Mixtures

Mixture-of-Experts (MoE) architectures decouple model capacity from computational cost, yet incur high memory footprints as parameters grow linearly with the number of experts. Recurrent Transformers achieve parameter efficiency by reusing layer weights, but typically lack the capacity for competitive language modeling. We propose Mixture of Reused Experts (MoRE), a hybrid that shares expert pools across groups of adjacent layers. Each layer retains its own router but selects from a larger shared pool, expanding the diversity of routing combinations without additional parameters. To enable shared experts to distinguish between layers, we introduce lightweight learnable depth embeddings that condition each layer's input before routing. Experiments across three model scales (114M-1.15B parameters) show that MoRE consistently achieves lower perplexity and stronger downstream performance than standard MoEs and state-of-the-art weight-sharing architectures at matched compute and parameter budgets, with only minimal modifications to existing MoE implementations.

LLMs latent-state reasoning methods replace discrete intermediate tokens with continuous states, such as weighted mixtures of token embeddings, to retain multiple possible reasoning directions rather than committing to one. Yet pretrained language models often fail to preserve these mixtures. We study why through a combination of theoretical analysis and controlled empirical investigations on a variety of models. We identify three independent, distinct sources of failure. First, transformer architectures already distort mixture geometry, and training substantially amplifies this effect. Moreover, the failure can occur even if the model transports mixtures perfectly linearly: the softmax readout and autoregressive feedback form a dynamical system that either amplifies small differences until one component of the mixture dominates or contracts different mixtures until they become indistinguishable. We verify this theoretical prediction empirically: the observed transition between contraction and amplification occurs near the theoretical threshold derived by our analysis, and pretrained-model rollouts lie predominantly on the amplifying side. Finally, we generalize to mixtures of many components and show that exact preservation generally requires context-dependent correction, whose required dimensionality can grow with the number of components.

When do text embeddings work as inputs to empirical analysis? Their use rests on an assumption: that we can trade text for its low-dimensional embedding, and lose little in doing so. I make that assumption precise under a generative model in which documents are mixtures of latent topics. I study two uses---clustering units in embedding space and controlling for high-dimensional text. A cluster of embeddings is a set of documents with similar topic mixtures; controlling for the embedding is equivalent to controlling for the topic mixture, so validity reduces to whether that mixture captures the confounding. In an application to 363 U.S. metropolitan areas, embedding-based clusters of LLM-generated economic descriptions recover interpretable economic archetypes and separate local employment dynamics more sharply than clustering on model residuals, or on a curated set of industry and demographic covariates.

Neural Architecture Search (NAS) has so far rarely been applied to Mixture-of-Experts (MoE) models, and existing MoE designs leave the alignment between experts and the structure of the data to emerge on its own. We propose an architecture search framework that makes this alignment an explicit search variable: the assignment of data clusters to experts is optimised jointly with the per-expert architectures. We cast the joint problem as a cluster-aware likelihood maximisation, show that it coincides with the incomplete-data maximum likelihood of a latent-variable mixture, and solve it by a generalised Expectation-Maximisation procedure whose otherwise intractable expert-quality term is supplied by an adaptively refined surrogate. We prove that the iterates converge whenever the surrogate errors are summable, and that at every limit point no candidate the search produces improves the true objective. On a heterogeneous image-classification mixture the method recovers the underlying domain partition on 95% of clusters without ever observing domain labels, and on that benchmark and a four-domain time-series forecasting one alike it outperforms the MoE and NAS baselines that likewise use no label information.

Transformers rely on position embedding mechanisms in long context modeling in most cases. Rotary Position Embedding (RoPE) embeds positional information with independent 2D rotations, forming relative position terms in self-attention. However, its pairwise, block-based, and decoupled structure limits deep mixing and robustness across channels. We propose HD-RoPE, which extends RoPE from independent 2D rotations to higher-dimensional rotations and introduces a Paley-I orthogonal basis to obtain balanced, isotropic, and dense phase mixing within each rotation subspace. This significantly enhances channel coupling and rotational degrees of freedom while maintaining orthogonal stability and the relative position closure property. Furthermore, HD-RoPE is easily optimized for engineering efficiency without introducing additional trainable parameters. We have conducted extensive evaluation results demonstrating that HD-RoPE achieves significant performance improvements over standard RoPE across various popular benchmarks and in both long and short contexts.

We study learning a mixture of $k$ Plackett-Luce models from multi-way ranking responses from annotators that may represent heterogeneous underlying preferences. This problem has many applications in AI alignment and preference optimization. Prior work has studied mixtures of Bradley-Terry models from pairwise comparisons. However, estimating a mixture of multi-way ranking models can become theoretically unidentifiable when $k$ exceeds $m/2$, where $m$ is the ranking length. We design an efficient algorithm to address this issue by first augmenting the rankings to a larger size (e.g., generating comparisons from a base model), followed by a gradient-based estimation to reduce inference cost (in the input embedding space). With this procedure in mind, we then fit a mixture of Plackett-Luce (PL) models via an expectation-maximization-style iteration, or MoPLEx in short. We conduct extensive experiments to verify this algorithm. First, we find that the gradient-based approximation estimates true probabilities with less than 5% error on models with up to 34 billion parameters. Second, MoPLEx improves clustering and ranking accuracy by an average of 43.7% and 15.2% over baselines using a single PL model or a mixture of Bradley-Terry models, on UltraFeedback and PERSONA datasets. These results demonstrate the effectiveness of MoPLEx for tackling multi-way rankings following heterogeneous preferences through measuring alignment via gradients.

We ask whether language-model pre-training can be decomposed into smaller, independently trainable jobs that can later be recomposed into a coherent larger model. We introduce Mixture of Training (MoT), a scaffolded modular pre-training procedure that partitions a target Transformer into contiguous layer blocks, trains each block inside a frozen pretrained aligner scaffold, and then recomposes the trained blocks with an optional short end-to-end adaptation pass. On a 1.3B-parameter Gemma-style model trained on C4, MoT provides a small-scale proof of mechanism: independently trained depth slices can be recomposed into a usable language model, and a quality-parity schedule reaches the same reported perplexity as the monolithic baseline. This parity setting processes more aggregate tokens and has a shorter idealized layer-equivalent critical path after aligner preparation; its effective compute advantage depends on reusing the aligner across runs. We therefore present MoT not as a general replacement for monolithic pre-training, but as a small-scale framework for studying whether scaffolded sub-runs can act as reusable training units.

Breast lesion detection in mammography remains a challenging task due to variations in image quality, lesion appearance, and population demographics across datasets. While current object detectors such as YOLO and DETR achieve strong results on individual datasets, their performance often degrades when trained on or applied across heterogeneous sources. To address this, we propose MammoMix, a novel framework based on Mixture-of-Experts (MoE) paradigm for robust and generalizable lesion detection. In MammoMix, each expert model is trained on a specific domain, allowing it to specialize in distinct characteristics of its source data. A gating mechanism adaptively weighs contributions from each expert based on input image, combining their outputs to enable domain-adaptive inference. To improve reliability, we further incorporate a calibration module, MoCAE, which adjusts confidence scores to reflect true predictive uncertainty. We evaluate MammoMix on 3 public mammography datasets: CSAW, DDSM, and DMID, covering diverse clinical settings. Results show that MammoMix outperforms baseline detectors in both average precision and reliability, particularly on datasets with greater variability. Our findings demonstrate that expert specialization and calibrated ensemble fusion significantly enhance model generalization and robustness. MammoMix offers a promising step toward dependable AI-assisted breast cancer screening across real-world clinical domains.

State Space Models (SSMs), as a mainstream research direction of linear Transformers, aim to achieve higher efficiency than standard Transformers in long-context modeling. However, existing SSMs suffer from limited input adaptivity and constrained memory capacity, leading to information loss when modeling ultra-long sequences. To address these limitations, we propose MixFormer, a novel linear Transformer that integrates a Mixture-of-Memory-Experts (MoE) mechanism. Specifically, the model maintains differentiated memory states through multiple collaborating memory experts and employs a novel Time-Aware Linear Attention (TALA) mechanism, which leverages learnable exponential decay functions and positional biases to dynamically update memory. This design enables the model to selectively reinforce important historical information while effectively mitigating memory dilution, substantially improving long-range dependency modeling. Experiments on long-sequence text and image generation tasks demonstrate that MixFormer not only achieves significant performance gains but also provides a more sustainable computational backbone for the next generation of web infrastructure.

Large language model-based multi-agent systems have recently shown strong potential for complex, long-horizon tasks. However, existing methods mainly rely on coarse prompt-level differentiation without parameter adaptation for diverse subtasks, resulting in insufficient inter-agent heterogeneity and limited specialized capability that bottleneck performance on tasks with complex requirements. To address this, we introduce a Task-Oriented Multi-Agent System with Mixture of Role-Subtask Experts (MoRSE) that distinguishes agents with (role, subtask)-conditional specialization at both the task structure and parameter levels. To make agents' responsibility explicit at the task structure level, we formulate a task-oriented multi-agent system that decomposes each task into a dependency-aware Directed Acyclic Graph of subtasks and assigns each agent a specific (role, subtask), introducing task-level specialization across collaborating agents. Additionally, to address the diverse role and subtask parameter adaptation demands, we propose a dynamic Mixture of (role, subtask) LoRA Experts module with a prototype-based semantic router for subtasks, augmenting agents with parameter-level specialization on a shared LLM substrate cost-effectively. Then, to co-optimize experts and router stably under sparse task rewards, we further propose a hierarchical group-relative policy optimization with two-layer credit assignment that isolates expert updates from the cross-route variance introduced by routing decisions, disentangling expert quality from routing quality. Experiments on code-generation benchmarks across three backbones demonstrate the effectiveness of our approach, with improvements in both whole-task and step-wise performance, and the gains from trained specialization generalize across held-out task categories and domains.

This paper introduces Mixtures of Geodesic Factor Analyzers (MGFA) on Riemannian homogeneous spaces. MGFA uses a geodesic factor model within each mixture component, providing greater expressiveness than mixtures of Riemannian radial distributions and enabling clustering of manifold-valued data with anisotropic subpopulations. We establish root-$n$ consistency for the MGFA maximum likelihood estimator (MLE), thereby filling a theoretical gap for mixtures of Riemannian radial distributions as a special case. We also propose an iterative estimation algorithm and implement it on spheres, shape spaces, and hyperbolic spaces. Numerical experiments show that MGFA substantially outperforms competing methods in well-specified regimes while remaining robust under model misspecification. Finally, case studies on corpus callosum and left hippocampus shape datasets demonstrate MGFA's effectiveness for both 2D contour and 3D shape analysis.

Accurate prediction of vapor--liquid equilibrium (VLE) for hydrocarbon-nitrogen mixtures remains challenging for cubic equations of state, particularly across broad ranges of composition and hydrocarbon chain length. While deep learning models can provide accurate predictions, they often lack interpretability and explicit analytical expressions. In this work, we propose a symbolic machine learning approach to discover interpretable symbolic corrections to Peng-Robinson equation-of-state (PR-EOS) predictions from experimental data. The proposed approach adopts a two-level strategy: symbolic expressions are first identified for individual hydrocarbon systems, after which their coefficients are represented as functions of carbon number to enable accurate prediction across different hydrocarbon systems. The results demonstrate significantly improved prediction accuracy over the original PR-EOS across all hydrocarbon-nitrogen systems. Overall, the proposed approach provides an interpretable symbolic correction framework for improving PR-EOS predictions of hydrocarbon-nitrogen VLE.

Mixtures of low-rank adaptation experts increase parameter-efficient capacity by routing each input through a subset of adapters. Recent dynamic routers activate more experts when the router or prediction is uncertain. This rule silently equates uncertainty with useful additional computation: an uncertain example may contain complementary, unqueried expert evidence, but it may instead remain ambiguous after every expert agrees. We formulate routing as certified value-of-information allocation. VI-MoLE learns the counterfactual risk remaining after each expert prefix, converts these predictions into simultaneous upper-risk certificates on held-out calibration data, and spends a global adapter budget on the token--layer action with the largest certified marginal risk reduction per unit cost. A terminal certificate then decides whether to answer or abstain. Unlike an uncertainty gate, this procedure distinguishes present ambiguity from recoverable and residual risk. We prove simultaneous certificate validity, optimal greedy allocation under diminishing certified gains, and allocation regret under value-estimation error. The evaluation protocol tests matched-compute accuracy, certificate coverage, risk--coverage, distribution shift, and tail latency against fixed and dynamic MoE-LoRA routers.

Real-world video arrives hazy, rainy, dark, or noisy, and a deployable restorer faces three demands at once: no degradation label, native 4K output, and stability in playback. Existing methods answer them separately and break on the joint problem, because per-frame degradation readings flip between frames, downsampled proxies erase the rain and noise they are meant to remove, and dense temporal alignment does not fit 4K memory. No paired benchmark even poses that problem, so we build one. UHV-4K-AIO renders physically modeled haze, rain, sensor noise, and low light over the same 100 clean 4K clips with shared depth and motion, and its construction exposes the split MoCRA is built on: haze and low light survive aggressive downsampling, while rain and noise exist only at native scale. Band-matched compositional conditioning follows, spending conditioning capacity, computation, and supervision in the band where each degradation lives. One dictionary of rank-1 atoms, recomposed sparsely per frame, conditions both a once-per-clip coarse branch and a shallow native-resolution refiner, in 3.6M parameters and with no optical flow. Trained once for all four tasks, MoCRA takes the best task-mean PSNR of eleven retrained image and video baselines, holds warping error at the level of the flow-based video models while never estimating motion, and restores native 4K in under half a second, against 1.7 seconds for the fastest baseline.

Whether large language models perform genuine algorithmic reasoning or mere pattern completion is hard to test, because most benchmarks lack a ground truth for correct inductive inference. We introduce F-ICL, an in-context-learning benchmark that supplies one exactly. Using the Turing-complete machine F, complement-symmetrised into sF to remove output-polarity bias, we exhaustively enumerate all 1.5 billion programs of length $L\le13$ and compute the Bayes-optimal posterior in closed form under a bounded universal (Levin--Solomonoff) prior; models are scored by how closely their served distributions approach it at matched evidence. Each task is paired with its bitwise complement, on which the optimum scores identically, so an original-twin gap isolates the model's inductive bias. Across 105 serving configurations spanning 37 open models (0.8B--675B) and frontier systems from four laboratories, models answer up to 92% of queries correctly, yet 45 of 46 models yield distributions farther from the optimum than a keystroke reference, and their behaviour is bracketed by low-order prefix statistics fitted only on visible evidence. That reference is itself an algorithmic mixture, induced by a print-only machine with no loops, so the panel's implied measure sits closer to a loop-free mixture than to the loop-bearing optimum, independently of the reference machine. Updating is also non-monotone, which no prior explains: a Bayes-rational solved set can only grow in this realisable, noiseless setting, yet added examples produce $6{,}545$ solved-to-unsolved transitions against $13{,}702$ gains. The gap is not predicted by accuracy (Spearman $ρ=-0.19$, $p=0.21$), does not close with scale or across frontier generations in the serving modes that expose distributions, and is widened by instruction and reasoning post-training. F-ICL is released as an open, reproducible benchmark and toolkit.

Large language models are increasingly used as synthetic research participants and are often validated by whether their marginal responses resemble human data. We study a fixed panel of sixteen lightweight persona-conditioned GPT-4.1 configurations in repeated strategic games. The panel met preregistered broad-reference condition-mean criteria in three of four repeated-game cells; the sole miss was 0.011 below the lower reference bound. Variation was strongly prompt-indexed, but its share depended on uncertainty assumptions: fixed-panel symmetric-Dirichlet sensitivities produced median between-prompt shares of 63%-71% under Jeffreys alpha=0.5 and 47%-53% under alpha=1, while finite-opportunity plug-in estimates were 85%-96%. Aggregate continuation-probability contrasts were +0.083 and +0.078, with conservative simultaneous 95% intervals [-0.171, +0.330] and [-0.181, +0.330]. The treatment jointly changed the continuation process and its textual representation. A separate wording-and-position operation shifted cooperation from 0/40 to 37/40 in the bare configuration, and a label conflict also revealed representation control. The original persona-level p13 result was not prospectively family-controlled, while a post-adjudication exact gate was structurally underpowered; p13 is therefore a replication target rather than a finding. External review exposed family-error, dependence, construct, and boundary-uncertainty defects, and zero-call reanalysis changed the interpretation without rewriting the historical record. The registered marginal criteria could be passed without precisely estimating the treatment-response object. A public capsule verifies 4,916 confirmatory Phase 3-5 runs with no live model calls. The results concern one fixed model-prompt panel and do not establish human substitutability.

In many classification problems, reliable instance-level labels are unavailable. However, it is often possible to construct weakly enriched unlabeled samples: datasets selected by different cuts, sources, populations, or experimental conditions that change latent class proportions without revealing them. Classification without Labels (CWoLa) shows that, in the binary case ($K=2$), a classifier trained to distinguish two impure mixtures with different class proportions can recover an optimal class discriminator without knowing the mixture proportions. We extend this principle to multiclass learning from several unlabeled mixtures ($K>2$), where the learner observes only mixture identity and neither latent class labels nor class-prior matrices. We prove that, for a multiclass mixture model, the Bayes-optimal mixture classifier $g^\star$ maps data points into a $(K-1)$-simplex embedded in mixture-posterior space. The $K$ vertices of this simplex are induced by the latent classes through the unknown mixing matrix. Leveraging this geometry, we propose prior-free procedures that train a standard classifier to distinguish mixture identities and then extract latent class structure using either post-hoc simplex fitting or a bottleneck architecture. Experiments on MNIST, CIFAR-10, and Galaxy10 DECaLS show that mixture identity alone can recover latent classes and their fractions in the mixture. By narrowing the gap between weakly supervised and fully supervised performance, we provide a mathematically grounded, scalable tool for multiclass discovery in label-scarce domains.

Large scale Bayesian nonparametrics (BNP) learner such as Stochastic Variational Inference (SVI) can handle datasets with large class number and large training size at fractional cost. Like its predecessor, SVI rely on the assumption of conjugate variational posterior to approximate the true posterior. A more challenging problem is to consider large scale learning on non-conjugate posterior. Recent works in this direction are mostly associated with using Monte Carlo methods for approximating the learner. However, these works are usually demonstrated on non-BNP related task and less complex models such as logistic regression, due to higher computational complexity. In order to overcome the issue faced by SVI, we develop a novel approach based on the recently proposed constant stepsize stochastic gradient ascent to allow large scale learning on non-conjugate posterior. Unlike SVI, our new learner does not require closed- form expression for the variational posterior expectatations. Our only requirement is that the variational posterior is differentiable. In order to ensure convergence in stochastic settings, SVI rely on decaying step-sizes to slow its learning. Inspired by SVI and Adam, we propose the novel use of adaptive stepsizes in our method to significantly improve its learning. We show that our proposed methods is compatible with ResNet features when applied to large class number datasets such as MIT67 and SUN397. Finally, we compare our proposed learner with several recent works such as deep clustering algorithms and showed we were able to produce on-par or outperform the state-of-the-art methods in terms of clustering measures.

Massively multilingual automatic speech recognition (ASR) models covering hundreds of languages must maintain robust performance across diverse linguistic and acoustic conditions. However, these models often encounter the curse of multilinguality, where model capacity is diluted across languages. To address this challenge, we propose Mixture of Language Group Experts (MoLGE), built upon speech self-supervised models (S3Ms). MoLGE assigns dedicated expert modules to clusters of similar languages, reducing the number of required submodules compared to conventional language-specific Mixture-of-Experts (MoE) schemes. It further integrates a hierarchical Low-Rank Adaptation (LoRA) strategy into the disentangled acoustic and linguistic components of the S3M architecture, enabling efficient modeling of language-specific characteristics while maintaining parameter efficiency. Further, we investigate the impact of language grouping strategies based on both linguistic and data-driven criteria on overall performance, providing an interpretable perspective on how language structure influences scalability in multilingual speech systems. In experiments, we evaluate MoLGE on a multilingual benchmark encompassing 495 languages. Results demonstrate that MoLGE consistently outperforms dense multilingual baselines with a minimal increase in trainable parameters. Notably, these language grouping strategies yield substantial improvements for both phonetic and orthographic aspects of ASR modeling. Our findings suggest that structured language specialization provides an effective pathway for massively scaling language coverage of multilingual ASR.

Pretrained molecular encoders are commonly evaluated through downstream prediction, but predictive accuracy alone does not establish that a learned representation captures reproducible scientific structure, adds information beyond strong conventional baselines, or transfers out of distribution. We present a reliability-aware audit of generic molecular representations for human olfaction across four distinct claims: global perceptual geometry, incremental predictive value beyond chemistry, cross-dataset replication, and mixture transfer to unseen components. Using the Keller-Vosshall and Bierling single-molecule rating datasets and the Ma binary-mixture dataset, we compare MoLFormer and ChemBERTa against RDKit descriptors and Morgan fingerprints under identity-controlled and matched evaluations. Human three-attribute rating geometry, based on intensity, pleasantness, and familiarity, is reproducible across participant splits (median RSA 0.743 and 0.855), whereas model-human alignment is substantially weaker (RSA 0.019-0.158). Learned embeddings do not consistently outperform conventional representations in global alignment, and MoLFormer provides no clear incremental predictive value beyond a combined RDKit-Morgan baseline in either single-molecule dataset. Human geometry shows positive but incomplete agreement across 63 shared molecules (RSA 0.331; 95% bootstrap interval [0.204, 0.507]). Under one strict unseen-component mixture split, incremental effects are outcome- and representation-dependent, with all intervals crossing zero. These results establish empirical boundaries for the evaluated generic molecular encoders and motivate a broader evaluation principle: representation quality in scientific domains should be assessed separately for target reliability, structural alignment, incremental information, replication, and out-of-distribution transfer.

Action Quality Assessment (AQA) aims to objectively evaluate performance quality from action videos. Most existing methods follow a ``one-by-one'' paradigm, training a separate model for each action type. This setting limits real-world deployment, as it requires prior action-type knowledge to select the corresponding model and suffers from poor generalization across diverse actions. To address these limitations, we study the challenging task of all-in-one AQA, which aims to assess heterogeneous actions within a single unified model. We propose a novel Mixture of Action Knowledge Experts (MoAKE) framework, designed to mitigate negative knowledge transfer caused by large semantic discrepancies among actions. MoAKE learns complementary experts that capture diverse action patterns within a shared semantic space and dynamically aggregates their knowledge to adapt the assessment to the input action. Each expert is tailored with segment-aware prototypes to handle varying temporal lengths, together with an Adaptive Intra- and Inter-Segment Relationship Modeling (AIISRM) module to model multi-granularity temporal dynamics. Furthermore, we establish comprehensive benchmarks for all-in-one as well as zero/few-shot AQA. Extensive experiments on three long-term datasets demonstrate that MoAKE significantly outperforms existing methods in the all-in-one setting, while also achieving consistent generalization on three short-term datasets under zero/few-shot evaluation. Code is available at https://github.com/XuHuangbiao/MoAKE.

Large Vision Language Models (LVLMs) require strong reasoning over both visual and textual input. Recent work suggests that cognitive elements, especially diverse representations and metacognition, correlate with better performance. Many of the needed perceptual functions are already provided by specialized domain-specific computer vision models, which act as the perceptual subsystem for detecting objects, localizing them, inferring states, recovering spatial layout, and reading text. The key challenge is to integrate these multi-encoder experts into a trustworthy, interpretable, and coherent representation that improves verifiability and reduces hallucinations. This is difficult because vision-language questions span different cognitive levels, yet most LVLM pipelines apply the same perception-reasoning routing regardless of the demand of each query. We propose an evidence-driven multimodal reasoning framework that utilizes a Bloom-inspired taxonomy as a hierarchical reasoning protocol. The two-stage cognitive verbalization first produces a Literal Evidence Summary by decomposing expert outputs into short, atomic evidence statements. It then performs Bloom Verbalization to turn these evidence items into a staged reasoning trace, and a lightweight Reasoning Trace Module quantitatively analyzes the trace to make evidence usage and reasoning progression explicit. Through this integration, we observed several improvements in perception and reasoning abilities. Moreover, the trace module provides quantitative evidence that different queries induce different cognitive entry levels and evidence-use trajectories that enable fine-grained analysis.

Multimodal Large Language Models (MLLMs) are typically designed under the assumption that all modalities available during training will also be accessible at inference. However, many real-world settings violate this assumption, requiring models to operate under a privileged modality setting, where auxiliary modalities are available only during training. While these modalities contain valuable information, existing MLLMs largely fail to leverage them effectively, as they treat modalities as interchangeable inputs rather than sources of complementary supervision. We propose Mixture of Probes (MoP), a novel framework that disentangles modality-specific and modality-general signals within the MLLM, allowing the model to preserve modality-dependent structure while learning transferable representations across modalities. At its core, MoP achieves this through a structured probing mechanism that extracts and organizes information from intermediate representations of a shared modality encoder, rather than relying only on final-layer alignment as done in existing MLLMs. To support this disentanglement, we further introduce MoP Cross-modal Training (MoP-X), a training strategy for MoP centered around a probe disentanglement loss that prevents probe collapse and encourages cross-modal learning. We evaluate MoP across two domains spanning eight tasks and four modalities under a comprehensive evaluation protocol tailored to the privileged modality setting, where each modality is independently treated as the sole input at inference time. MoP consistently outperforms strong MLLM baselines, achieving up to 65% relative improvement, demonstrating that auxiliary modalities, even when unavailable at inference, can provide substantial gains when effectively leveraged during training. Code, model checkpoints, and evaluation protocols will be made available at https://github.com/Sony/MoP.

Two-tower retrievers compress each user into a single embedding, limiting their ability to serve diverse interests. Multi-interest models give each user several heads scored by a maximum inner product, but their hard-routing training under-utilizes heads (routing collapse) and gives no per-user estimate of how much each interest matters for serving. We present \textbf{BACH} (\emph{Bayesian Admixture of Contrastive Heads}), which casts multi-interest two-tower retrieval as a per-user mixture over the heads, fit by variational inference. The soft mixture trains every head (mitigating collapse), produces a per-user weighting of the interests that is reused at serving, and admits a shared global-codebook variant with precomputable retrieval. On three large-scale benchmarks, MovieLens-20M, Taobao, and Netflix, BACH improves top-of-ranking retrieval over hard-routing multi-interest and single-vector baselines at every head count; we further find that scoring every candidate by its best head, consistent with serving, outperforms the usual target-routed training, and that BACH improves further still.

Multi-query vehicle ReID aims to leverage complementary information from diverse views for robust feature learning. However, current methods suffer from simplistic feature fusion and thus easily ignores some important view information and cross-view relationships. To handle these problems, this work presents a novel approach called Mixture of Enhanced-View Experts (EV-MoE), which enhances the feature representation of each view and efficiently integrate the view-specific enhanced features by MoE, for robust multi-query ReID. In particular, we design a mixture of enhanced-view experts module, which consists of two parts including view-specific feature enhancement sub-Module (VFEM) and dynamic multi-view fusion sub-Module (DMFM). Moreover, we further introduce Multi-view Alignment Loss (MAL), which aligns features through bidirectional crossview contrastive learning and reconstruction constraints, addressing the challenges of consistency between multi-query features and single-image features. In addition, to evaluate multi-query ReID in real-world environments, we collect LCRI-1K, a largescale vehicle ReID dataset with 1,090 identities, 107,805 images, across 23,637 cameras, where each vehicle appears in an average of 67.5 cameras, providing a comprehensive benchmark to test the robustness in complex environments. Extensive experiments demonstrate the robustness of CAFNet in addressing the multiquery vehicle ReID problem. The code is available at https: //github.com/xiaozhen28/CAFNet.

Pattern recognition problems arise in a variety of physical image processing situations, and convolutional neural networks are a popular scheme for the required feature extraction and classification tasks. The classical networks use diffusion-based smearing and block-wise pooling to downsample the image data and capture important structural features. In this work, we propose and demonstrate a more efficient quantum-inspired strategy involving a mixture of experts. It is a hybrid classical-quantum framework. The quantum part consists of amplitude encoding of the images, convolution using local unitary operations, multiple experts processing the same image with different parameters, and feature extraction using quantum stabiliser codes. The classical part then jointly processes the features extracted by different experts using a standard fully connected neural network for image class prediction. Using MNIST and Fashion-MNIST datasets as benchmarks, we demonstrate that the joint expert analysis outperforms the individual expert one, as well as reduces the failure rate of image class prediction by around a factor of two. The overhead of our quantum-inspired strategy is only moderate on GPU workstations, which makes our proposal a practical alternative to existing classical schemes. We also point out how the quantum part of our framework can be executed on a quantum processor.

Normalising flows provide a powerful variational family for approximate inference, yet individual architectures often fail to generalise across heterogeneous posterior geometries. We revisit mixture-based flow formulations and introduce \emph{AMF\mbox{-}VI\mbox{-}sEMA}, a two-stage framework featuring a \emph{stable global weighting} mechanism based on a \emph{Simplex Exponential Moving Average} (sEMA) update. In Stage1, a heterogeneous set of experts (\textsc{RealNVP}, \textsc{MAF}, \textsc{RBIG}) are trained independently to specialise in distinct structural regimes. In Stage2, expert parameters are frozen and global mixture weights are learned through a temperature-controlled softmax of average log-likelihoods, followed by a smooth EMA update on the probability simplex. This design produces a tractable, data-agnostic gating mechanism (without per-sample gating or gradient backpropagation through weights) that adaptively reallocates capacity while avoiding component collapse. We evaluate the framework on ten posterior benchmarks: six canonical 2D synthetic families (Banana, X-Shaped, Bimodal, Multimodal, Two-moons, Rings) and four real/low-dimensional Bayesian targets (BLR, BPR, Weibull, Real-GMM2), with stronger baselines (\textsc{NICE}, \textsc{ResFlow}, and EM-Mixing). Comprehensive evaluation covers NLL, KL divergence, Wasserstein-2 distance, and MMD, together with diagnostics of mixture dynamics, hyperparameter sensitivity, and cross-seed robustness. Empirically, \emph{AMF\mbox{-}VI\mbox{-}sEMA} achieves consistent NLL improvements over its predecessor \emph{AMF\mbox{-}VI} and avoids the catastrophic transport failures of single-flow baselines, while maintaining stable weight trajectories ($N_{\mathrm{eff}}{>}1.4$ on all datasets) with minimal computational overhead.

Post-training of frontier language models is conducted on curated task suites, and inevitably leaves a distribution shift between training and deployment environments. This exposes developers to generalization failures, which are relatively poorly understood. To better understand such generalization failures, we believe the community should construct clean demonstrations under simplified conditions. To facilitate this, we propose a simple and flexible way to construct language models which fail to generalize in controllable ways when subsequently trained with Reinforcement Learning (RL) on a given distribution of training tasks. Our construction uses Supervised Fine-Tuning on a dataset of a mixture of transcripts corresponding to a collection of 'conditional policies', which can each independently be assigned certain behaviors on each different task distribution, to obtain a model that is then well approximated as a 'mixture of conditional policies.' We observe that RL training then selects for policies that obtain the highest reward on the training distribution. This can produce striking behaviors: in a controlled setting with two distributions containing identical questions prepended with two different 'trigger strings', RL training on either distribution actively degrades performance on the other to zero, even though the underlying task is identical. We also use our construction to illustrate two novel ways in which generalization may fail in future language models, corresponding to distribution shifts of task coverage and temporal context respectively. While our construction is deliberately simple and may not closely resemble 'natural' generalization failures, the resulting 'model organisms' are of interest for alignment stress-testing and generalization science, and can be used as existence proofs that training success and generalization can come apart in structured ways.

Most data-mixing methods assume the corpus has already been partitioned into groups, and the choice of those groups determines what a mixer can express. Existing labels, including provenance, topic or format taxonomies, and flat embedding clusters, commit to one semantic axis at one granularity; changing the resolution rebuilds the labels. We argue the bottleneck is the label system, not the mixer, and provide a hierarchical one. HERMES is a data-derived labeling substrate: a Learned Semantic Transform followed by 3-stage residual vector quantization annotates each document once into a coarse-to-fine code whose prefix length controls granularity up to approximately 130k cells. At coarse granularity HERMES sits at a plateau with KMeans-family methods on standard clustering metrics, so the contribution is the substrate, not the clusterer. On 1B-parameter, 25B-token pre-training, the hierarchy exposes an interaction fixed-granularity pipelines cannot test: at one prefix length, a combined Stage-2 rule contrast, equal-subbucket coverage versus size-proportional within-bucket quality top-30%, lifts a 16-task capability macro-average by +0.0253; at the next finer level, the same rule loses its measurable edge as candidate pools contract approximately 5x. HERMES reframes data mixture design from choosing among fixed label sets to navigating a reusable, data-derived granularity hierarchy.

In Large Language Model (LLM) training, data mixing plays a pivotal role in determining model performance. Recent methods optimize mixture weights via proxy models, but they rely on the assumption of static data distributions. As a result, when the underlying data pool shifts, these methods require costly retraining from scratch. This limitation restricts their ability to scale seamlessly from small settings to larger data pools and model sizes. In this paper, we propose CausalMix to address this limitation by casting data mixture optimization as a causal inference problem. We formulate the statistical features of the data pool as covariates and the domain mixture as the treatment. After fitting a causal model on 512 runs of Qwen2.5-0.5B to estimate the Conditional Average Treatment Effect (CATE), we extrapolate the optimal mixture for an 800K data pool and apply it to train a 7B model. Furthermore, we successfully generalize the framework to long chain-of-thought data on Qwen3-4B-Base. By leveraging causal modeling to isolate confounding biases, CausalMix dynamically infers state-dependent optimal data mixtures. Extensive experiments show that the mixture guided by CausalMix consistently improves performance across multiple downstream tasks, outperforming RegMix and other baselines. In addition, we use the CATE Interpreter to provide visual analysis of the learned mixing strategy. Overall, CausalMix offers a causal and interpretable framework for optimizing LLM data mixtures.

Visual AutoRegressive modeling (VAR) has pioneered a coarse-to-fine multi-scale autoregressive generative paradigm, demonstrating strong capabilities in image generation. However, VAR still suffers from inherent deficiencies in multi-scale representation learning. Specifically, lower scales primarily capture global semantics, while higher scales focus on fine-grained details. Employing a shared architecture across scales induces optimization conflicts. Moreover, due to the causal autoregressive process, inaccurate semantics at early scales can propagate and significantly degrade the final output. To address these issues, we introduce a scale-aware token-routed Mixture of Experts (MoE) architecture, allowing scale-adaptive expert selection, thereby facilitating decoupled representation learning across scales. In addition, we enhance semantic modeling at early scales by incorporating external self-supervised features. Unlike naive alignment, we analyse and design a residual feature aggregation scheme tailored to the VAR paradigm. Extensive experiments show that our method significantly improves both training efficiency and generation quality. On the ImageNet 256*256 benchmark, our model achieves a superior FID compared to the dense baseline while requiring only half of the default training epochs and a smaller parameter budget, with a merely marginal increase in training cost. Moreover, the performance gap further widens with larger training epochs.

Parameter-efficient fine-tuning (PEFT) reparameterizes weight updates in a fixed basis: low-rank adapters operate in the spatial domain, while a recent line of spectral methods operates in a fixed Fourier domain. We argue that the choice of domain is itself a design degree of freedom that should be learned, and that no single basis is optimal across tasks, layers, or tokens. We introduce Fractional-Fourier Mixture of Experts, a mixture-of-experts adapter in which every expert carries a learnable fractional-Fourier order that continuously interpolates between the spatial domain (recovering vanilla LoRA) and the Fourier domain (recovering a spectral adapter). Routing tokens through experts that occupy different points on this spatial-spectral continuum lets the model place each low-rank update in the domain where it is most compact, and -- because fractional-Fourier operators of different orders are mutually incoherent -- makes the experts naturally decorrelated, which reduces interference and improves multi-task composition. The order is a single scalar per expert, trained with a separate optimizer, and the transform is computed with an $\mathcal{O}(d\log d)$ chirp--FFT surrogate, so Fractional-Fourier Mixture of Experts adds negligible cost over standard MoE-LoRA. Across commonsense, mathematical, code, and knowledge benchmarks on LLaMA-3.1-8B and Qwen2.5-7B, Fractional-Fourier Mixture of Experts improves over strong MoE-LoRA and spectral baselines -- including FlyLoRA, FourierMoE, and HMoRA -- while keeping the active-parameter budget small, and analysis shows that the learned orders specialize by task and layer in interpretable ways.

Low-resolution face recognition (LR-FR) remains a challenging task due to poor feature extraction and aggregation, as probe images often contain limited identity information resulting from extreme degradations such as blur, occlusion, and low contrast. Additionally, the domain gap between high-resolution (HR) gallery images and low-resolution (LR) probe images poses a significant challenge. A single feature encoder struggles to generalize effectively across both domains when fine-tuned on an LR dataset, and this issue is further magnified by catastrophic forgetting. To address these challenges, we propose FaceMoE, an effective adaptation of Mixture of Experts (MoE) transfomer architecture for low-resolution face-recognition . Specifically, we introduce multiple specialized feed-forward network (FFN) experts and incorporate a top-k router, which dynamically assigns tokens to appropriate experts. This design emergently promotes specialization across experts for different semantic regions of the face, which enables FaceMoE to perform resolution-aware feature extraction. Moreover, the top-k router facilitates sparse expert activation, enabling the model to preserve pretrained knowledge when finetuned on a LR dataset, while increasing model capacity without proportional computational overhead. FaceMoE is trained with a combined face recognition loss, router z-loss, and load balancing loss to ensure expert specialization and stable training. To the best of our knowledge, this is the first work leveraging MoE for LR-FR. Extensive experiments across eleven datasets, spanning HR, mixed-quality, and LR benchmarks, demonstrate that FaceMoE significantly outperforms state-of-the-art methods. Code: https://github.com/Kartik-3004/FaceMoE

Composing independently trained LoRA adapters into a single large language model is useful for multi-domain adaptation, especially when the original training data cannot be shared. A common approach is to use MoE-style routing over LoRA experts, but for frozen pretrained adapters, soft weighted combinations can change the unit-scale additive update under which each LoRA module was originally trained. We propose \textbf{Hard-Routed MoR-LoRA}, a two-stage framework for composing frozen reasoning LoRA experts through unit-scale hard selection. First, domain-specific LoRA adapters are trained independently using reinforcement learning from verifiable feedback to obtain reasoning experts. Then, all experts are frozen, reasoning traces are distilled from them, and only a lightweight shared router together with a small attention LoRA is trained for integration. The router selects exactly one expert per token using hard top-1 routing, while a straight-through estimator enables gradient-based training. Experiments across five benchmarks, multiple model scales, and additional model families show that Hard-Routed MoR-LoRA preserves expert behavior while requiring substantially fewer trainable parameters than soft-routing mixture baselines. Our analysis further shows that normalized soft mixtures often concentrate most routing mass on a single expert, suggesting that hard unit-scale routing provides a simple and efficient abstraction for frozen LoRA expert composition.

Existing multi-agent debate frameworks suffer from two critical limitations: they rely on static architectures where agent roles and coordination patterns are fixed at design time, and they require instantiating multiple model copies, incurring substantial computational overhead. We propose Mixture of Debaters (MoD), a unified framework that enables dynamic self-debate within a single model by leveraging the Mixture-of-Experts paradigm. We address three key challenges in adapting MoE for dialectical reasoning: (1) dual-routing that decouples role allocation from process flow, dynamically determining when to debate versus when to synthesize; (2) momentum switching that smooths token-level routing with local context, reducing expert-switch jitter; and (3) unified self-debate that encapsulates diverse debating personas into lightweight expert modules, eliminating inter-agent communication while preserving behavioral diversity. Extensive experiments on multimodal benchmarks demonstrate that MoD outperforms both single-model baselines and conventional multi-agent systems, achieving superior accuracy with 3.7x lower latency and 87% reduction in token consumption.The source code can be accessed at https://github.com/YongLD/MoD.

Federated Learning (FL) emerged as a promising distributed machine learning paradigm. However, extending FL to the class incremental learning scenarios introduces unique challenges: 1) Capacity conflict and catastrophic forgetting from the shared model overloading, 2) Heterogeneity from Non-Independent and Identically Distributed (Non-IID) data, and 3) Synchronized class misalignment. In this paper, we propose \textbf{F}isher-Routed \textbf{M}i\textbf{X}ture of Experts for \textbf{Fed}erated Class-Incremental Learning (\textsc{FedFMX}), a novel framework to address these challenges via adaptive expert specialization across clients. The crucial insight is to route each sample to an expert subset that jointly optimizes knowledge acquisition and retention. Specifically, we introduce a Fisher-Routed Expert Scoring (FRES) module to estimate expert importance via Fisher-based stability cost and gradient-based plasticity gain. Then, we design an Adaptive Expert Selection (AES) module by quantifying marginal contributions for adaptive expert subset determination. Finally, by the routing-aware regularization (RAR), we achieve load balance and efficient FL training. We theoretically prove the $\mathcal{O}(T^{-1})$ convergence rate. Extensive experiments on multiple benchmarks compared with state-of-the-art methods demonstrate the superiority of \textsc{FedFMX}.

Building performant Vision-Language Models (VLMs) requires carefully curating large-scale training datasets, yet the community lacks systematic benchmarks for evaluating such curation strategies. We introduce DataComp for VLMs (DCVLM), a benchmark for controlled data-centric experiments to improve VLM training. As part of DCVLM, we collect 160 datasets spanning four data types -- image-caption pairs, multimodal interleaved documents, text-only, and instruction-tuning data -- into a corpus of 6T multimodal tokens. DCVLM allows participants to test curation strategies (filtering, mixing, formatting, sampling) across 1B-8B models and 6.25B-200B token budgets. Models are then evaluated on a carefully selected suite of up to 52 downstream benchmarks across 9 domains. We conduct extensive experiments on DCVLM and find that data mixing, not filtering, is key to a high-quality training dataset: instruction-heavy mixtures scale better than caption-heavy ones, with gains widening at larger scales. The resulting dataset, DCVLM-Baseline, enables training an 8B VLM to 63.6% accuracy on our 33-task core suite with 200B training tokens. Compared to FineVision, the state-of-the-art open VLM training dataset, this represents an improvement of +5.4pp. DCVLM and all accompanying artifacts will be made publicly available at https://www.datacomp.ai/dcvlm/.

As expressive text-to-speech (TTS) and voice conversion (VC) systems increasingly generate non-verbal vocalizations (NVVs) to enhance naturalness, reliable speaker verification (SV) becomes essential to objectively assess identity consistency across both verbal and non-verbal segments. Yet current SV systems generalize poorly to NVVs, and fine-tuning on NVV data causes catastrophic forgetting of speech performance. We present the first systematic study across 10 NVV types and propose a framework combining frozen Data2Vec self-supervised features with ECAPA-TDNN, enhanced by a Mixture of Experts (MoE) module with learned domain-aware routing. A conditional distillation loss on speech inputs via a pretrained teacher retains speech-to-speech accuracy, while a contrastive loss bridges the speech-NVV domain gap. Our method reduces speech-NVV EER from 38.93% to 22.66% over a pretrained baseline, and improves speech EER from 13.17% to 9.24% via distillation.

Data mixture selection is critical for Large Language Model pretraining. Existing methods such as RegMix select a single static mixture by fitting a regression model on small-scale proxy runs. We propose RegMix-D, a simple extension of RegMix to dynamic mixing. Our key observation is that proxy runs produce not only endpoint losses, but also full loss trajectories, which can be used to further improve data mixture. By training regression model on these trajectories, we can predict optimal mixtures at multiple training stages. RegMix-D supports two deployment modes: an offline variant that generates a complete mixture schedule before target training, and an online variant that adapts the mixture during training using observed loss. Experiments on 25B tokens of the Pile dataset with a 1B parameter target model show that RegMix-D consistently improves over RegMix and DoReMi across 13 downstream tasks while remaining proxy-efficient: it surpasses RegMix even with only 128 proxy models (25% of RegMix's proxy compute budget).

Pretraining language models with extended context windows enhances their ability to leverage rich information during generation. Existing methods split input sequences into chunks, broadcast them across multiple devices, and compute attention block by block which incurs significant communication overhead. While feasible in high-speed clusters, these methods are impractical for decentralized training over low-bandwidth connections. We propose a compression method for communication-efficient context parallelism in decentralized settings, achieving a remarkable compression rate of over 95% with negligible overhead and no loss in convergence. Our key insight is to exploit the intrinsic low-rank structure of activation outputs by dynamically constraining them to learned mixtures of subspaces via efficient reparameterizations. We demonstrate scaling billion-parameter decentralized models to context lengths exceeding 100K tokens on networks as slow as 300Mbps, matching the wall-clock convergence speed of centralized models on 100Gbps interconnects.

While large and diverse datasets have driven recent advances in large models, identifying the optimal data mixture for pre-training and post-training remains a significant open problem. We address this challenge with FASTMIX, a novel framework that automates data mixture discovery while training only a single proxy model. Instead of relying on predefined heuristics or resource-intensive simulations, FASTMIX jointly optimizes mixture coefficients and model parameters, substantially improving efficiency and scalability over prior approaches. At the core of FASTMIX is a reformulation of mixture selection as a bilevel optimization problem. Under this reformulation, we show that optimizing mixture ratios is mathematically equivalent to assigning per-source loss weights under uniform source sampling. This embeds the mixture coefficients directly into the differentiable iterative optimization objective, enabling efficient, gradient-based optimization of both mixture and model. To solve the optimization problem, FASTMIX implements an approximate iterative optimization procedure, alternating between (i) updating model parameters on data sampled according to current mixture ratios (inner loop) and (ii) updating mixture ratios based on validation feedback (outer loop). Across pre- and post-training, FASTMIX outperforms baselines while drastically reducing search cost. Code (https://github.com/hrtan/fastmix)

The dense token-to-token interaction pattern of standard dot-product attention remains a central bottleneck in scaling Transformer architectures to long contexts. We introduce \textbf{Gaussian Mixture Attention (GMA)}, a probabilistic attention-style sequence mixer that replaces explicit pairwise query--key comparison with routing through $K$ learned Gaussian mixture components. Queries and keys are mapped to posterior \textit{responsibility} vectors over a shared latent routing space; their overlap defines an implicit responsibility-space affinity, while values are written into and read from a $K$-slot latent memory. By exploiting the associativity of matrix multiplication, GMA avoids materializing the induced $N\times N$ affinity matrix and instead uses two responsibility matrices whose dominant activation storage scales as $\mathcal{O}(NK)$ rather than $\mathcal{O}(N^2)$ for fixed $K$. We formulate bidirectional and causal variants of GMA, provide an end-to-end differentiable parameterization of the Gaussian mixture components, and analyze its responsibility-modulated gradient structure, constrained non-negative low-rank affinity interpretation, and local routing stability. Empirically, GMA exhibits the intended fixed-$K$ linear memory scaling and is competitive with attention-style baselines on long-context classification, while causal GMA improves over tested linear/random-feature attention variants on WikiText-103 but remains behind optimized causal SDPA and Mamba in the current implementation. Analysis of learned responsibilities further shows broad component usage and moderate alignment with surface-form token categories, supporting GMA as a probabilistic, interpretable, fixed-$K$ linear-time attention-style alternative rather than a universal replacement for optimized softmax attention or state-space models.

We study the task of density estimation, where we hope to accurately estimate a probability density from $n$ samples. A textbook method for density estimation in total variation distance is the minimum-distance estimator approach, where we conclude both the algorithm and the analysis merely from bounding the VC dimension of a particular concept class (the so-called Yatracos class). While this technique has originally yielded sharp guarantees primarily for total variation distance, in this work we extend the minimum-distance estimator approach for learning within Hellinger distance. Our main observation is that we may produce an analogous recipe for Hellinger (where we only require bounding the VC dimension of a related concept class) by drawing connections to recent results yielding reverse data processing inequalities. This recipe is flexible enough to accommodate fast algorithms originally designed for total variation distance; by modifying the approach of Acharya et al. (2017) we conclude the first near-linear time algorithm for learning classes including univariate mixtures of log-concave densities and mixtures of Gaussians (with arbitrary variances), with near-optimal sample complexity.

The spatiotemporal evolution of many physical, chemical, and biological systems is described by nonlinear partial differential equations (PDEs). Recently, deep neural network-based surrogate models have emerged as efficient alternatives to computationally expensive numerical PDE solvers. In this work, we propose a physics-constrained deep neural network as a surrogate model to learn the microstructural evolution of a binary mixture, in which conservation of the order parameter is imposed directly on the network output as a hard constraint. We train the model to accurately predict the time-evolution of phase separation in binary mixtures governed by the Cahn-Hilliard equation. We show that predictions from our trained surrogate model remain stable and accurate over long-time rollouts for both critical and off-critical mixtures and preserve the mixture composition throughout evolution. In contrast, a variant in which conservation is enforced only via a penalty term in the loss function drifts away from the initial composition and significantly loses predictive accuracy over the same rollout. This establishes that the hard constraint is essential for long-time stability and order parameter conservation. We also show that our model accurately captures the growth of domain size and is consistent with the Lifshitz-Slyozov domain-growth law. These results demonstrate the effectiveness of the proposed framework for modeling systems with conserved kinetics, and the construction extends directly to other systems with conserved quantities.

The rapid progress of large language models (LLMs) has opened up a new frontier for automatic speech recognition (ASR), making their effective integration a critical and challenging research direction. To this end, this work proposes a projector-based LLM-ASR framework targeting the key challenges of multilingual generalization and modality alignment. Our approach incorporates a Mixture of Experts (MoE) architecture to improve cross-lingual adaptability, and a Continuous Integrate-and-Fire (CIF) mechanism for dynamic downsampling and modality alignment. Experimental results show that the combination of these components yields substantial performance improvements, surpassing strong baseline models. The proposed method represents a step toward building more accurate, robust, and generalizable LLM-based ASR systems.

We study component recovery and mixing-matrix estimation from unlabeled finite mixtures whose observable distributions share the same latent components but have unknown mixing weights. The main identifying signal is marginal independence: each component is assumed to be independent on at least one coordinate pair, but no labels, clean component samples, or mixing weights are observed. We first prove a structural result for product components: under linear independence of the univariate marginals, any independent affine combination of the components must coincide with a single component. We then extend this principle to observable mixtures and show that, under full-rank and no-cancellation conditions, marginally independent affine combinations recover the corresponding latent components. When every component is independent on some coordinate pair, all components are identifiable, and the mixing matrix is recoverable under the stated completion conditions. Finally, we propose a Product-Marginal Maximum Mean Discrepancy (PM-MMD) estimator over affine combinations of the observable mixtures and prove uniform convergence and stability under approximate marginal independence. This framework also separates the empirical roles of the assumptions: irreducibility is, in general, not directly testable from the unlabeled mixtures alone, whereas marginal independence yields a candidate-level diagnostic through held-out PM-MMD. Controlled and flow-cytometry experiments show when marginal independence provides a useful recovery signal. In the reported multi-component comparisons, condition-aware representative selection stabilizes PM-MMD and improves recovery relative to clustering, factorization, and pairwise mixture-proportion baselines using the same unlabeled mixtures.

The capabilities of large language models (LLMs) significantly depend on training data drawn from various domains. Optimizing domain-specific mixture ratios can be modeled as a bi-level optimization problem, which we simplify into a single-level penalized form and solve with twin networks: a proxy model trained on primary data and a dynamically updated reference model trained with additional data. Our proposed method, Twin Networks for bi-level DatA mixturE optiMization (TANDEM), measures the data efficacy through the difference between the twin models and up-weights domains that benefit more from the additional data. TANDEM provides theoretical guarantees and wider applicability, compared to prior approaches. Furthermore, our bi-level perspective suggests new settings to study domain reweighting such as data-restricted scenarios and supervised fine-tuning, where optimized mixture ratios significantly improve the performance. Extensive experiments validate TANDEM's effectiveness in all scenarios.

Bounding-box regression is a fundamental component of object detection, playing a critical role in precise object localization. Existing Intersection-over-Union (IoU)-based loss functions extend the IoU objective by incorporating geometric penalties, such as center-distance and aspect-ratio mismatch, to improve bounding-box regression. However, these penalties typically remain fixed throughout training and do not account for the optimization dynamics in which predicted boxes initially exhibit large center-distance and shape errors, with later stages focusing on improving overlap with the ground truth. To address this limitation, we introduce MoEIoU, a mixture-of-experts based regression loss that jointly models overlap, center alignment, and aspect-ratio mismatch. MoEIoU aggregates these components using a log-sum-exp function, which emphasizes the dominant localization error while maintaining smooth contributions from other terms. Additionally, a curriculum-based weighting schedule is employed to prioritize correcting box position and shape in early training stages and improving overlap in later stages. We evaluated proposed MoEIoU on PASCAL VOC, HRIPCB, and MS COCO using multiple YOLO architectures, along with large-scale simulation experiments. It consistently outperforms standard and recent state-of-the-art losses, demonstrating faster convergence and improved localization accuracy. We further show that this adaptive aggregation improves existing IoU-based losses, yielding consistent gains and providing more effective optimization guidance for bounding-box regression in object detection frameworks.

Retrieval-augmented generation is intensively studied to ground large language models on external evidence. However, retrieving from a unified knowledge base could inevitably introduce irrelevant information that may mislead generation for complex reasoning. Inspired by the conditional computation of mixture of experts (MoE), where a router sparsely selects specialized experts alongside shared ones for each input, we propose \textbf{M}ixture \textbf{o}f experts for \textbf{G}raph-based Retrieval-Augmented Generation, i.e., \textbf{MoG}. It organizes knowledge into two core components: (i) diverse, always-accessible hub graphs that encode semantically and structurally central knowledge and provide contextual clues for expert activation, and (ii) sparsely activated expert graphs that contain domain-specific evidence. MoG first accesses hub graphs to identify general evidence and derive contextual clues. Then, a topology-aware router dynamically activates a limited set of expert graphs conditioned on the query, thereby confining retrieval to a focused evidence subspace. Extensive experiments on challenging benchmarks show that MoG consistently outperforms strong baselines, with over 20% relative improvement on MuSiQue. Our code is available in https://github.com/DEEP-PolyU/MoG.

We study the problem of learning Gaussian mixture models under overparameterization. Prior work has shown that while overparameterization is essential for avoiding spurious local optima and enables global recovery of the ground-truth model using the gradient-EM (expectation-maximization) algorithm, it can dramatically slow down the local rate of convergence. Under certain assumptions on the mixture weights, we show that a standard divergence measure minimized by statistical learning procedures possesses a manifold of slow growth on which the well-known Polyak stepsize reduces the loss geometrically, and design a gradient-based method that converges to minimizers at a locally linear rate. Additionally, we show that our method converges to nearly optimal solutions -- up to a natural misspecification threshold -- for mixtures with arbitrary weights. At a high level, the method alternates between several "short" gradient descent steps that approach the manifold and "long" Polyak steps that contract the distance to minimizers. Our results suggest that slow convergence is not an intrinsic challenge of overparameterization, but can be overcome by exploiting the favorable structure of the loss landscape.

Pre-training data mixtures are commonly tuned by running small-scale experiments and extrapolating to the target training budget. When high-quality data is scarce and must be repeated, this extrapolation frequently fails, but the source of the failure has not been isolated. We show that a primary culprit is a repetition mismatch: because high-quality datasets are small, their repetition rate changes as the training budget grows, shifting the optimal mixture in ways that small-scale proxy experiments do not anticipate. A subsampling procedure that matches the target repetition rate controls for this effect. In a two-source setting combining limited high-quality data with web crawl, a single repetition-controlled experiment using only 1/16 of the target tokens recovers a mixture within 0.10 of the optimum on Wiki-Text for a 1.17B parameter model, compared to an error of 0.85 without repetition control. Achieving comparable accuracy without repetition control requires multiple training horizons, consuming 19%, 44%, and 94% of the target token budget when using the results from two, three, and four horizons respectively. With three data sources, the larger mixture space requires more than a single experiment to constrain, but the approach remains effective: at the 757M scale, just two repetition-controlled horizons recover the optimal mixture, outperforming baselines that instead require the full two-source experiments to construct. Our results reveal that repetition dynamics, not scale alone, shape whether small-scale mixture experiments generalize. More broadly, they suggest that data repetition deserves treatment as a first-class variable in mixture optimization, rather than an inconvenient side effect of limited data.

The pretraining data mixture of Large Language Models (LLMs) constitutes their "digital DNA", shaping model behaviors, capabilities, and failure modes. Yet this composition is rarely disclosed, making post-hoc auditing of data combination or provenance difficult. In this work, we formalize $\textbf{Data Mixture Surgery (DMS)}$: given only generated text from a target LLM, estimate the domain-level distribution of its pretraining corpus under a predefined taxonomy. We propose $\textbf{LLMSurgeon}$, a strong framework that casts DMS as an inverse problem under the label-shift assumption. Rather than directly aggregating classifier outputs, LLMSurgeon estimates a calibrated $\textit{soft}$ confusion matrix and solves a constrained inverse problem to correct systematic domain confusion and recover the latent mixture prior. To evaluate, we introduce $\textbf{LLMScan}$, a recipe-verifiable evaluation suite built from open-source LLMs with transparent pretraining mixtures. Across LLMScan, LLMSurgeon recovers domain mixtures with high fidelity under fixed protocols. Our work presents a practical, post-hoc approach for auditing the digital DNA of foundation models without access to their training data.

High-density electroencephalography (HD-EEG) enables fine-grained measurement of cortical activity but requires expensive hardware and lengthy setup times, limiting its clinical and research accessibility. We propose EMAG (EEG Mixture of Anisotropic Gaussians), a differentiable framework that reconstructs HD-EEG signals from a sparse subset of low-density (LD) electrodes by representing brain electrical sources as a mixture of anisotropic 4D space-time Gaussians. EMAG places a mixture of multiple Gaussians at each point of a spherical brain grid, each parameterized by a full 4 x 4 precision matrix, enabling anisotropic spatial spreads and explicit coupling between spatial and temporal dimensions. The forward model renders scalp EEG via differentiable Gaussian field contributions at electrode locations, enabling end-to-end training without explicit source localization supervision. We evaluate EMAG on three public EEG benchmarks (Localize-MI, SEED, and SEED-IV) at super-resolution factors of 2x through 8/16x. EMAG outperforms the current state-of-the-art EEG super-resolution method at most super-resolution factors on three standard benchmarks (Localize-MI, SEED, SEED-IV). The explicit Gaussian parameterization further enables direct visualization and interpretability of learned brain source configurations, potentially opening avenues for clinical and neuroscientific applications, such as source localization or biomarker discovery.

Machine learning for molecular property prediction has focused largely on pure compounds, even though many practical applications depend on mixtures with intermolecular interactions. Recent work has expanded the availability of mixture datasets, but evaluation still focuses mainly on absolute accuracy. However, absolute errors in mixtures conflate pure-component contributions with deviations from ideal mixing. We propose an evaluation framework that decomposes mixture-property error into pure-compound and interaction (non-ideal) components. The framework combines leakage-aware split protocols, ideal-mixture baselines, and excess-property metrics. To support reproducible benchmarking, we curate seven matched pure and mixture physicochemical property datasets. Across multiple mixture-property tasks and model families, we find that strong absolute accuracy can mask poor recovery of non-ideal mixture behavior, and that performance drops substantially under strict molecule splits. These results identify transfer to unseen molecules as a central challenge in molecular mixture machine learning and motivate evaluation beyond absolute accuracy alone.

When multiple LLM agents solve the same problem, standard practice compresses each agent's reasoning into a majority vote or layered synthesis, treating agreement as the finish line. We show this is unnecessarily lossy: an LLM aggregator that reads complete reasoning traces recovers correct solutions even when agents unanimously agree, with beneficial corrections consistently outweighing harmful ones -- the \emph{aggregation paradox}. Majority voting has a ceiling that perturbation diversity does not raise (error correlations are identical); the aggregator's gain comes from trace-level complementarity, assembling correct intermediate steps from minority chains that voting discards. These findings motivate Self-Consistent Mixture of Agents which generates trace diversity through semantic-preserving input perturbations, safeguards the majority via anchored refinement with provable non-degradation guarantees, and always synthesizes -- never gates on consensus. A single model with perturbation-induced trace variation outperforms heterogeneous model pools across structured reasoning, PhD-level science, competition mathematics, and competitive programming. The unit of aggregation should be the reasoning trace, not the answer.

We design a class of additive noise mechanisms that satisfy $(\varepsilon, δ)$-differential privacy (DP) for scalar, real-valued query functions with known sensitivities, with a particular focus on moderate and low-privacy regimes. These mechanisms, which we call \textit{mixture mechanisms}, are constructed by mixing multiple Gaussian distributions that share the same variance but differ in their means and mixture weights. The resulting distributions can be interpreted as convex combinations of a zero-mean Gaussian (as used in the analytic Gaussian mechanism) and additional Gaussians whose means depend on the sensitivity of the query function. We derive tight conditions on the variances required for $(\varepsilon, δ)$-DP and provide efficient algorithms to compute them. Compared to the analytic Gaussian mechanism, our mechanisms yield substantially lower expected noise amplitudes ($l_1$-loss) and variances ($l_2$-loss for zero-mean distributions). In the low-privacy regime that motivates our design, our mechanisms approach optimality, mitigating nearly all of the optimality gap of the analytic Gaussian mechanism.

Knowledge distillation (KD) transfers knowledge from a large teacher model to a smaller student. In language modeling, the student is trained either on tokens sampled from the teacher (hard labels) or the teacher's full next-token distribution (soft labels). Despite soft labels appear strictly richer, we find that mixing hard and soft labels consistently yields better results. Crucially, we show that this gain cannot be explained by closer teacher matching during training. Instead, it comes from reduced exposure bias, the mismatch between training and inference distributions. To explain this phenomenon, we introduce the Bridge-Garden Decomposition theory, which categorizes generation steps into two types: Bridges, where the next token must be exact, and Gardens, where it can be flexible. We show that hard-only KD excels in Bridges by avoiding risky deviations, while soft-only KD preserves diversity in Gardens. A hybrid strategy handles both cases and, as a result, reduces exposure bias across the sequence. Guided by this theory, we develop a family of Bridge-Garden hybrid supervision methods that adaptively balance hard and soft labels. Across a primary suite of seven teacher-student pairs (including Qwen, Llama, Gemma, and DeepSeek) and benchmarks in reasoning and coding, our approach outperforms divergence-based and on-policy KD baselines while reducing training cost by 9.7x, enabling efficient model compression. Code is available at https://github.com/ghwang-s/bridge_garden_hybrid_kd_release.

The effectiveness of multi-agent LLM deliberation depends not only on the agents' individual predictions, but also on how they communicate and collaborate. We study this mechanism through the lens of Friedkin-Johnsen (FJ) opinion dynamics, a tractable model for analyzing stubbornness, influence, and opinion change in multi-agent systems that captures empirically observed deliberation patterns. We show that the FJ parameters are input-dependent, turning multi-agent deliberation into a mixture of experts. This perspective implies that multi-agent systems can outperform single agents and static ensembles when routing reflects agent competence. Since competence is latent in practice, we analyze how influence is established through observable proxies: agents' self-assessed confidence, their perceived confidence, and initial alignment with other agents' views.

While Large Language Models (LLMs) are commonly fine-tuned to handle domain-specific tasks before being applied to vertical applications, adapting them to complex scenarios with diverse specialized knowledge remains challenging. Meanwhile, Mixture-of-Experts (MoE) architecture has risen as a crucial paradigm for training LLMs, and some recent works have also incorporated MoE into Parameter-Efficient Fine-Tuning (PEFT) to propose the Mixture of Low-rank Experts (MoE-LoRA), to enhance the power of low-rank adapters for learning complicated knowledge. However, conventional gating mechanisms in MoE typically apply only a scalar reweighing to selected experts, thereby limiting their underlying capacity of representation and generalization. Motivated and enabled by the low-rank structures in MoE-LoRA, we propose RotMoLE, a specialized MoE framework for low-rank experts featuring an additional rotation gate. Beyond simple scaling, RotMoLE implements a rotation mechanism for each selected expert, enabling superior expert exploitation and specialization for learning diverse data, especially when expert candidates are limited. Empirical results on complex multi-task and multilingual training scenarios validate our effectiveness.

We introduce a user defined probabilistic polygonal representation for plane curves. Given a curve, we select vertices on the curve and connect consecutive vertices by line segments to obtain a polygonal approximation. Each segment is equipped with a user defined uncertainty parameter in the normal direction. This yields a collection of thin probabilistic geometric primitives that retain the geometrz of the underlying curve while extending it beyond the idealized deterministic one dimensional formulation. For each segment, we define a Random Variable that is uniform distributed in the tangent direction of the segment and Gaussian distributed in the normal direction of the segment. By matching the first and the second central moments, this construction induces a Gaussian component whose mean lies at the segment midpoint and whose covariance encodes both tangential and normal uncertainty. Combining the segment wise components with appropriate weights yields a Gaussian Mixture Model (GMM) representation of the user defined probabilistic polygonal representation of the plane curve. The proposed framework provides an analytically tractable probabilistic model that preserves local geometry, and uncertainty in the normal direction. It applies to smooth, closed, open, non regular, and self intersecting plane curves, allows adaptive discretization and varying uncertainty in the normal direction, and as a result supports uncertainty aware geometric modeling. Experiments on a collection of canonical plane curves show that the resulting GMM capture local tangent, local normal, and local arc length; resulting in the global shape of the underlying curves to be truthfully captured as well. The representation is particularly relevant for applications in uncertainty aware CAD and digital twins, probabilistic obstacle modeling in robotics, and probabilistic trajectory planning.