A general theory of stochastic extensive forms is developed to bridge two concepts of information flow: decision trees and refined partitions on the one side, filtrations from probability theory on the other. Instead of the traditional "nature" agent, this framework uses a single lottery draw to select a tree of a given decision forest. Each "personal" agent receives dynamic updates from an own oracle on the lottery outcome and makes partition-refining choices adapted to this information. This theory addresses a key limitation of existing approaches in extensive form theory, which struggle to model continuous-time stochastic processes, such as Brownian motion, as outcomes of "nature" decision making. Additionally, a class of stochastic extensive forms based on time-indexed action paths is constructed, encompassing a wide range of models from the literature and laying the groundwork for an approximation theory for stochastic differential games in extensive form.
Expected Improvement (EI) is arguably the most widely used acquisition function in Bayesian optimization. However, it is often challenging to enhance the performance with EI due to its sensitivity to numerical precision. Previously, Hutter et al. (2009) tackled this problem by using Gaussian process trained on the log-transformed objective function and it was reported that this trick improves the predictive accuracy of GP, leading to substantially better performance. Although Hutter et al. (2009) offered the closed form of their EI, its intermediate derivation has not been provided so far. In this paper, we give a friendly derivation of their proposition.
Large language models (LLMs) have demonstrated strong capabilities in text understanding and generation. However, they often lack factuality, producing a mixture of true and false information, especially in long-form generation. In this work, we investigates the factuality of long-form text generation across various large language models (LLMs), including GPT-4, Gemini-1.5-Pro, Claude-3-Opus, Llama-3-70B, and Mistral. Our analysis reveals that factuality scores tend to decline in later sentences of the generated text, accompanied by a rise in the number of unsupported claims. Furthermore, we explore the effectiveness of different evaluation settings to assess whether LLMs can accurately judge the correctness of their own outputs: Self-Known (the percentage of supported atomic claims, decomposed from LLM outputs, that the corresponding LLMs judge as correct) and Self-Unknown (the percentage of unsupported atomic claims that the corresponding LLMs judge as incorrect). The results indicate that even advanced models like GPT-4 and Gemini-1.5-Pro fail to achieve perfect Self-Known scores, while their Self-Unknown scores remain notably above zero, reflecting ongoing uncertainty in their self-assessments. Moreover, we find a correlation between higher Self-Known scores and improved factuality, while higher Self-Unknown scores are associated with lower factuality. Interestingly, even without significant changes in the models' self-judgment (Self-Known and Self-Unknown), the number of unsupported claims can increases, likely as an artifact of long-form generation. These findings show the limitations of current LLMs in long-form generation, and provide valuable insights for improving factuality in long-form text generation.
Despite advances in Large Multi-modal Models, applying them to long and untrimmed video content remains challenging due to limitations in context length and substantial memory overhead. These constraints often lead to significant information loss and reduced relevance in the model responses. With the exponential growth of video data across web platforms, understanding long-form video is crucial for advancing generalized intelligence. In this paper, we introduce SALOVA: Segment-Augmented LOng Video Assistant, a novel video-LLM framework designed to enhance the comprehension of lengthy video content through targeted retrieval process. We address two main challenges to achieve it: (i) We present the SceneWalk dataset, a high-quality collection of 87.8K long videos, each densely captioned at the segment level to enable models to capture scene continuity and maintain rich descriptive context. (ii) We develop robust architectural designs integrating dynamic routing mechanism and spatio-temporal projector to efficiently retrieve and process relevant video segments based on user queries. Our framework mitigates the limitations of current video-LMMs by allowing for precise identification and retrieval of relevant video segments in response to queries, thereby improving the contextual relevance of the generated responses. Through extensive experiments, SALOVA demonstrates enhanced capability in processing complex long-form videos, showing significant capability to maintain contextual integrity across extended sequences.
In our previous work [Ma and Chan (2023)], we presented a feedforward unitary equivariant neural network. We proposed three distinct activation functions tailored for this network: a softsign function with a small residue, an identity function, and a Leaky ReLU function. While these functions demonstrated the desired equivariance properties, they limited the neural network's architecture. This short paper generalises these activation functions to a single functional form. This functional form represents a broad class of functions, maintains unitary equivariance, and offers greater flexibility for the design of equivariant neural networks.
With the expanding use of the short-form video format in advertising, social media, entertainment, education and more, there is a need for such media to both captivate and be remembered. Video memorability indicates to us how likely a video is to be remembered by a viewer who has no emotional or personal connection with its content. This paper presents the results of using generative outpainting to expand the screen size of a short-form video with a view to improving its memorability. Advances in machine learning and deep learning are compared and leveraged to understand how extending the borders of video screensizes can affect their memorability to viewers. Using quantitative evaluation we determine the best-performing model for outpainting and the impact of outpainting based on image saliency on video memorability scores
Lyrics generation presents unique challenges, particularly in achieving precise syllable control while adhering to song form structures such as verses and choruses. Conventional line-by-line approaches often lead to unnatural phrasing, underscoring the need for more granular syllable management. We propose a framework for lyrics generation that enables multi-level syllable control at the word, phrase, line, and paragraph levels, aware of song form. Our approach generates complete lyrics conditioned on input text and song form, ensuring alignment with specified syllable constraints. Generated lyrics samples are available at: https://tinyurl.com/lyrics9999
We introduce SymbolFit, a framework that automates parametric modeling by using symbolic regression to perform a machine-search for functions that fit the data while simultaneously providing uncertainty estimates in a single run. Traditionally, constructing a parametric model to accurately describe binned data has been a manual and iterative process, requiring an adequate functional form to be determined before the fit can be performed. The main challenge arises when the appropriate functional forms cannot be derived from first principles, especially when there is no underlying true closed-form function for the distribution. In this work, we develop a framework that automates and streamlines the process by utilizing symbolic regression, a machine learning technique that explores a vast space of candidate functions without requiring a predefined functional form because the functional form itself is treated as a trainable parameter, making the process far more efficient and effortless than traditional regression methods. We demonstrate the framework in high-energy physics experiments at the CERN Large Hadron Collider (LHC) using five real proton-proton collision datasets from new physics searches, including background modeling in resonance searches for high-mass dijet, trijet, paired-dijet, diphoton, and dimuon events. We show that our framework can flexibly and efficiently generate a wide range of candidate functions that fit a nontrivial distribution well using a simple fit configuration that varies only by random seed, and that the same fit configuration, which defines a vast function space, can also be applied to distributions of different shapes, whereas achieving a comparable result with traditional methods would have required extensive manual effort.
There is a lack of benchmarks for evaluating large language models (LLMs) in long-form medical question answering (QA). Most existing medical QA evaluation benchmarks focus on automatic metrics and multiple-choice questions. While valuable, these benchmarks fail to fully capture or assess the complexities of real-world clinical applications where LLMs are being deployed. Furthermore, existing studies on evaluating long-form answer generation in medical QA are primarily closed-source, lacking access to human medical expert annotations, which makes it difficult to reproduce results and enhance existing baselines. In this work, we introduce a new publicly available benchmark featuring real-world consumer medical questions with long-form answer evaluations annotated by medical doctors. We performed pairwise comparisons of responses from various open and closed-source medical and general-purpose LLMs based on criteria such as correctness, helpfulness, harmfulness, and bias. Additionally, we performed a comprehensive LLM-as-a-judge analysis to study the alignment between human judgments and LLMs. Our preliminary results highlight the strong potential of open LLMs in medical QA compared to leading closed models. Code & Data: https://github.com/lavita-ai/medical-eval-sphere
We introduce DAHL, a benchmark dataset and automated evaluation system designed to assess hallucination in long-form text generation, specifically within the biomedical domain. Our benchmark dataset, meticulously curated from biomedical research papers, consists of 8,573 questions across 29 categories. DAHL evaluates fact-conflicting hallucinations in Large Language Models (LLMs) by deconstructing responses into atomic units, each representing a single piece of information. The accuracy of these responses is averaged to produce the DAHL Score, offering a more in-depth evaluation of hallucinations compared to previous methods that rely on multiple-choice tasks. We conduct experiments with 8 different models, finding that larger models tend to hallucinate less; however, beyond a model size of 7 to 8 billion parameters, further scaling does not significantly improve factual accuracy. The DAHL Score holds potential as an efficient alternative to human-annotated preference labels, being able to be expanded to other specialized domains. We release the dataset and code in public.
The performance of linear receive beamforming in continuous-aperture array (CAPA)-based uplink communications is analyzed. Three continuous beamforming techniques are proposed under the criteria of maximum-ratio combining (MRC), zero-forcing (ZF), and minimum mean-squared error (MMSE). \romannumeral1) For \emph{MRC beamforming}, a closed-form expression for the beamformer is derived to maximize per-user signal power. The achieved uplink rate and mean-squared error (MSE) in detecting received data symbols are analyzed. \romannumeral2) For \emph{ZF beamforming}, a closed-form beamformer is derived based on channel correlation to eliminate interference. As a further advance, its optimality in maximizing effective channel gain while ensuring zero inter-user interference is proven. \romannumeral3) \emph{MMSE beamforming} is established as the optimal linear receive approach for CAPAs in terms of maximizing per-user rate and minimizing MSE. Closed-form expressions are derived for the MMSE beamformer and the achievable sum-rate and sum-MSE. It is mathematically proven that all proposed beamformers lie within the signal subspace spanned by users' spatial responses. Numerical results demonstrate that CAPAs outperform conventional spatially-discrete arrays (SPDAs) by achieving higher sum-rates and lower sum-MSEs under the proposed linear beamforming techniques.
Data assimilation (DA) combines partial observations with a dynamical model to improve state estimation. Filter-based DA uses only past and present data and is the prerequisite for real-time forecasts. Smoother-based DA exploits both past and future observations. It aims to fill in missing data, provide more accurate estimations, and develop high-quality datasets. However, the standard smoothing procedure requires using all historical state estimations, which is storage-demanding, especially for high-dimensional systems. This paper develops an adaptive-lag online smoother for a large class of complex dynamical systems with strong nonlinear and non-Gaussian features, which has important applications to many real-world problems. The adaptive lag allows the DA to utilize only observations within a nearby window, significantly reducing computational storage. Online lag adjustment is essential for tackling turbulent systems, where temporal autocorrelation varies significantly over time due to intermittency, extreme events, and nonlinearity. Based on the uncertainty reduction in the estimated state, an information criterion is developed to systematically determine the adaptive lag. Notably, the mathematical structure of these systems facilitates the use of closed analytic formulae to calculate the online smoother and the adaptive lag, avoiding empirical tunings as in ensemble-based DA methods. The adaptive online smoother is applied to studying three important scientific problems. First, it helps detect online causal relationships between state variables. Second, its advantage of computational storage is illustrated via Lagrangian DA, a high-dimensional nonlinear problem. Finally, the adaptive smoother advances online parameter estimation with partial observations, emphasizing the role of the observed extreme events in accelerating convergence.
This study investigates the linguistic understanding of Large Language Models (LLMs) regarding signifier (form) and signified (meaning) by distinguishing two LLM evaluation paradigms: psycholinguistic and neurolinguistic. Traditional psycholinguistic evaluations often reflect statistical biases that may misrepresent LLMs' true linguistic capabilities. We introduce a neurolinguistic approach, utilizing a novel method that combines minimal pair and diagnostic probing to analyze activation patterns across model layers. This method allows for a detailed examination of how LLMs represent form and meaning, and whether these representations are consistent across languages. Our contributions are three-fold: (1) We compare neurolinguistic and psycholinguistic methods, revealing distinct patterns in LLM assessment; (2) We demonstrate that LLMs exhibit higher competence in form compared to meaning, with the latter largely correlated to the former; (3) We present new conceptual minimal pair datasets for Chinese (COMPS-ZH) and German (COMPS-DE), complementing existing English datasets.
We present SimpleQA, a benchmark that evaluates the ability of language models to answer short, fact-seeking questions. We prioritized two properties in designing this eval. First, SimpleQA is challenging, as it is adversarially collected against GPT-4 responses. Second, responses are easy to grade, because questions are created such that there exists only a single, indisputable answer. Each answer in SimpleQA is graded as either correct, incorrect, or not attempted. A model with ideal behavior would get as many questions correct as possible while not attempting the questions for which it is not confident it knows the correct answer. SimpleQA is a simple, targeted evaluation for whether models "know what they know," and our hope is that this benchmark will remain relevant for the next few generations of frontier models. SimpleQA can be found at https://github.com/openai/simple-evals.
It is a market practice to express market-implied volatilities in some parametric form. The most popular parametrizations are based on or inspired by an underlying stochastic model, like the Heston model (SVI method) or the SABR model (SABR parametrization). Their popularity is often driven by a closed-form representation enabling efficient calibration. However, these representations indirectly impose a model-specific volatility structure on observable market quotes. When the market's volatility does not follow the parametric model regime, the calibration procedure will fail or lead to extreme parameters, indicating inconsistency. This article addresses this critical limitation - we propose an arbitrage-free framework for letting the parameters from the parametric implied volatility formula be random. The method enhances the existing parametrizations and enables a significant widening of the spectrum of permissible shapes of implied volatilities while preserving analyticity and, therefore, computation efficiency. We demonstrate the effectiveness of the novel method on real data from short-term index and equity options, where the standard parametrizations fail to capture market dynamics. Our results show that the proposed method is particularly powerful in modeling the implied volatility curves of short expiry options preceding an earnings announcement, when the risk-neutral probability density function exhibits a bimodal form.
In this work, we propose a low-cost rate splitting (RS) technique for a multi-user multiple-input single-output (MISO) system operating in frequency division duplex (FDD) mode. The proposed iterative optimisation algorithm only depends on the second-order statistical channel knowledge and the pilot training matrix. Additionally, it offers a closed-form solution in each update step. This reduces the design complexity of the system drastically as we only need to optimise the precoding filters in every coherence interval of the covariance matrices, instead of doing that in every channel state information (CSI) coherence interval. Moreover, since the algorithm is based on closed-form solutions, there is no need for interior point solvers like CVX, which are typically required in most state-of-the-art techniques.
The capacity of long-term memory seems to be extremely large, capable of storing information spanning almost a lifetime. Why does it have such a vast capacity? Why are some memories so enduring? What is the actual physical form of long-term memory? In the movie Inside Out, it is depicted as individual orbs containing information. Is that really the case? Simply explaining this by saying that the cortex has many neurons, numerous neural connections, and complex electrochemical activity between them is not sufficient to answer these fundamental questions. We need to uncover the theory hidden behind these phenomena.In essence, a neural network is equivalent to a very large directed graph, with a massive number of nodes and directed connections. This paper posits that the physical form of long-term memory is a connected subgraph within this complex directed graph. This subgraph is capable of linking together the disparate fragments of the same event, spread across different sensory cortices, to form associations. This provides a physical realization of the engram theory. The robustness of the connected subgraph and the resources it consumes can explain various memory behaviors.Based on anatomical, brain imaging and electrophysiological evidence, this paper constructs a probabilistic connectivity model and uses theorems from graph theory to prove the ease of constructing connected subgraphs. Finally, it explains why the potential capacity for memory is immense.
This work proposes a novel degradation-infused energy portfolio allocation (DI-EPA) framework for enabling the participation of battery energy storage systems in multi-service electricity markets. The proposed framework attempts to address the challenge of including the rainflow algorithm for cycle counting by directly developing a closed-form of marginal degradation as a function of dispatch decisions. Further, this closed-form degradation profile is embedded into an energy portfolio allocation (EPA) problem designed for making the optimal dispatch decisions for all the batteries together, in a shared economy manner. We term the entity taking these decisions as `facilitator' which works as a link between storage units and market operators. The proposed EPA formulation is quipped with a conditional-value-at-risk (CVaR)-based mechanism to bring risk-averseness against uncertainty in market prices. The proposed DI-EPA problem introduces fairness by dividing the profits into various units using the idea of marginal contribution. Simulation results regarding the accuracy of the closed-form of degradation, effectiveness of CVaR in handling uncertainty within the EPA problem, and fairness in the context of degradation awareness are discussed. Numerical results indicate that the DI-EPA framework improves the net profit of the storage units by considering the effect of degradation in optimal market participation.
This paper investigates the capabilities of text-to-audio music generation models in producing long-form music with prompts that change over time, focusing on soundtrack generation for Tabletop Role-Playing Games (TRPGs). We introduce Babel Bardo, a system that uses Large Language Models (LLMs) to transform speech transcriptions into music descriptions for controlling a text-to-music model. Four versions of Babel Bardo were compared in two TRPG campaigns: a baseline using direct speech transcriptions, and three LLM-based versions with varying approaches to music description generation. Evaluations considered audio quality, story alignment, and transition smoothness. Results indicate that detailed music descriptions improve audio quality while maintaining consistency across consecutive descriptions enhances story alignment and transition smoothness.
We propose an entropy-stable conservative flux form neural network (CFN) that integrates classical numerical conservation laws into a data-driven framework using the entropy-stable, second-order, and non-oscillatory Kurganov-Tadmor (KT) scheme. The proposed entropy-stable CFN uses slope limiting as a denoising mechanism, ensuring accurate predictions in both noisy and sparse observation environments, as well as in both smooth and discontinuous regions. Numerical experiments demonstrate that the entropy-stable CFN achieves both stability and conservation while maintaining accuracy over extended time domains. Furthermore, it successfully predicts shock propagation speeds in long-term simulations, {\it without} oracle knowledge of later-time profiles in the training data.