Recent advances in large vision-language models (VLMs) have shown remarkable progress in solving the text-promptable object counting problem. Representative methods typically specify text prompts with object category information in images. This however is insufficient for training the model to accurately distinguish the number of objects in the counting task. To this end, we propose QUANet, which introduces novel quantity-oriented text prompts with a vision-text quantity alignment loss to enhance the model's quantity awareness. Moreover, we propose a dual-stream adaptive counting decoder consisting of a Transformer stream, a CNN stream, and a number of Transformer-to-CNN enhancement adapters (T2C-adapters) for density map prediction. The T2C-adapters facilitate the effective knowledge communication and aggregation between the Transformer and CNN streams. A cross-stream quantity ranking loss is proposed in the end to optimize the ranking orders of predictions from the two streams. Extensive experiments on standard benchmarks such as FSC-147, CARPK, PUCPR+, and ShanghaiTech demonstrate our model's strong generalizability for zero-shot class-agnostic counting. Code is available at htt
The geometric shapes of the outside world objects hide an undisclosed emotional, psychological, artistic, aesthetic and shape-generating potential; they may attract or cause fear as well as a variety of other emotions. This suggests that living beings with vision perceive geometric objects within an information-handling process. However, not many studies have been performed for a better understanding of visual perception from the view of information theory and mathematical modelling, but the evidence first found by Attneave (1954) suggests that the concepts and techniques of information theory may shed light on a better and deeper understanding of visual perception. The quantity of information function can theoretically explain the concentration of information on the visual contours, and, based on this, we first propose the concept of the quantity of information continuous splines for visualization of shapes from a given set of discrete data without adding any in-between points with curvature extreme. Additionally, we first discover planar curve with a constant quantity of information function and demonstrate one of the conditions when a monotonic curvature curve has a constant qua
We show how the fundamental entropic inequality proved recently in [arXiv:2408.15306] can be applied to obtain a useful relation for the Holevo quantity of discrete and continuous ensembles of quantum states. This relation gives a tight upper bound on the Holevo quantity of a given ensemble $μ$ expressed in terms of the Holevo quantities of two auxiliary ensembles $μ_+$ and $μ_-$ produced by $μ$. Among others, this implies quite accurate upper bounds on the Holevo quantity of a discrete ensemble of quantum states expressed via the probabilities and the metric characteristics of an ensemble.
Scalable oversight studies methods of training and evaluating AI systems in domains where human judgment is unreliable or expensive, such as scientific research and software engineering in complex codebases. Most work in this area has focused on methods of improving the quality of labels. Recent work by Burns et al. (2023) considers the complementary problem of training models with low-quality labels, finding that large pretrained models often have an inductive bias towards producing correct answers. In practice, however, neither label quantity nor quality is fixed: practitioners face a quantity-quality tradeoff. In this paper, we explore the microeconomics of the quantity-quality tradeoff on binary NLP classification tasks used in Burns et al. (2023). While sample-efficient learning has been studied extensively, little public research has focused on scalable elicitation: eliciting capabilities from pretrained models subject to labeling cost constraints. We find that this setting has novel dynamics caused by the tradeoff between label quantity and quality, as well as the model's existing latent capabilities. We observe three regimes of eliciting classification knowledge from pretra
Quantitative information plays a crucial role in understanding and interpreting the content of documents. Many user queries contain quantities and cannot be resolved without understanding their semantics, e.g., ``car that costs less than $10k''. Yet, modern search engines apply the same ranking mechanisms for both words and quantities, overlooking magnitude and unit information. In this paper, we introduce two quantity-aware ranking techniques designed to rank both the quantity and textual content either jointly or independently. These techniques incorporate quantity information in available retrieval systems and can address queries with numerical conditions equal, greater than, and less than. To evaluate the effectiveness of our proposed models, we introduce two novel quantity-aware benchmark datasets in the domains of finance and medicine and compare our method against various lexical and neural models. The code and data are available under https://github.com/satya77/QuantityAwareRankers.
This study addresses the multi-item multi-period order allocation problem under all-unit quantity discounts (AUQD) and blending ratios. A manufacturer makes a single product that requires mixing/assembling multiple ingredients/components with pre-determined blending ratios. We consider a single supplier offering quantity-based discounts which introduces non-linearities to the problem. The objective is to minimize procurement cost which includes purchasing, inventory, and ordering costs. We develop a solution procedure that systematically generates a finite dominating set (FDS) of order quantities guaranteed to include an optimal solution to the problem. A Mixed Integer Linear Programming (MILP) model based on the FDS. Our procedure guarantees optimality and eliminates the need for nonlinear discount modeling. Numerical experiments demonstrate that the proposed MILP achieves optimal solutions with significantly reduced computational effort, up to 99% faster for large-scale instances compared to conventional formulations. Sensitivity analyses reveal that the model dynamically adapts to changes in holding costs, shifting between bulk-purchasing and just-in-time strategies, and identif
The Holevo quantity and the $SU(2)$-invariant states have particular importance in quantum information processing. We calculate analytically the Holevo quantity for bipartite systems composed of spin-$j$ and spin-$\frac{1}{2}$ subsystems with $SU(2)$ symmetry, when the projective measurements are performed on the spin-$\frac{1}{2}$ subsystem. The relations among the Holevo quantity, the maximal values of the Holevo quantity and the states are analyzed in detail. In particular, we show that the Holevo quantity increases in the parameter region $F<F_d$ and decreases in region $F>F_d$ when $j$ increases, where $F$ is function of temperature in thermal equilibrium and $F_d=j/(2j+1)$, and the maximum value of the Holevo quantity is attained at $F=1$ for all $j$. Moreover, when the dimension of system increases, the maximal value of the Holevo quantity decreases.
The paper introduces a procedure for determining an approximation of the optimal amount of photovoltaics (PVs) for powering water distribution networks (WDNs) through grid-connected PVs. The procedure aims to find the PV amount minimizing the total expected cost of the WDN over the lifespan of the PVs. The approach follows an iterative process, starting with an initial estimate of the PV quantity, and then calculating the total cost of WDN operation. To calculate the total cost of the WDN, we sample PV power profiles that represent the future production based on a probabilistic PV production model. Simulations are conducted assuming these sampled PV profiles power the WDN, and pump flow rates are determined using a control method designed for PV-powered WDNs. Following the simulations, the overall WDN cost is calculated. Since we lack access to derivative information, we employ the derivative-free Nelder-Mead method for iteratively adjusting the PV quantity to find an approximation of the optimal value. The procedure is applied for the WDN of Randers, a Danish town. By determining an approximation of the optimal quantity of PVs, we observe a 14.5\% decrease in WDN costs compared to
CLIP has demonstrated great versatility in adapting to various downstream tasks, such as image editing and generation, visual question answering, and video understanding. However, CLIP-based applications often suffer from misunderstandings regarding user intent, leading to discrepancies between the required number of objects and the actual outputs in image generation tasks. In this work, we empirically investigate the quantity bias in CLIP. By carefully designing different experimental settings and datasets, we comprehensively evaluate CLIP's understanding of quantity from text, image, and cross-modal perspectives. Our experimental results reveal a quantity bias in CLIP embeddings, impacting the reliability of downstream tasks.
We study the equilibria of uniform price auctions where many asymmetric bidders have flat demands up to their respective quantity constraints. We present an iterative procedure that systematically finds an equilibrium outcome as well as an ascending auction that has this outcome as a dominant strategy equilibrium outcome. Demand reduction and low price equilibrium may occur since it is advantageous for a bidder to give up some of his/her demand and get the remaining demand at a low price rather than to get his/her entire demand at a higher price. We show that a low price equilibrium is the only possible equilibrium when no bidder's quantity constraint is large enough to cover the supply.
The problem of the directionality of genome evolution is studied. Based on the analysis of C-value paradox and the evolution of genome size we propose that the function-coding information quantity of a genome always grows in the course of evolution through sequence duplication, expansion of code, and gene transfer from outside. The function-coding information quantity of a genome consists of two parts, p-coding information quantity which encodes functional protein and n-coding information quantity which encodes other functional elements except amino acid sequence. The evidences on the evolutionary law about the function-coding information quantity are listed. The needs of function is the motive force for the expansion of coding information quantity and the information quantity expansion is the way to make functional innovation and extension for a species. So, the increase of coding information quantity of a genome is a measure of the acquired new function and it determines the directionality of genome evolution.
I discuss various aspects of the concept of a quantity in physics and metrology and related consideration in reference documents of IUPAP, IUPAC, ISO, IEC, and JCGM.
Quantities are essential in documents to describe factual information. They are ubiquitous in application domains such as finance, business, medicine, and science in general. Compared to other information extraction approaches, interestingly only a few works exist that describe methods for a proper extraction and representation of quantities in text. In this paper, we present such a comprehensive quantity extraction framework from text data. It efficiently detects combinations of values and units, the behavior of a quantity (e.g., rising or falling), and the concept a quantity is associated with. Our framework makes use of dependency parsing and a dictionary of units, and it provides for a proper normalization and standardization of detected quantities. Using a novel dataset for evaluation, we show that our open source framework outperforms other systems and -- to the best of our knowledge -- is the first to detect concepts associated with identified quantities. The code and data underlying our framework are available at https://github.com/vivkaz/CQE.
Addiction is a major societal issue leading to billions in healthcare losses per year. Policy makers often introduce ad hoc quantity limits-limits on the consumption or possession of a substance-something which current economic models of addiction have failed to address. This paper enriches Bernheim and Rangel (2004)'s model of addiction driven by cue-triggered decisions by incorporating endogenous choice of how much of the addictive good to consume, instead of just whether or not consumption happens. Stricter quality limits improve welfare as long as they do not preclude the myopically optimal level of consumption.
Software engineering capabilities are increasingly important to the success of economic and political blocs. This paper analyzes quantity and quality of software engineering research output originating from the US, Europe, and China over time. The results indicate that the quantity of research is increasing across the board with Europe leading the field. Depending of the scope of the analysis, either the US or China come in second. Regarding research quality, Europe appears to be lagging the other blocs, with China having caught up to and even having overtaken the US over time.
An algebraic structure underlying the quantity calculus is proposed consisting in an algebraic fiber bundle, that is, a base structure which is a free Abelian group together with fibers which are one dimensional vector spaces, all of them bound by algebraic restrictions. Subspaces, tensor product and quotient spaces are considered as well as homomorphisms to end with a classification theorem of these structures. The new structure provides an axiomatic foundation for quantity calculus and gives complete justification within its framework of the way that quantity calculus is actually performed. It is hoped that this exposition helps to clarify the role of the interviening concepts of quantity, quantity value, quantity dimension and their relation with a system of units, particularly, the SI.
This article includes a survey of the historical development and theoretical structure of the pre-modern theory of magnitudes and numbers. In Part 1, work, insights and controversies related to quantity calculus from Euler onward are reviewed. In Parts 2 and 3, we define scalable monoids and, as a special case, quantity spaces; both can be regarded as universal algebras. Scalable monoids are related to rings and modules, and quantity spaces are to scalable monoids as vector spaces are to modules. Subalgebras and homomorphic images of scalable monoids can be formed, and tensor products of scalable monoids can be constructed as well. We also define and investigate congruence relations on scalable monoids, unit elements of scalable monoids, basis-like substructures of scalable monoids and quantity spaces, and scalar representations of elements of quantity spaces. The mathematical theory of quantity spaces is presented with a view to metrological applications. This article supersedes arXiv:1503.00564 and complements arXiv:1408.5024.
An arithmetic word problem typically includes a textual description containing several constant quantities. The key to solving the problem is to reveal the underlying mathematical relations (such as addition and subtraction) among quantities, and then generate equations to find solutions. This work presents a novel approach, Quantity Tagger, that automatically discovers such hidden relations by tagging each quantity with a sign corresponding to one type of mathematical operation. For each quantity, we assume there exists a latent, variable-sized quantity span surrounding the quantity token in the text, which conveys information useful for determining its sign. Empirical results show that our method achieves 5 and 8 points of accuracy gains on two datasets respectively, compared to prior approaches.
We point out that Ecker's local integral quantity agrees with Huisken's global integral quantity at infinity for ancient mean curvature flows if Huisken's one is finite on each time-slice. In particular, this means that the finiteness of Ecker's integral quantity at infinity implies the finiteness of the entropy at infinity.
The Holevo bound is a keystone in many applications of quantum information theory. We propose "weak maximal Holevo quantity" with weak measurements as the generalization of the standard Holevo quantity which is defined as the optimal projective measurements. The scenarios that weak measurements is necessary are that only the weak measurements can be performed because for example the system is macroscopic or that one intentionally tries to do so such that the disturbance on the measured system can be controlled for example in quantum key distribution protocols. We evaluate systematically the weak maximal Holevo quantity for Bell-diagonal states and find a series of results. Furthermore, we find that weak measurements can be realized by noise and project measurements.