For each of $T$ time steps, $m$ experts report probability distributions over $n$ outcomes; we wish to learn to aggregate these forecasts in a way that attains a no-regret guarantee. We focus on the fundamental and practical aggregation method known as *logarithmic pooling* -- a weighted average of log odds -- which is in a certain sense the optimal choice of pooling method if one is interested in minimizing log loss (as we take to be our loss function). We consider the problem of learning the best set of parameters (i.e.

Mixture-of-Experts (MoE) models have shown strong potential in scaling language models efficiently by activating only a small subset of experts per input. However, their widespread deployment remains limited due to the high memory overhead associated with storing all expert parameters, particularly as the number of experts increases. To address this challenge, prior works have explored expert dropping and merging strategies, yet they often suffer from performance drop at high compression ratios. In this paper, we introduce PuzzleMoE, a training-free MoE compression method that achieves both high accuracy and efficient inference through two key innovations: First, PuzzleMoE performs sparse expert merging by identifying element-wise weight redundancy and specialization. It uses a dual-mask to capture both shared and expert-specific parameters. Second, to avoid the overhead of storing binary masks and signs, PuzzleMoE introduces a bit-packed encoding scheme that reuses underutilized exponent bits, enabling efficient MoE inference on GPUs. Extensive experiments demonstrate that PuzzleMoE can compress MoE models by up to 50% while maintaining accuracy across various tasks. Specifically, it outperforms prior MoE compression methods by up to 16.7% on MMLU at 50% compression ratio, and achieves up to 1.28\times inference speedup.

We introduce a highly expressive yet distinctly tractable family for black-box variational inference (BBVI). Each member of this family is a weighted product of experts (PoE), and each weighted expert in the product is proportional to a multivariate $t$-distribution. These products of experts can model distributions with skew, heavy tails, and multiple modes, but to use them for BBVI, we must be able to sample from their densities. We show how to do this by reformulating these products of experts as latent variable models with auxiliary Dirichlet random variables. These Dirichlet variables emerge from a Feynman identity, originally developed for loop integrals in quantum field theory, that expresses the product of multiple fractions (or in our case, $t$-distributions) as an integral over the simplex. We leverage this simplicial latent space to draw weighted samples from these products of experts -- samples which BBVI then uses to find the PoE that best approximates a target density. Given a collection of experts, we derive an iterative procedure to optimize the exponents that determine their geometric weighting in the PoE. At each iteration, this procedure minimizes a regularized Fisher divergence to match the scores of the variational and target densities at a batch of samples drawn from the current approximation. This minimization reduces to a convex quadratic program, and we prove under general conditions that these updates converge exponentially fast to a near-optimal weighting of experts. We conclude by evaluating this approach on a variety of synthetic and real-world target distributions.

Retired electric vehicle batteries offer immense potential to support low-carbon energy systems, but uncertainties in their degradation behavior and data inaccessibilities under second-life use pose major barriers to safe and scalable deployment. This work proposes a Physics-Informed Mixt ure of Experts (PIMOE) network that computes battery degradation trajectories using partial, field-accessible signals in a single cycle. PIMOE leverages an adaptive multi-degradation prediction module to classify degradation mode s using expert weight synthe sis underpinned by capacity-voltage and relaxation data, producing latent degradation trend embeddings. These are input to a use-dependent recurrent network for long-term trajectory prediction. V a lidated on 207 batteries across 77 use conditions and 67,902 cycles, PIMOE achieves an average mean absolute percentage (MAPE) errors of 0.88% with a 0.43 ms inference time. Compared to the state-of-the-art Informer and PatchTST, it reduces computational time and MAPE by 50%, respectively. Compatible with random state of charge region sampling, PIMOE suppor ts 150-cycle forecasts with 1.50% average and 6.26% maximum MAPE, and operates effe ctively even with pruned 5M B training data. Broadly, PIMOE framework offers a deployable, history-free solu tion for battery degradation trajectory computation, redefining how second-life energy storage systems are asse ssed, optimized, and integrated into the sustainable energy landscape.

Large language models (LLMs) such as GPTs and Mixtral-8x7B have revolutionized machine intelligence due to their exceptional abilities in generic ML tasks. Transiting LLMs from datacenters to edge devices brings benefits like better privacy and availability, but is challenged by their massive parameter size and thus unbearable runtime costs. To this end, we present EdgeMoE, an on-device inference engine for mixture-of-expert (MoE) LLMs -- a popular form of sparse LLM that scales its parameter size with almost constant computing complexity. EdgeMoE achieves both memory- and compute-efficiency by partitioning the model into the storage hierarchy: non-expert weights are held in device memory; while expert weights are held on external storage and fetched to memory only when activated. This design is motivated by a key observation that expert weights are bulky but infrequently used due to sparse activation. To further reduce the expert I/O swapping overhead, EdgeMoE incorporates two novel techniques: (1) expert-wise bitwidth adaptation that reduces the expert sizes with tolerable accuracy loss; (2) expert preloading that predicts the activated experts ahead of time and preloads it with the compute-I/O pipeline. On popular MoE LLMs and edge devices, EdgeMoE showcase significant memory savings and speedup over competitive baselines. The code is available at https://github.com/UbiquitousLearning/mllm.

Personalized large language models (LLMs) aim to tailor their outputs to user preferences. Recent advances in parameter-efficient fine-tuning (PEFT) methods have highlighted the effectiveness of adapting population-level LLMs to personalized LLMs by fine-tuning user-specific parameters with user history. However, user data is typically sparse, making it challenging to adapt LLMs to specific user patterns. To address this challenge, we propose PROgressive PERsonalization (PROPER), a novel progressive learning framework inspired by meso-level theory in social science. PROPER bridges population-level and user-level models by grouping users based on preferences and adapting LLMs in stages. It combines a Mixture-of-Experts (MoE) structure with Low Ranked Adaptation (LoRA), using a user-aware router to assign users to appropriate groups automatically. Additionally, a LoRA-aware router is proposed to facilitate the integration of individual user LoRAs with group-level LoRAs. Experimental results show that PROPER significantly outperforms SOTA models across multiple tasks, demonstrating the effectiveness of our approach.

For each of T time steps, m experts report probability distributions over n outcomes; we wish to learn to aggregate these forecasts in a way that attains a no-regret guarantee. We focus on the fundamental and practical aggregation method known as *logarithmic pooling* -- a weighted average of log odds -- which is in a certain sense the optimal choice of pooling method if one is interested in minimizing log loss (as we take to be our loss function). We consider the problem of learning the best set of parameters (i.e. We assume (by necessity) that the adversarial choices of outcomes and forecasts are consistent, in the sense that experts report calibrated forecasts. Imposing this constraint creates a (to our knowledge) novel semi-adversarial setting in which the adversary retains a large amount of flexibility.

Large Language Models (LLMs) based on Mixture-of-Experts (MoE) architecture are showing promising performance on various tasks. However, running them on resource-constrained settings, where GPU memory resources are not abundant, is challenging due to huge model sizes. Existing systems that offload model weights to CPU memory suffer from the significant overhead of frequently moving data between CPU and GPU. In this paper, we propose Fiddler, a resource-efficient inference engine with CPU-GPU orchestration for MoE models. The key idea of Fiddler is to use the computation ability of the CPU to minimize the data movement between the CPU and GPU. Our evaluation shows that Fiddler can run the uncompressed Mixtral-8x7B model, which exceeds 90GB in parameters, to generate over $3$ tokens per second on a single GPU with 24GB memory, showing an order of magnitude improvement over existing methods. The code of Fiddler is publicly available at \url{https://github.com/efeslab/fiddler}

In this paper, a new method based on TOPSIS and optimization models is proposed for multi-attribute group decision-making in the environment of interval-valued intuitionistic fuzzy sets.Firstly, by minimizing the sum of differences between individual evaluations and the overallconsistent evaluations of all experts, a new optimization model is established for determining expert weights. Secondly, based on TOPSIS method, the improved closeness index for evaluating each alternative is obtained. Finally, the attribute weight is determined by establishing an optimization model with the goal of maximizing the closeness of each alternative, and it is brought into the closeness index so that the alternatives can be ranked. Combining all these together, the complete fuzzy multi-attribute group decision-making algorithm is formulated, which can give full play to the advantages of subjective and objective weighting methods. In the end, the feasibility and effectiveness of the provided method are verified by a real case study.

Weight-sharing supernet has become a vital component for performance estimation in the state-of-the-art (SOTA) neural architecture search (NAS) frameworks. Although supernet can directly generate different subnetworks without retraining, there is no guarantee for the quality of these subnetworks because of weight sharing. In NLP tasks such as machine translation and pre-trained language modeling, we observe that given the same model architecture, there is a large performance gap between supernet and training from scratch. Hence, supernet cannot be directly used and retraining is necessary after finding the optimal architectures. In this work, we propose mixture-of-supernets, a generalized supernet formulation where mixture-of-experts (MoE) is adopted to enhance the expressive power of the supernet model, with negligible training overhead. In this way, different subnetworks do not share the model weights directly, but through an architecture-based routing mechanism. As a result, model weights of different subnetworks are customized towards their specific architectures and the weight generation is learned by gradient descent. Compared to existing weight-sharing supernet for NLP, our method can minimize the retraining time, greatly improving training efficiency. In addition, the proposed method achieves the SOTA performance in NAS for building fast machine translation models, yielding better latency-BLEU tradeoff compared to HAT, state-of-the-art NAS for MT. We also achieve the SOTA performance in NAS for building memory-efficient task-agnostic BERT models, outperforming NAS-BERT and AutoDistil in various model sizes.