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As multimodal agents accumulate increasingly long interaction histories, effectively retrieving and utilizing past information becomes critical for long-term interaction. Existing memory systems typically rely on semantic retrieval over compressed memories and expose predefined representations, which may miss relevant memories and overlook heterogeneous evidence needs across queries. We introduce \textbf{\hivemem}, a multimodal memory framework that interleaves \textbf{\textsc{H}}or\textbf{\textsc{i}}zontal Memory Expansion with \textbf{\textsc{Ve}}rtical Evidence Composition. For horizontal memory expansion, \hivemem organizes memory episodes into a relational graph using textual and visual anchors, expanding semantically retrieved seeds with related neighbors to recover complementary information. For vertical evidence composition, each retrieved memory retains multiple evidence forms, including compact summaries, captions, grounded visual views, raw images, and interaction history. A lightweight trainable selector independently composes an evidence subset for each retrieved memory, enabling query-adaptive utilization of heterogeneous multimodal information. This two-dimensional design jointly broadens memory coverage and adapts the evidence contributed by individual memories. Experiments across three multimodal memory benchmarks show that \hivemem consistently improves task performance across base models while reducing token consumption by about 90\% compared with the most efficient competing multimodal baselines.

Modern data systems often require aggregating information from multiple sources: some might be entirely untrustworthy, while the remaining presumably reliable sources may still suffer from a small amount of corruption. We study robust mean estimation under this practical scenario, which is formulated through the double corruption model: samples are divided among $N$ users, each with $n$ samples. $\varepsilon$ fraction of the users could be arbitrarily corrupted, while each of the remaining ``good'' users still have $α$-fraction ($α>0$) of corrupted samples. The goal is to estimate the unknown mean $μ$ with small $\ell_2$ error. This is a challenging scenario because we must handle two types of adversarial corruption: user-level corruption and sample-level corruption. When the unknown distribution has covariance matrix bounded by the identity matrix, we design a sum-of-squares (SoS) algorithm that achieves an $\ell_2$ error of $\sqrtα$ with probability at least $2/3$ as long as the total number of samples $nN=\widetildeΩ(d/α)$. The estimation error and sample complexity are min-max optimal under the mild condition. For comparison, treating all $nN$ samples as $(\varepsilon+α)$-corrupted and applying standard robust mean estimation only achieves an error of $\sqrt{\varepsilon+α}$. Thus, our new algorithm removes the adverse effect of untrustworthy users and achieves the optimal error as if only sample-level corruption is present. Also, our SoS algorithm extends to the heterogeneous setting where each user's local mean could be additionally shifted by $\sqrtβ$ in $\ell_2$ distance. We show that an error of $O(\sqrt{α+β})$ can be achieved with probability at least $2/3$ when $nN=\widetildeΩ(d/(α+β))$.

Inverse kinematics (IK) converts end-effector pose commands into joint motion, and many vision-language-action (VLA) policies rely on it to act on a given arm and to transfer across embodiments. Precise IK remains laborious: redundancy and singularities complicate the inverse mapping, execution depends on hand-tuned controllers, and training data on physical robots are costly to collect. We present PolicyIK, a goal-conditioned reinforcement learning policy for high-precision IK. It updates joint-position references from pose feedback and observes its accumulated reference relative to the measured joints, so it can retain the offset that the position controller needs at rest. Two-scale pose errors with an error-dependent action gain resolve millimeter residuals while preserving large motions. Progress and dwell rewards teach it to both reach the tolerance and stay within it. In simulation, a single attempt by the trained PPO policy keeps the mean errors over the final second within 1 mm and 0.2° on 93.5% of held-out tasks, and a deployment protocol raises success to 98.9%. When trained directly on a physical arm with an off-policy RL learner, PolicyIK achieves higher reaching and holding success than all four classical IK controllers under the same time budgets. In simulated pick-and-place, PolicyIK executes the end-effector commands of the $π_{0.5}$ VLA policy with 95.7% success. These results show that reinforcement learning can provide high-precision inverse kinematics for robot arms. Code is available at https://github.com/Tinaliu0123/PolicyIK.