Recent developments in AI for Mathematics (AI4Math), especially Large Language Model (LLM)-driven theorem provers, has achieved remarkable success in formal proof generation for well-defined mathematical problems through Interactive Theorem Proving (ITP) languages. However, current systems remain fundamentally limited in tackling frontier research mathematics, such as discovering new theorems or resolving open conjectures, which are often open-ended, under-specified, and involve multiple layers of abstraction. We argue that the next leap in AI4Math systems requires a decisive shift from predefined problem-solvers to research agents that can address frontier mathematical challenges with rigorous formal mathematical reasoning. In this position paper, we provide a systematic review of the field, covering datasets, auto-formalization, and proof synthesis. More importantly, we identify core limitations of existing systems in serving as mathematical research agents, examining issues across datasets, relational structure, mathematical exploration, tool ecosystem, and human-AI collaboration, outlining a strategic road-map for the future of AI4Math.
Remote sensing image fusion and semantic interpretation are usually optimized separately, so reconstruction quality need not preserve downstream retrieval utility. We propose LANCE, which uses structured language as an explicit, indexable semantic state. A frozen vision-language model maps the input to a closed-vocabulary text record; a language-conditioned generator fuses the imagery; and a dense verifier with a differentiable continuous summarizer re-describes the output. Text-text consistency and anti-collapse contrastive text-mask losses with negative queries close the loop without dense annotations or VLM fine-tuning. A variational EM formulation yields a per-step contraction result under regularity assumptions, distinguishing semantic faithfulness from verifier overfitting. Across seven test sets on GF2, QuickBird, WorldView-III, and WorldView-II, LANCE improves reduced-scale reference metrics by up to 11.7% (median 2.1%) over the strongest learning baseline. Independent evaluation using a held-out VLM and a supervised aerial detector yields gains of +6.4 mAP and +0.072 open-vocabulary F1 over the closest competitor. Text perturbations, cross-verifier transfer, and pseudo-RGB ablations examine the mechanisms underlying these gains. The framework connects image fusion to verifiable semantic representations for multimodal retrieval and knowledge management.
Multimodal Emotion Recognition (MER) systems often suffer from missing modalities in real-world scenarios. Existing methods usually generate, align, or distill missing modalities as a whole, overlooking the heterogeneous nature of the information carried by each modality. Such holistic treatment mixes inferable shared semantics with uncertain modality-specific details, yielding unstable representations and degrading robustness. To address this issue, we propose the Primitive Memory Distillation (PriMD) framework. Unlike existing methods, PriMD takes an intra-modal perspective and focuses on how different types of information within a modality differ in recoverability. PriMD first disentangles cross-modal shared semantics from modality-specific representations, and then discretizes the latter into learnable semantic primitives to construct modality-specific memory banks. When modalities are missing, PriMD is a teacher-student framework that the student model uses the shared semantics of available modalities as queries to dynamically retrieve primitives. It compensates for missing modality-specific information within a constrained memory space and aligns with the teacher model. Extensive experiments on IEMOCAP, CMU-MOSI, and CMU-MOSEI demonstrate that PriMD achieves state-of-the-art performance and consistently stronger robustness across a wide range of missing-modality settings, while mitigating the instability caused by holistic feature inference. Our code and project website are available at https://www.jiaqizhang-sengoku.com/Code/PriMD and https://www.jiaqizhang-sengoku.com/PriMD/ , respectively.