Product of Experts

Long-tailed classification poses a reliability challenge because models trained on imbalanced data are unevenly reliable across frequent and underrepresented classes. While existing methods address imbalance through re-balancing, adjustment, representation learning, or multi-expert modeling, they rarely estimate which expert should be trusted for each class. This paper proposes CLEAR (Class-wise reLiability-aware Expert Aggregation for long-tailed Recognition), a modular ensemble framework for long-tailed classification. CLEAR generates diverse experts through threshold-based structured sampling while preserving the full label space, then estimates a class-wise trust score for each expert using a smoothed class-wise precision formulation. During inference, expert predictions are combined through class-wise generalized product-of-experts aggregation, allowing different experts to be emphasized for different classes. Experiments on CIFAR-100-LT, ImageNet-LT, and Places-LT across multiple backbones show that CLEAR achieves competitive overall accuracy and particularly strong few-shot performance. These results support class-wise expert reliability as a useful design principle for long-tailed ensemble learning.

Robot demonstration datasets used to train vision-language-action policies can contain a subtle but harmful failure mode: trajectories that are behaviorally correct but paired with the wrong language instruction. We study post-hoc auditing of these Instruction-Trajectory Mismatches (ITMs). Unlike failed rollouts, ITMs often look plausible, and can corrupt the language-behavior mapping learned by the policy. We propose Multimodal Probabilistic Fusion (MMPF), a training-free auditing framework that treats each modality as an expert, estimates a task-label distribution from local neighborhood agreement and global prototype similarity, and then fuses modalities with predictive-entropy weighting in a product of experts. Across LIBERO benchmarks with injected instruction mismatches and noisy real-robot data, MMPF achieves the strongest overall ITM detection and label correction accuracy. We also show that auditing improves most downstream policy learning in settings where language is needed to disambiguate the task. We demonstrate in real robot experiments that our method can achieve improved policy performance and show the trade-off of filtering demonstrations compared to relabeling.

Model merging aims to combine existing single-task solutions into a multi-task solution without additional data-driven fine-tuning.~Most existing approaches achieve this using geometric properties of local solution spaces. However, such geometric views provide limited guidance for scoring how statistically useful each task-specific update direction is across tasks during merging. To address this, we formulate model merging from a new perspective of probabilistic inference under a product-of-experts (PoE) scenario where each single-task solution defines an energy-based expert model (EBM) over the merged parameters. We show that several existing model merging methods arise as special cases of our framework under energy designs that impose implicit Gaussian assumptions on directional residuals between merged and task-specific models. Empirically, we find that these residuals are often heavy-tailed which exposes a mismatch with the imposed light-tailed Gaussian structures. We address this with a heavy-tailed PoE design based on Cauchy experts, which better captures the observed residual behavior while admitting a provably convergent inference procedure. Experiments across multiple tasks and architectures show significant improvements over state-of-the-arts baselines. Our code is available at https://github.com/MinhLong210/PoE-EBM-Merging.git.

Diffusion language models (DLMs) offer substantial speed advantages through parallel decoding, but the lack of token dependencies limits generation quality compared to autoregressive (AR) models. Recent progress attempts to bridge the gap via importance sampling, with DLM being the proposal and AR being the target. However, due to the huge gap between their distributions, the sampling requires a large number of particles and is thus expensive to compute. In this paper, we introduce PoE-Bridge, a novel decoding framework that drastically improves generation speed and accuracy by introducing an intermediate distribution to bridge the gap. The distribution is constructed as a Product-of-Experts (PoE) of the DLM proposal and the AR target. With the intermediate distribution, we first use the DLM to draft multiple continuations in parallel, then apply rejection sampling to verify the drafted tokens and move the resulting candidates toward the PoE. We then use importance sampling to further correct the PoE-aligned candidates toward the AR target. We further propose several improved techniques, including mixed-temperature sampling for enhanced diversity and elastic rejection windows for reducing wasted verification. Empirically, PoE-Bridge achieves significantly improved accuracy with $5\times$ speedup over the standard DLM decoding approach, and recovers at least 95% of the target AR model's performance, efficiently advancing most of the quality gap on challenging mathematical reasoning and coding tasks. Our code is available at https://github.com/juntongshi48/poe-bridge.

Missing modalities are prevalent in real-world Alzheimer's disease (AD) assessment and pose a significant challenge to multimodal learning, particularly when the distribution of observed modality subsets differs between training and deployment. Such missingness pattern mismatch induces a conditional representation shift across modality subsets. Existing approaches that rely on implicit imputation or modality synthesis often fail to explicitly model modality availability and uncertainty, leading to overconfident dependence on synthesized features, reduced robustness, and miscalibrated uncertainty estimates. To address these limitations, we propose PRA-PoE, an incomplete multimodal learning framework that is equipped with Prototype-anchored Representation Alignment (PRA) and an Uncertainty-aware Product of Experts (UA-PoE) fusion mechanism. First, PRA uses learnable global prototypes and availability-conditioned tokens to encode modality availability, distinguish observed from missing modalities, re-synthesize features for missing modalities, and adaptively refine observed representations to align latent spaces across modality subsets, with the goal of reducing representation shift under varying missingness patterns. Second, UA-PoE models each modality as a Gaussian expert and performs closed-form Product of Experts fusion, where experts with higher uncertainty are automatically down-weighted via lower precision, improving uncertainty reliability. We evaluate PRA-PoE under a clinically realistic protocol by training with naturally missing data and testing on all non-empty modality combinations. PRA-PoE consistently outperforms the state-of-the-art across datasets, achieving a 5.4% relative improvement in average accuracy on ADNI and a 10.9% relative gain in average F1 on OASIS-3 over the strongest baseline across all non-empty modality subsets.

ARC-AGI-2 is a benchmark of human-intuitive visual puzzles that measures a machine's ability to generalize from limited examples, interpret symbolic meaning, and flexibly apply rules in varying contexts. In this paper, we discuss our approach to solving the ARC-AGI-2 puzzles with TinyLM, with additional fine-tuning at test time, including Test-Time-Training (TTT) and Products of Experts (POE). Our model achieves 96.1% accuracy on the training set and 21.7% accuracy on the evaluation set.

Many agents in real-world environments cannot reliably communicate their goals through language, including household pets, pre-verbal infants, and other non-speaking embodied agents. In such settings, intent must be inferred from incomplete behavioral observations in context-rich environments. This creates a core ambiguity: observable behavior is often noisy or underspecified, while context provides strong prior information but can also induce brittle shortcut predictions if used naively. We present CatSignal, a Bayesian-inspired probabilistic framework for multimodal intent inference that models spatial context as a prior-like constraint and behavioral observations as evidence. Rather than treating context as an ordinary input feature, our method uses a context-gated Product-of-Experts formulation to compute posterior-like intent distributions from context, pose dynamics, and acoustic cues. We instantiate this formulation in a household cat setting as a focused proof-of-concept for intent inference in non-speaking agents. Under Leave-One-Video-Out evaluation on a multimodal domestic cat dataset, the proposed prior-guided fusion achieves the best overall accuracy of 77.72%, outperforming feature concatenation (71.83%) and stronger late-fusion baselines. More importantly, it substantially reduces context-driven shortcut failures in ambiguous cases. While simpler fusion strategies remain competitive in Macro-F1 and selective prediction, the proposed model provides the strongest overall accuracy and the best suppression of context-based shortcut collapse.

Programming robots to perform complex tasks is often difficult and time consuming, requiring expert knowledge and skills in robot software and sometimes hardware. Imitation learning is a method for training robots to perform tasks by leveraging human expertise through demonstrations. Typically, the assumption is that those demonstrations are performed by a single, highly competent expert. However, in many real-world applications that use user demonstrations for tasks or incorporate both user data and pretrained data, such as home robotics including assistive robots, this is unlikely to be the case. This paper presents research towards a system which can leverage suboptimal demonstrations to solve ambiguous tasks; and particularly learn from its own failures. This is a negative-feedback system which achieves significant improvement over purely positive imitation learning for ambiguous tasks, achieving a 90% improvement in success rate against a system that does not utilise negative feedback, compared to a 50% improvement in success rate when utilised on a real robot, as well as demonstrating higher efficacy, memory efficiency and time efficiency than a comparable negative feedback scheme. The novel scheme presented in this paper is validated through simulated and real-robot experiments.

Large vision-language models (LVLMs) employ multi-modal in-context learning (MM-ICL) to adapt to new tasks by leveraging demonstration examples. While increasing the number of demonstrations boosts performance, they incur significant inference latency due to the quadratic computational cost of Transformer attention with respect to the context length. To address this trade-off, we propose Parallel In-Context Learning (Parallel-ICL), a plug-and-play inference algorithm. Parallel-ICL partitions the long demonstration context into multiple shorter, manageable chunks. It processes these chunks in parallel and integrates their predictions at the logit level, using a weighted Product-of-Experts (PoE) ensemble to approximate the full-context output. Guided by ensemble learning theory, we introduce principled strategies for Parallel-ICL: (i) clustering-based context chunking to maximize inter-chunk diversity and (ii) similarity-based context compilation to weight predictions by query relevance. Extensive experiments on VQA, image captioning, and classification benchmarks demonstrate that Parallel-ICL achieves performance comparable to full-context MM-ICL, while significantly improving inference speed. Our work offers an effective solution to the accuracy-efficiency trade-off in MM-ICL, enabling dynamic task adaptation with substantially reduced inference overhead.