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Customer experience (CX) agents use tools and large language models to address customer requests and guide conversational interactions with an organization's products. Improving these agents, especially in regulated industries, is difficult: they must detect intent, follow complex operational policies and use tools reliably. Manual end-to-end testing offers limited coverage, while live experiments expose customers to failures that can erode trust. We present a hypothesis-driven simulation workflow for screening candidate CX agents before deployment. Synthetic customers react to agent responses and simulated tool outputs enable multi-step agentic workflows without invoking production backends. We use the Snowglobe simulator on Nubank's Card Delivery agent and its expanded successor, Card Management - Nubank's highest-volume chat-support agent in Brazil. Across 4 deployed versions, simulated and production version-level binary evaluator scores show high correlation. Simulation-guided iteration increased transactional net promoter score (tNPS) by 36.69 points in a live A/B test. We also screened open-weight configurations in over 16,000 simulated conversations. In a subsequent live A/B test, the selected model increased self-service rate (SSR) by 8.82 percentage points to the highest level observed at Nubank, with no statistically significant change in tNPS. Simulation made broad exploration of models, reasoning settings, and prompts feasible without customer exposure, enabling production improvements that would have been impractical to pursue through live experimentation alone.

LLM-based medical assistants that follow a patient across visits need a memory that keeps the patient's clinical state correct as it changes. We examine the errors of five memory systems on longitudinal medical dialogue and find three recurring causes: the retrieved evidence gives an outdated state, includes another person's health facts, or lacks a safety fact the answer depends on. We present MedGraph, a graph memory built for these three cases. Construction extracts dated facts from each session, attributes each fact to the person it describes, and links medication, diagnosis, and measurement records into chains that keep earlier states. Retrieval ranks the patient's chains as units, reads each chain at the time the question asks about, and adds the original dialogue text; a patient profile lists every recorded safety fact with every question. On MedMemoryBench, MedGraph has the highest overall accuracy with both a GPT and a Qwen backbone, 10.5 and 10.4 points above the strongest of five baselines, with efficient memory construction and answering in the GPT setting.

We present \textsc{Ginger}, a state-of-the-art open-source C++ library for graph-based approximate nearest neighbor search (ANNS). We developed \textsc{Ginger} at Google to push the speed and memory efficiency of graph search on large and high-dimensional embedding datasets. \textsc{Ginger} surpasses existing ANNS libraries with regards to query throughput and indexing time while matching the memory footprint of the most space-efficient competitors. \textsc{Ginger} builds upon recent advances in proximity graph construction (PiPNN) and vector quantization (TurboQuant). We introduce Nested TurboQuant (NTQ), a two-level quantizer which supports low precision graph navigation and high precision reranking in a single code. This representation achieves near floating point precision with $2.6\times$ less memory. We also compress the size of our proximity graphs by up to $2.5\times$ without impacting query throughput. We combine graph reordering with a new lossless compression codec called AdaptiveGap, which builds upon StreamVByte. At $95\%$ recall, \textsc{Ginger} speeds up query throughput by an average of $1.8\times$ over each dataset's fastest competitor and by at least $2.3\times$ over any single library. This lead grows to $2.9\times$ over compact libraries on high-dimensional embeddings.

We study token dynamics in deep Mamba models, with a particular focus on the attracting role of the first token. Unlike attention mechanisms, where token interactions are governed by positive scalar coefficients, Mamba dynamics involve full matrix-valued interaction coefficients with no positivity or definiteness guarantees. This structural difference makes Mamba dynamics substantially harder to analyze and prevents the direct application of existing techniques for attention-based models. To overcome this challenge, we introduce a new analytical framework based on a high-dimensional invariant box and a sharp exit-time argument, which together recover an effective form of sign-definiteness. Using this framework, we characterize the possible limit points of token trajectories and prove explicit exponential convergence rates. Our analysis reveals that the first token has privileged dynamics: its limiting direction attracts subsequent tokens, inducing token clustering and attention-sink phenomena in deep Mamba models. We further show that this attraction mechanism extends to broader sequence dynamics, including state-space models, causal attention, and classical time-series models. Experiments on Falcon-Mamba-7B validate our predictions, showing that concentration on the first token increases with depth and dominates in later layers.

Online Convex Optimization with memory and time-varying constraints (COCO-M) is a recently-introduced framework that captures the dynamics of stateful online learning and non-stochastic control with budget constraints. Despite its expressive power, COCO-M remains largely understudied. In this work, we tackle this problem in its full scale, providing an optimistic algorithm that incorporates untrusted predictions to tame universal dynamic regret and cumulative constraint violation. Our analysis leverages a potent reduction from memory to delay and treats state-dependent gradients as delayed feedback. We establish the first bounds that adapt to both environment non-stationarity (path length $P_T$) and prediction accuracy, while lifting previous restrictive assumptions such as functional separability. En route to these results, we derive findings of independent interest for the memory-to-delay reduction, and for delayed OCO with time-varying constraints. The proposed framework ensures sublinear worst-case guarantees that improve with prediction accuracy, reaching $\mathcal O(1)$ regret under perfect predictions, with cumulative constraint violation (CCV) $\mathcal O(\sqrt{T})$ for unknown $P_T$ and $\mathcal O(\log T)$ for known or online observable $P_T$ , while recovering the optimal COCO rates when memory disappears.