Dirichlet process mixture of Gaussians (DPMG) has been used in the literature for clustering and density estimation problems. However, many real-world data exhibit cluster distributions that cannot be captured by a single Gaussian. Modeling such data sets by DPMG creates several extraneous clusters even when clusters are relatively well-defined.

It has been long argued that, because of inherent ambiguity and noise, the brain needs to represent uncertainty in the form of probability distributions. The neural encoding of such distributions remains however highly controversial. Here we present a novel circuit model for representing multidimensional real-valued distributions using a spike based spatio-temporal code. Our model combines the computational advantages of the currently competing models for probabilistic codes and exhibits realistic neural responses along a variety of classic measures. Furthermore, the model highlights the challenges associated with interpreting neural activity in relation to behavioral uncertainty and points to alternative populationlevel approaches for the experimental validation of distributed representations. Core brain computations, such as sensory perception, have been successfully characterized as probabilistic inference, whereby sensory stimuli are interpreted in terms of the objects or features that gave rise to them [1, 2].

We develop a model by choosing the maximum entropy distribution from the set of models satisfying certain smoothness and independence criteria; we show that inference on this model generalizes local kernel estimation to the context of Bayesian inference on stochastic processes. Our model enables Bayesian inference in contexts when standard techniques like Gaussian process inference are too expensive to apply. Exact inference on our model is possible for any likelihood function from the exponential family. Inference is then highly efficient, requiring only O (log N) time and O (N) space at run time. We demonstrate our algorithm on several problems and show quantifiable improvement in both speed and performance relative to models based on the Gaussian process.

A determinantal point process (DPP) is a probabilistic model of set diversity compactly parameterized by a positive semi-definite kernel matrix. To fit a DPP to a given task, we would like to learn the entries of its kernel matrix by maximizing the log-likelihood of the available data. However, log-likelihood is non-convex in the entries of the kernel matrix, and this learning problem is conjectured to be NP-hard [1]. Thus, previous work has instead focused on more restricted convex learning settings: learning only a single weight for each row of the kernel matrix [2], or learning weights for a linear combination of DPPs with fixed kernel matrices [3]. In this work we propose a novel algorithm for learning the full kernel matrix. By changing the kernel parameterization from matrix entries to eigenvalues and eigenvectors, and then lower-bounding the likelihood in the manner of expectation-maximization algorithms, we obtain an effective optimization procedure. We test our method on a real-world product recommendation task, and achieve relative gains of up to 16.5% in test log-likelihood compared to the naive approach of maximizing likelihood by projected gradient ascent on the entries of the kernel matrix.

Learning and memory in the brain are implemented by complex, time-varying changes in neural circuitry. The computational rules according to which synaptic weights change over time are the subject of much research, and are not precisely understood. Until recently, limitations in experimental methods have made it challenging to test hypotheses about synaptic plasticity on a large scale. However, as such data become available and these barriers are lifted, it becomes necessary to develop analysis techniques to validate plasticity models. Here, we present a highly extensible framework for modeling arbitrary synaptic plasticity rules on spike train data in populations of interconnected neurons. We treat synaptic weights as a (potentially nonlinear) dynamical system embedded in a fully-Bayesian generalized linear model (GLM). In addition, we provide an algorithm for inferring synaptic weight trajectories alongside the parameters of the GLM and of the learning rules. Using this method, we perform model comparison of two proposed variants of the well-known spike-timing-dependent plasticity (STDP) rule, where nonlinear effects play a substantial role. On synthetic data generated from the biophysical simulator NEURON, we show that we can recover the weight trajectories, the pattern of connectivity, and the underlying learning rules.

We present a new probabilistic model for transcribing piano music from audio to a symbolic form. Our model reflects the process by which discrete musical events give rise to acoustic signals that are then superimposed to produce the observed data. As a result, the inference procedure for our model naturally resolves the source separation problem introduced by the the piano's polyphony. In order to adapt to the properties of a new instrument or acoustic environment being transcribed, we learn recording-specific spectral profiles and temporal envelopes in an unsupervised fashion. Our system outperforms the best published approaches on a standard piano transcription task, achieving a 10.6% relative gain in note onset F

We analyze a reweighted version of the Kikuchi approximation for estimating the log partition function of a product distribution defined over a region graph. We establish sufficient conditions for the concavity of our reweighted objective function in terms of weight assignments in the Kikuchi expansion, and show that a reweighted version of the sum product algorithm applied to the Kikuchi region graph will produce global optima of the Kikuchi approximation whenever the algorithm converges. When the region graph has two layers, corresponding to a Bethe approximation, we show that our sufficient conditions for concavity are also necessary. Finally, we provide an explicit characterization of the polytope of concavity in terms of the cycle structure of the region graph. We conclude with simulations that demonstrate the advantages of the reweighted Kikuchi approach.

Recent advancements in reinforcement learning (RL) have achieved great success in fine-tuning diffusion-based generative models. However, fine-tuning continuous flow-based generative models to align with arbitrary user-defined reward functions remains challenging, particularly due to issues such as policy collapse from overoptimization and the prohibitively high computational cost of likelihoods in continuous-time flows. In this paper, we propose an easy-to-use and theoretically sound RL fine-tuning method, which we term Online Reward-Weighted Conditional Flow Matching with Wasserstein-2 Regularization (ORW-CFM-W2). Our method integrates RL into the flow matching framework to fine-tune generative models with arbitrary reward functions, without relying on gradients of rewards or filtered datasets. By introducing an online reward-weighting mechanism, our approach guides the model to prioritize high-reward regions in the data manifold. To prevent policy collapse and maintain diversity, we incorporate Wasserstein-2 (W2) distance regularization into our method and derive a tractable upper bound for it in flow matching, effectively balancing exploration and exploitation of policy optimization. We provide theoretical analyses to demonstrate the convergence properties and induced data distributions of our method, establishing connections with traditional RL algorithms featuring Kullback-Leibler (KL) regularization and offering a more comprehensive understanding of the underlying mechanisms and learning behavior of our approach. Extensive experiments on tasks including target image generation, image compression, and text-image alignment demonstrate the effectiveness of our method, where our method achieves optimal policy convergence while allowing controllable trade-offs between reward maximization and diversity preservation.

In the context of the rapid dissemination of multimedia content, identifying disinformation on social media platforms such as TikTok represents a significant challenge. This study introduces a hybrid framework that combines the computational power of deep learning with the interpretability of fuzzy logic to detect suspected disinformation in TikTok videos. The methodology is comprised of two core components: a multimodal feature analyser that extracts and evaluates data from text, audio, and video; and a multimodal disinformation detector based on fuzzy logic. These systems operate in conjunction to evaluate the suspicion of spreading disinformation, drawing on human behavioural cues such as body language, speech patterns, and text coherence. Two experiments were conducted: one focusing on context-specific disinformation and the other on the scalability of the model across broader topics. For each video evaluated, high-quality, comprehensive, well-structured reports are generated, providing a detailed view of the disinformation behaviours.

This paper introduces a unified theoretical framework for modeling temporal memory dynamics, combining concepts from temporal logic, memory decay models, and hierarchical contexts. The framework formalizes the evolution of propositions over time using linear and branching temporal models, incorporating exponential decay (Ebbinghaus forgetting curve) and reactivation mechanisms via Bayesian updating. The hierarchical organization of memory is represented using directed acyclic graphs to model recall dependencies and interference. Novel insights include feedback dynamics, recursive influences in memory chains, and the integration of entropy-based recall efficiency. This approach provides a foundation for understanding memory processes across cognitive and computational domains. Let t R represent a temporal parameter.