Diffusion theory of decision making in continuous report.

Linking the diffusion model and general recognition theory: Circular diffusion with bivariate-normally distributed drift rates

Reading comparisons across transparent and opaque orthographies indicate critical differences that may reveal the mechanisms involved in orthographic decoding across orthographies. Here, we address the role of criterion and speed of processing in accounting for performance differences across languages. We used binary tasks involving orthographic (words–pseudowords), and non-orthographic materials (female–male faces), and analyzed results based on Ratcliff’s Diffusion model. In the first study, 29 English and 28 Italian university students were given a lexical decision test. English observers made more errors than Italian observers while showing generally similar reaction times. In terms of the diffusion model, the two groups differed in the decision criterion: English observers used a lower criterion. There was no overall cross-linguistic difference in processing speed, but English observers showed lower values for words (and a smaller lexicality effect) than Italians. In the second study, participants were given a face gender judgment test. Female faces were identified slower than the male ones with no language group differences. In terms of the diffusion model, there was no difference between groups in drift rate and boundary separation. Overall, the new main finding concerns a difference in decision criterion limited to the orthographic task: English individuals showed a more lenient criterion in judging the lexicality of the items, a tendency that may explain why, despite lower accuracy, they were not slower. It is concluded that binary tasks (and the Diffusion model) can reveal cross-linguistic differences in orthographic processing which would otherwise be difficult to detect in standard single-word reading tasks.

Diffusion models of decision making, in which successive samples of noisy evidence are accumulated to decision criteria, provide a theoretical solution to von Neumann’s (1956) problem of how to increase the reliability of neural computation in the presence of noise. I introduce and evaluate a new neurally-inspired dual diffusion model, the linear drift, linear infinitesimal variance (LDLIV) model, which embodies three features often thought to characterize neural mechanisms of decision making. The accumulating evidence is intrinsically positively-valued, saturates at high intensities, and is accumulated for each alternative separately. I present explicit integral-equation predictions for the response time distribution and choice probabilities for the LDLIV model and compare its performance on two benchmark sets of data to three other models: the standard diffusion model and two dual diffusion model composed of racing Wiener processes, one between absorbing and reflecting boundaries and one with absorbing boundaries only. The LDLIV model and the standard diffusion model performed similarly to one another, although the standard diffusion model is more parsimonious, and both performed appreciably better than the other two dual diffusion models. I argue that accumulation of noisy evidence by a diffusion process and drift rate variability are both expressions of how the cognitive system solves von Neumann’s problem, by aggregating noisy representations over time and over elements of a neural population. I also argue that models that do not solve von Neumann’s problem do not address the main theoretical question that historically motivated research in this area.

Diffusion models have gained significant attention in the field of generative modeling due to their capability to produce high-quality samples. However, recent studies show that applying a uniform treatment to all distributions during the training of diffusion models is sub-optimal. In this paper, we present a comprehensive theoretical analysis of the forward process in diffusion models. Our findings indicate that distribution variations are not uniform throughout the diffusion process, with the sharpest changes occurring during the initial stages. Moreover, we observe that the initial distribution converges to a Gaussian distribution at an exponential rate, indicating that different initial distributions rapidly become quite similar during the forward diffusion process. Consequently, employing a uniform timestep sampling strategy does not effectively capture these dynamics, potentially leading to sub-optimal training outcomes for diffusion models. To remedy this, we introduce the Bidirectional Beta-Tuned Diffusion Model (BB-TDM). The BB-TDM leverages the Beta distribution to design the timestep sampling distribution and enhance the separation between different initial distributions during the diffusion process. By selecting appropriate parameters, the BB-TDM ensures that the timestep sampling distribution is aligned with the properties of the forward diffusion process and moderates the convergence speed of different initial distributions. Extensive experiments across various benchmark datasets on different diffusion models confirm the efficacy of the proposed BB-TDM.

The circular diffusion model represents continuous outcome decision making as evidence accumulation by a two-dimensional Wiener process with drift on the interior of a disk, whose radius represents the decision criterion for the task. The hitting point on the circumference of the disk represents the decision outcome and the hitting time represents the decision time. The Girsanov change-of-measure theorem applied to the first-passage time distribution for the Euclidean distance Bessel process yields an explicit expression for the joint distribution of decision outcomes and decision times for the model. A problem with the expression for the joint distribution obtained in this way is that the change-of-measure calculation magnifies numerical noise in the series expression for the Bessel process, which can make the expression unstable at small times when the drift rate or decision criterion is large. We introduce a new method that uses an asymptotic approximation to characterize the Bessel process at short times and the series expression for the large times. The resulting expressions are stable across all parts of the parameter space likely to be of interest in experiments, which greatly simplifies the task of fitting the model to data. The new method applies to the spherical and hyperspherical generalizations of the model and to versions of it in which the drift rates are normally distributed across trials with independent or correlated components.

Neutron reflectivity and Fourier transform infrared spectroscopy measurements are used to profile the deprotection reaction−diffusion front with nanometer resolution in a model photoresist polymer using three perfluoroalkane-based photoacid generators (PAG) with varying chain lengths. As expected, the spatial extent of the deprotection reaction front increases with decreasing PAG size. Although the total extent of deprotection increases with increasing postexposure bake time for each PAG, the reaction−diffusion of deprotection does not propagate continuously into the photoresist polymer. The form of the deprotection reaction front changes because the diffusion process is affected by the changing polymer composition. The data are well described by a reaction−diffusion model that includes a simple acid-trapping term and does not require a varying PAG diffusivity. This high-resolution profiling, together with modeling, illustrates details of the coupled diffusion and deprotection reaction processes that affe...

The rapid development of online social networks (OSNs) renders them a powerful platform for information diffusion on a massive scale. OSNs generate enormous propagation traces. An important question is how to model the real-world information diffusion process. Although considerable studies have been conducted in this field, the temporal characteristics have not been fully addressed yet. This thesis addresses the issue of modeling the temporal dynamics of the information diffusion process. Based on empirical findings drawn from large-scale propagation traces of a popular OSN in China, we demonstrate that the temporal characteristics has a significant impact on the diffusion dynamics. Hence, a series of new temporal information diffusion models have been proposed by incorporating these temporal features. Experimental results demonstrate that these proposed models are more accurate and practical than existing discrete diffusion models. Moreover, one application of information diffusion models, i.e., the revenue maximization problem, is studied. Specifically, the thesis consists of three major parts: 1) preliminaries, i.e., introduction of research platform and collected dataset, 2) modeling social influence diffusion from three different temporal aspects, and 3) monetizing OSNs through designing intelligent pricing strategies in the diffusion process to realize the goal of revenue maximization.
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\nFirstly, the research platform is introduced and the statistical properties of the data derived from this platform are investigated. We choose Renren, the dominant social network website in China, as our research platform and study its information propagation mechanisms. Specifically, we concentrate on the propagation of “sharing video” behaviors, and collect data on more than 2.8 million Renren users and over 209 million diffusion traces. The analysis result shows that the video access patterns in OSNs differ significantly from Youtube-like systems, which makes understanding the video propagation behaviors in OSNs an important research task.
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\nSecondly, the temporal modeling of information diffusion is explored. By investigating temporal features using real diffusion traces, we find that three factors should be considered in building realistic diffusion models, including, information propagation latency, multiple influential sources and user diversities. We then develop models to explain the information propagation process by incorporating these factors, and demonstrate that the models reflect reality well.
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\nFinally, revenue maximization in the information diffusion process is studied. Specifically, the pricing factor is explicitly incorporated into the product diffusion process. To realize the goal of revenue maximization, we develop a Dynamic Programming Based Heuristic (DPBH) to obtain the optimal pricing sequence. Application of the DPBH in the revenue maximization problem shows that it performs well in both the expected revenue achieved and in running time. This leads to fundamental ramifications to many related OSN marketing applications.

Demand forecasting plays an important role in demand management, and product diffusion model had been used to forecast the demand of new products for several years. Bass diffusion model describes the empirical adoption curve by using two important factors, namely, the coefficients of innovation and imitation. In 1975, R-L model incorporated the “price” decision variable into diffusion model. A generalized Bass model incorporated price and advertising policies into the original Bass model to analyze empirical new product diffusion process. In this research a system dynamics diffusion model was constructed to model the dynamical diffusion process of a new product. In addition to the four factors, the effect of product brand was added into the system dynamics model. The model was tested and results revealed that the prediction capability of the proposed system dynamics model is better than those of Bass diffusion model, R-L model and generalized Bass model.

Denoising diffusion models have shown a powerful capacity for generating high-quality image samples by progressively removing noise. Inspired by this, we present a diffusion-based mesh denoiser that progressively removes noise from mesh. In general, the iterative algorithm of diffusion models attempts to manipulate the overall structure and fine details of target meshes simultaneously. For this reason, it is difficult to apply the diffusion process to a mesh denoising task that removes artifacts while maintaining a structure. To address this, we formulate a structure-preserving diffusion process. Instead of diffusing the mesh vertices to be distributed as zero-centered isotopic Gaussian distribution, we diffuse each vertex into a specific noise distribution, in which the entire structure can be preserved. In addition, we propose a topology-agnostic mesh diffusion model by projecting the vertex into multiple 2-D viewpoints to efficiently learn the diffusion using a deep network. This enables the proposed method to learn the diffusion of arbitrary meshes that have an irregular topology. Finally, the denoised mesh can be obtained via refinement based on 2-D projections obtained from reverse diffusion. Through extensive experiments, we demonstrate that our method outperforms the state-of-the-art mesh denoising methods in both quantitative and qualitative evaluations.

A population dependent diffusion model with a stochastic extension

This study provides an examination of the effect of public news on inter-day exchange-rate return volatility. Unlike previous studies, the impacts ofboth U.S. and foreign macroeconomic news announcements are examined in the currency futures market for the Japanese yen, British pound, and Deutsche mark. Diffusion and jump-diffusion process models are developed which contain parameters conditional on the release of news. These models are estimated using the method of maximum likelihood, and are tested versus unconditional diffusion and jump-diffusion models using likelihood ratio tests. The results reveal that conditional variance diffusion and jump-diffusion process models dominate the equivalent non-conditional models. Over the period studied (January 1988–December 1990) U.S. merchandise trade balance and industrial production announcements had a significantly greater impact on trading period volatility than money supply or inflation announcements did. Foreign news was also found to have a substantially lower effect on foreign trading-period variance than U.S. news had on U.S. trading period variance. In addition, the correlation between the yen, pound, and mark was highest on days of U.S. macroeconomic news. Thus, this study provides evidence that the currency return generating process is not characterized by a simple diffusion process over trading and non-trading periods. Further, the release of U.S. and foreign macroeconomic news has been shown to provide additional understanding of the currency return process over and above that of more complex models such as a jump-diffusion process.

An integrative model of network activity during episodic memory retrieval and a meta-analysis of fMRI studies on source memory retrieval

The timescale over which magma rises to the surface during a volcanic eruption is a critical parameter that controls eruption style but is challenging to determine. Melt embayments, which are pockets of magma trapped within crystals but are still open to the host magma, tend to develop volatile (e.g., H2O, CO2) concentration gradients during ascent through the process of diffusion. These gradients are increasingly used as output constraints for diffusion models to calculate total ascent time. However, there are two main assumptions associated with the method that have yet to be properly evaluated. First, the diffusion models tend to be carried out in 1D, which may be less accurate than 3D models if the embayment narrows near the opening. This geometry has more complicated volatile flux pathways that 1D models cannot account for. Second, the models typically assume that volatile contents follow equilibrium saturation trends defined by depth below the surface, which may not be accurate for high silica magmas. For these compositions, a significant supersaturation of volatiles may be needed for volatile exsolution to start, depending on the availability of suitable crystal phases for bubble nucleation. This nucleation lag delays the start of diffusion as well and could influence modeled timescales. We developed 3D diffusion models to evaluate the degree of inaccuracy in calculated timescales introduced by these assumptions for high silica magmas. We built synthetic embayments with variable 3D geometries and imposed both equilibrium and disequilibrium ascent conditions in our models. Our results indicate that the inaccuracy introduced by embayment geometry in 1D diffusion models increases as the diameter of the embayment opening decreases. This degree of inaccuracy is also tied to diffusion duration – as it increases, so does the relative error in timescales retrieved by 1D models fitting 3D-generated profiles. Once the diffusion front extends beyond the narrow, “necked” region of the embayment, relative error increases with increasing diffusion time. However, volatile disequilibrium behavior does not appear to significantly impact modeled timescales. These results indicate that embayment geometry is a critical variable that must be accounted for whereas delayed nucleation is of secondary influence.

Generalizing the hypergraph Laplacian via a diffusion process with mediators

Neuroimaging studies suggest that the cerebellum might play a role in both speech perception and speech perceptual learning. However, it remains unclear what this role is: does the cerebellum help shape the perceptual decision, or does it contribute to the timing of perceptual decisions? To test this, we used transcranial direct current stimulation (tDCS) in combination with a speech perception task. Participants experienced a series of speech perceptual tests designed to measure and then manipulate (via training) their perception of a phonetic contrast. One group received cerebellar tDCS during speech perceptual learning, and a different group received sham tDCS during the same task. Both groups showed similar learning-related changes in speech perception that transferred to a different phonetic contrast. For both trained and untrained speech perceptual decisions, cerebellar tDCS significantly increased the time it took participants to indicate their decisions with a keyboard press. By analyzing perceptual responses made by both hands, we present evidence that cerebellar tDCS disrupted the timing of perceptual decisions, while leaving the eventual decision unaltered. In support of this conclusion, we use the drift diffusion model to decompose the data into processes that determine the outcome of perceptual decision-making and those that do not. The modeling suggests that cerebellar tDCS disrupted processes unrelated to decision-making. Taken together, the empirical data and modeling demonstrate that right cerebellar tDCS dissociates the timing of perceptual decisions from perceptual change. The results provide initial evidence in healthy humans that the cerebellum critically contributes to speech timing in the perceptual domain.