LLM-based agents have been widely applied as personal assistants, capable of memorizing information from user messages and responding to personal queries. However, there still lacks an objective and automatic evaluation on their memory capability, largely due to the challenges in constructing reliable questions and answers (QAs) according to user messages. In this paper, we propose MemSim, a Bayesian simulator designed to automatically construct reliable QAs from generated user messages, simultaneously keeping their diversity and scalability. Specifically, we introduce the Bayesian Relation Network (BRNet) and a causal generation mechanism to mitigate the impact of LLM hallucinations on factual information, facilitating the automatic creation of an evaluation dataset. Based on MemSim, we generate a dataset in the daily-life scenario, named MemDaily, and conduct extensive experiments to assess the effectiveness of our approach. We also provide a benchmark for evaluating different memory mechanisms in LLM-based agents with the MemDaily dataset.

Speculative decoding is a promising approach for accelerating large language models. The primary idea is to use a lightweight draft model to speculate the output of the target model for multiple subsequent timesteps, and then verify them in parallel to determine whether the drafted tokens should be accepted or rejected. To enhance acceptance rates, existing frameworks typically construct token trees containing multiple candidates in each timestep. However, their reliance on token-level verification mechanisms introduces two critical limitations: First, the probability distribution of a sequence differs from that of individual tokens, leading to suboptimal acceptance length. Second, current verification schemes begin from the root node and proceed layer by layer in a top-down manner.

A fundamental challenge in probabilistic modeling is to balance expressivity and inference efficiency. Tractable probabilistic models (TPMs) aim to directly address this tradeoff by imposing constraints that guarantee efficient inference of certain queries while maintaining expressivity. In particular, probabilistic circuits (PCs) provide a unifying framework for many TPMs, by characterizing families of models as circuits satisfying different structural properties. Because the complexity of inference on PCs is a function of the circuit size, understanding the size requirements of different families of PCs is fundamental in mapping the trade-off between tractability and expressive efficiency. However, the study of expressive efficiency of circuits are often concerned with exact representations, which may not align with model learning, where we look to approximate the underlying data distribution closely by some distance measure.

We propose a framework for learning maps between probability distributions that broadly generalizes the time dynamics of flow and diffusion models. To enable this, we generalize stochastic interpolants by replacing the scalar time variable with vectors, matrices, or linear operators, allowing us to bridge probability distributions across multiple dimensional spaces. This approach enables the construction of versatile generative models capable of fulfilling multiple tasks without task-specific training. Our operator-based interpolants not only provide a unifying theoretical perspective for existing generative models but also extend their capabilities. Through numerical experiments, we demonstrate the zero-shot efficacy of our method on conditional generation and inpainting, fine-tuning and posterior sampling, and multiscale modeling, suggesting its potential as a generic task-agnostic alternative to specialized models.

Transfer learning is a powerful paradigm for leveraging knowledge from source domains to enhance learning in a target domain. However, traditional transfer learning approaches often focus on scalar or multivariate data within Euclidean spaces, limiting their applicability to complex data structures such as probability distributions. To address this, we introduce a novel framework for transfer learning in regression models, where outputs are probability distributions residing in the Wasserstein space. When the informative subset of transferable source domains is known, we propose an estimator with provable asymptotic convergence rates, quantifying the impact of domain similarity on transfer efficiency. For cases where the informative subset is unknown, we develop a data-driven transfer learning procedure designed to mitigate negative transfer. The proposed methods are supported by rigorous theoretical analysis and are validated through extensive simulations and real-world applications.

We propose an algorithm with improved query-complexity for the problem of hypothesis selection under local differential privacy constraints. Given a set of $k$ probability distributions $Q$, we describe an algorithm that satisfies local differential privacy, performs $\tilde{O}(k^{3/2})$ non-adaptive queries to individuals who each have samples from a probability distribution $p$, and outputs a probability distribution from the set $Q$ which is nearly the closest to $p$. Previous algorithms required either $\Omega(k^2)$ queries or many rounds of interactive queries. Technically, we introduce a new object we dub the Scheff\'e graph, which captures structure of the differences between distributions in $Q$, and may be of more broad interest for hypothesis selection tasks.

Speculative decoding is a promising approach for accelerating large language models. The primary idea is to use a lightweight draft model to speculate the output of the target model for multiple subsequent timesteps, and then verify them in parallel to determine whether the drafted tokens should be accepted or rejected. To enhance acceptance rates, existing frameworks typically construct token trees containing multiple candidates in each timestep. However, their reliance on token-level verification mechanisms introduces two critical limitations: First, the probability distribution of a sequence differs from that of individual tokens, leading to suboptimal acceptance length. Second, current verification schemes begin from the root node and proceed layer by layer in a top-down manner.

The integration of logic programs with embedding models resulted in a class of neurosymbolic frameworks that jointly learn symbolic rules and representations for the symbols in the logic (constant or predicate). The key idea that enabled this integration was the differentiable relaxation of unification, the algorithm for variable instantiation during inference in logic programs. Unlike unification, its relaxed counterpart exploits the similarity between symbols in the embedding space to decide when two symbols are semantically equivalent. We show that this similarity between symbols violates the transitive law of equivalence, leading to undesirable side effects in learning and inference. To alleviate those side effects, we are the first to revamp the well-known possible world semantics of probabilistic logic programs into new semantics called equivalence semantics. In our semantics, a probabilistic logic program induces a probability distribution over all possible equivalence relations between symbols, instead of a probability distribution over all possible subsets of probabilistic facts. We propose a factorization of the equivalence distribution using latent random variables and characterize its expressivity. Additionally, we propose both exact and approximate techniques for reasoning in our semantics. Experiments on well-known benchmarks show that the equivalence semantics leads to neurosymbolic models with up to 42% higher results than state-of-the-art baselines.

We propose a framework for learning maps between probability distributions that broadly generalizes the time dynamics of flow and diffusion models. To enable this, we generalize stochastic interpolants by replacing the scalar time variable with vectors, matrices, or linear operators, allowing us to bridge probability distributions across multiple dimensional spaces. This approach enables the construction of versatile generative models capable of fulfilling multiple tasks without task-specific training. Our operator-based interpolants not only provide a unifying theoretical perspective for existing generative models but also extend their capabilities. Through numerical experiments, we demonstrate the zero-shot efficacy of our method on conditional generation and inpainting, fine-tuning and posterior sampling, and multiscale modeling, suggesting its potential as a generic task-agnostic alternative to specialized models.

Quantum machine learning (QML) aims to accelerate machine learning tasks by exploiting quantum computation. Previous work studied a QML algorithm for selecting sparse subnetworks from large shallow neural networks. Instead of directly solving an optimization problem over a large-scale network, this algorithm constructs a sparse subnetwork by sampling hidden nodes from an optimized probability distribution defined using the ridgelet transform. The quantum algorithm performs this sampling in time $O(D)$ in the data dimension $D$, whereas a naive classical implementation relies on handling exponentially many candidate nodes and hence takes $\exp[O(D)]$ time. In this work, we construct and analyze a quantum-inspired fully classical algorithm for the same sampling task. We show that our algorithm runs in time $O(\operatorname{poly}(D))$, thereby removing the exponential dependence on $D$ from the previous classical approach. Numerical simulations show that the proposed sampler achieves empirical risk comparable to exact sampling from the optimized distribution and substantially lower than sampling from the non-optimized uniform distribution, while also exhibiting exponentially improved runtime scaling compared with the conventional classical implementation. These successful dequantization results show that sparse subnetwork selection via optimized sampling can be achieved classically with polynomial data-dimension scaling on conventional computers without quantum hardware, providing an alternative to the existing quantum algorithm.