SO(3)-equivariant networks are the dominant models for machine learning interatomic potentials (MLIPs). The key operation of such networks is the ClebschGordan (CG) tensor product, which is computationally expensive. To accelerate the computation, we develop tensor decomposition networks (TDNs) as a class of approximately equivariant networks in which CG tensor products are replaced by low-rank tensor decompositions, such as the CANDECOMP/PARAFAC (CP) decomposition. With the CP decomposition, we prove (i) a uniform bound on the induced error of SO(3)-equivariance, and (ii) the universality of approximating any equivariant bilinear map. To further reduce the number of parameters, we propose path-weight sharing that ties all multiplicity-space weights across the O(L3)CG paths into a single shared parameter set without compromising equivariance, where L is the maximum angular degree.

We introduce MOSDT, the first algorithm designed for multi-agent offline safe reinforcement learning (MOSRL), alongside MOSDB, the first dataset and benchmark for this domain. Different from most existing knowledge distillation-based multiagent RL methods, we propose policy self-distillation (PSD) with a new global information reconstruction scheme by fusing the observation features of all agents, streamlining training and improving parameter efficiency. We adopt full parameter sharing across agents, significantly slashing parameter count and boosting returns up to 38.4-fold by stabilizing training. We propose a new plug-and-play cost binary embedding (CBE) module, which binarizes cumulative costs as safety signals and embeds the signals into return features for efficient information aggregation. On the strong MOSDB benchmark, MOSDT achieves state-of-the-art (SOTA) returns in 14 out of 18 tasks (across all base environments including MuJoCo, Safety Gym, and Isaac Gym) while ensuring complete safety, with only 65%of the execution parameter count of a SOTA single-agent offline safe RL method CDT.

We introduce MOSDT, the first algorithm designed for multi-agent offline safe reinforcement learning (MOSRL), alongside MOSDB, the first dataset and benchmark for this domain. Different from most existing knowledge distillation-based multi-agent RL methods, we propose policy self-distillation (PSD) with a new global information reconstruction scheme by fusing the observation features of all agents, streamlining training and improving parameter efficiency. We adopt full parameter sharing across agents, significantly slashing parameter count and boosting returns up to 38.4-fold by stabilizing training. We propose a new plug-and-play cost binary embedding (CBE) module, which binarizes cumulative costs as safety signals and embeds the signals into return features for efficient information aggregation. On the strong MOSDB benchmark, MOSDT achieves state-of-the-art (SOTA) returns in 14 out of 18 tasks (across all base environments including MuJoCo, Safety Gym, and Isaac Gym) while ensuring complete safety, with only 65% of the execution parameter count of a SOTA single-agent offline safe RL method CDT.

The discovery of the *lazy neuron phenomenon* (Li et al., 2022), where fewer than 10% of the feedforward networks (FFN) parameters in trained Transformers are activated per token, has spurred significant interests in *activation sparsity* for enhancing large model efficiency. While notable progress has been made in translating such sparsity to wall-time benefits across CPUs, GPUs, and TPUs, modern Transformers have moved away from the ReLU activation function crucial to this phenomenon. Existing efforts on re-introducing activation sparsity, e.g., by reverting to ReLU or applying top-k masking, often degrade model quality, increase parameter count, or complicate training.

Empirical insights into MLPs are important for multiple reasons.