#01Oct 21, 2026
eess.IV
Geometric Algebra for Neural Networks: A Survey
Tao Zhong, Kaison Fong, Keqin Wang and 1 more
Geometric algebra (GA) unifies geometric primitives and transformations in a single algebraic framework. Neural networks designed around this framework often represent features as multivectors and constrain layer operations to respect the algebraic structure, enabling principled treatment of geometric transformations and, in many cases, built-in equivariance. This survey reviews geometric algebra neural networks, including their building blocks, equivariant properties, application domains, empirical performance, and software support. We provide an algebra-selection guide, an empirical comparison of GA-based and other equivariant architectures, and a failure-mode analysis covering training pathologies, deployment constraints, and performance limitations. Across the surveyed literature, the strongest evidence for GA-based architectures appears in settings with explicit geometric symmetries and heterogeneous geometric entities; evidence for broader advantages in parameter efficiency, interpretability, and dense prediction is comparatively limited and uneven. We therefore conclude that geometric algebra neural networks are not universally superior to well-tuned non-GA equivariant baselines, and outline open problems in algebra selection, numerical stability, scalable implementation, and reproducible evaluation.
#02Oct 21, 2026
cs.RO
Multimodal Embodied Agents: A Unified Capability-centric Perspective from Computer-Use to Robot-Use
Yanzhe Chen, Ziyi Yang, Jifeng Zhu and 14 more
Multimodal agents (MMAs) sustain interaction through reasoning, memory, tools, and feedback, most visibly as computer-use agents, while robotic systems (RSs) couple sensing and actuation under physical dynamics. We define multimodal embodied agents (MMEAs) as goal-directed systems that couple multimodal task reasoning with physical action and revise decisions from the resulting feedback. This raises a central question: what changes when a multimodal agent moves from computer-use to robot-use? We introduce PAPAV, a unified capability-centric framework of five recurring functions: Perceive the current state, Anticipate action effects, Plan a feasible course, Act through an interface or body, and Verify the outcome. Defined by function rather than architecture, these capabilities let PAPAV identify what all three share and then compare MMEAs with MMAs and with RSs. Five physical constraints, from partial observability to unverifiable outcomes, leave fewer choices fixed in advance and less room to reverse errors. Across 64 benchmarks, explicit evaluation centers on Act; only 5 assess Anticipate and 3 assess Verify, leaving both largely hidden behind task success. These constraints also frame the open challenges we identify. PAPAV therefore provides a common basis for designing reliable physical agents and measuring progress across all five capabilities rather than task success alone.
#03Oct 21, 2026
cs.CL
Environment Duels: A Microcosm of LLM Co-Evolution
Shibo Jin, Zhiqiu Xu, Yiling Zou and 2 more
Through a tangle of real-world interactions, from synthetic training pipelines to data shared on the open web, frontier LLMs absorb what their predecessors and competitors create. How well does each model play its role in this ecosystem, as a creator and as a solver? We introduce Environment Duels, a dynamic agentic benchmark that evaluates both capabilities on interactive environments. Each model writes environments, each with a privileged hint, aiming for tasks that capable solvers fail without the hint and pass with it. Across nine frontier LLMs, solving and authoring prove to be distinct skills: the strongest solvers are not the strongest authors, while smaller models learn more from how others played and write the hardest environments and the most useful hints. Beyond the scores, the pairwise interactions form a microcosm of how models affect one another. Head-to-head outcomes are transitive and so yield a stable ranking; independent authors converge on the same designs; and in a reinforcement-learning study with Qwen3.8-27B, the learner's hint lift on an author's environments tracks how much training on those environments improves it on held-out reasoning and agentic benchmarks, whether the environments are its own or another model's. Each of these patterns has a counterpart in how models shape one another outside the duel. By staging these interactions under controlled conditions, Environment Duels offers a window onto how LLMs teach, challenge and learn from one another. Code is available at https://github.com/LLM-Duels/EnvDuels.
#04Oct 21, 2026
cs.LG
From Classifier Heads to Encoder Prototypes: Personalized Federated Learning with Head-Derived Clustering
Amirardalan Dehghanpour, Arian Noori, Ehsan Tanghatari and 2 more
Personalized federated learning must decide which clients should share representations. We introduce HDC-FL (Head-Derived Clustering for Personalized Federated Learning), which reads that decision off a signal shared-encoder training already produces: the client-specific classifi- er heads. At periodic refresh rounds the server projects the cached heads into a normalized low-rank descriptor space, groups the descriptors, builds one encoder prototype per group from the cached client encoders, and returns to each client a soft mixture of those prototypes paired with its own unchanged head. Client-specific heads are never averaged or distributed to oth- er clients; the shared-encoder trajectory is left intact; and no second optimization trajectory, additional local objective, or post-training fine-tuning stage is required. Across 11 CIFAR-10 and CIFAR-100 configurations covering label-subset, Dirichlet and rotation heterogeneity with ResNet-18 and MobileNetV2 encoders, HDC-FL is competitive with the strongest personalized and clustered baselines in macro-averaged mean accuracy and attains the numerically highest macro-averaged worst-client and bottom-20% accuracy among the evaluated methods. The tail results distinguish methods that look similar when only their means are compared. A controlled donor-swap diagnostic further finds positive donor-ranking associations between head similarity and encoder compatibility in all three settings tested, most clearly under covariate shift.
#05Oct 21, 2026
cs.CL
GoiBERT: Compact Vietnamese Language Models via Two-Stage Knowledge Distillation
Quang Anh Kiet Tran, Nam Anh Tran, Manh Hung Trinh and 3 more
Vietnamese pre-trained encoders have improved rapidly, but the strongest ones are large, multilingual-vocabulary models or depend on external word segmentation, which makes them costly to deploy. We present GoiBERT, a family of two compact Vietnamese encoders with 26M and 49M parameters that operate directly on raw text. GoiBERT learns from two complementary teachers. A same-tokenizer Vietnamese encoder first teaches general-purpose representations. A much larger teacher then provides task-level guidance through soft labels that are generated without ever labeling its own training data. Across eight benchmarks covering text classification, aspect-based sentiment analysis, natural language inference, and named entity recognition, GoiBERT-large achieves the highest average score among non-teacher models. It does so with fewer than half the parameters of the strongest compact baseline and twice its throughput. GoiBERT-base retains 99% of that baseline's performance at a quarter of its size. Our analysis shows that compression is nearly lossless for sentiment and classification tasks but remains costly for inference and entity recognition, which points to clear directions for future work. Our code and models are available at: https://github.com/Nhantran65/GoiBERT.git