accuracy of long-form text generation in topics that reflect regional diversity. We also examine the feasibility of running the FActScore pipeline using non-English Wikipedia and provide comprehensive guidelines on multilingual factual evaluation for regionally diverse topics.
This paper presents a groundbreaking multimodal, multi-task, multi-teacher joint-grained knowledge distillation model for visually-rich form document understanding. The model is designed to leverage insights from both fine-grained and coarse-grained levels by facilitating a nuanced correlation between token and entity representations, addressing the complexities inherent in form documents. Additionally, we introduce new inter-grained and cross-grained loss functions to further refine diverse multi-teacher knowledge distillation transfer process, presenting distribution gaps and a harmonised understanding of form documents. Through a comprehensive evaluation across publicly available form document understanding datasets, our proposed model consistently outperforms existing baselines, showcasing its efficacy in handling the intricate structures and content of visually complex form documents.
This paper introduces a short rate model in continuous time that adds one or more memory (delay) components to the Merton model (Merton 1970, 1973) or the Vasi\v{c}ek model (Vasi\v{c}ek 1977) for the short rate. The distribution of the short rate in this model is normal, with the mean depending on past values of the short rate, and a limiting distribution exists for certain values of the parameters. The zero coupon bond price is an affine function of the short rate, whose coefficients satisfy a system of delay differential equations. This system can be solved analytically, obtaining a closed formula. An analytical expression for the instantaneous forward rate is given: it satisfies the risk neutral dynamics of the Heath-Jarrow-Morton model. Formulae for both forward looking and backward looking caplets on overnight risk free rates are presented. Finally, the proposed model is calibrated against forward looking caplets on SONIA rates and the United States yield curve.