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User embeddings are central components of modern recommendation, personalization, and behavioral modeling systems. Though these embeddings can compactly encode rich behavioral information, they are inherently dense and opaque, limiting interpretability. To address this gap, we argue that user embeddings can be understood as sparse superpositions of interpretable behavioral modes. This structure is directly predicted by generative models of user behavior for linear embeddings and extends approximately to deep-learning representations by the superposition hypothesis. Superimposed modes can naturally be recovered by sparse dictionary learning methods, such as sparse autoencoders (SAEs), and recovered modes can be automatically named and queried in natural language. We validate mode recovery against known ground truth on synthetic data, where SAEs recover modes better than classical sparse baselines, including on transformer-encoded embeddings. We then apply the method to classical and transformer-based user embeddings from two real-world datasets. We also show how the corresponding natural-language labels enable zero-shot audience retrieval and characterization over embeddings never trained on text. The framework is post-hoc and model-agnostic, requiring no modification to the upstream embedding system.

LLM-based generative recommendation reads long, text-rich interaction histories but generates only short semantic identifiers (SIDs). This asymmetry makes supervised fine-tuning inefficient: encoding the history is expensive, yet each history usually provides supervision for only one target. We present Merge and Branch (M&B) to reduce input cost and learn more from each encoded history. Merge compresses each historical item's SID and text into a small number of learned tokens. Branch uses the compressed history to predict multiple target SIDs. To share history computation while keeping these targets independent, M&B organizes each example as a shallow, wide tree. We develop tree FlashAttention to execute this layout efficiently, processing the shared history once and propagating gradients from every branch for end-to-end training. A tree-structured key/value cache extends history sharing to constrained decoding. Experiments on public benchmarks show that M&B outperforms strong recommendation baselines while substantially improving training and decoding efficiency. Online A/B tests on a large-scale e-commerce platform suggest that M&B effectively combines item text with multi-target supervision, yielding statistically significant gains in per-user clicks, orders, and GMV.

Reliable robotic manipulation requires both semantic understanding and precise control in three-dimensional space. However, vision-language-action (VLA) foundations largely inherit visual representations from 2D vision-language pre-training, while spatial supervision is often introduced only during task-specific adaptation. Developing spatial understanding as a transferable foundation-model capability therefore calls for learning from broader robot experience. We present SLA, a Spatial-Language-Action Model that scales implicit spatial alignment to continual pre-training and maintains it during downstream post-training. Initialized from a pretrained pi05 policy, SLA jointly optimizes action prediction and alignment between intermediate visual embeddings and spatial representations from a frozen 3D perception model. We curate and unify heterogeneous robot datasets to support spatial learning across diverse embodiments, tasks, and scenes. To accommodate this diversity, we introduce feature-dependent gates that adaptively aggregate visual embeddings from multiple VLA layers for spatial supervision. The teacher further exploits partially available depth and camera calibration alongside RGB observations, enabling effective use of heterogeneous geometric annotations. Probabilistic state dropout encourages reliance on visual cues and mitigates overfitting to demonstration trajectories. All auxiliary components are used only during training, allowing direct reuse of pretrained VLA weights and preserving the original inference architecture.

Large language model agents increasingly retrieve tools from large catalogs, yet most retrievers rank each tool independently by request similarity. For multi tool tasks, this recovers the goal matching tool while omitting prerequisite tools required by the workflow. We introduce LIBRA, a framework for Library Induction by Runtime Assembly that turns a flat tool catalog into an executable tool library. An LLM proposes per tool contracts of candidate invocations, reusable outputs and state changes, and success conditions; LIBRA then tests these compositions in a sandbox and retains the relations supported at runtime. Constructed before user queries, the library requires no dependency annotations, tool use trajectories, or task specific training, and supports both one-shot and agentic retrieval. On AppWorld, BFCL, and SciToolEval, LIBRA improves one-shot Recall and NDCG over the same dense retriever by 7.9 and 3.7 percentage points on average. Within ToolReAGt, it yields corresponding gains of 4.5 and 2.9 points after ten retrieval iterations.

Reinforcement learning (RL) has become a standard post-training method for diffusion models, but most RL objectives roll out the current policy at every iteration, and with a many-step sampler these rollouts typically dominate the cost of training. Few-step models cut this cost, yet they model an average velocity over an interval, whereas existing RL objectives are built for an instantaneous velocity with a many-step sampler. We adapt RL objectives to few-step models systematically in three phases, namely a transformation, a decomposition and an adaptation. The transformation to $x$-space expresses each objective we consider through a common policy prediction, at the clean end by default and at an explicitly marked level for transition or flow-map objectives, so that objectives stated over densities, velocities or rewards become comparable. The decomposition writes the gradient of each of these objectives as the sum of a self-regression toward a reference and a reward augmentation, so that a method reduces, at the gradient level, to a choice of anchors and weights. The adaptation computes each anchor from a few-step model at the end of its transport or along its tangent, with the instantaneous velocity recovered from the network itself or from an auxiliary network. This yields few-step versions of FlowGRPO, AWM, DiffusionNFT, DiffusionOPSD and ReFL in one modular codebase. In our experiments, reward-gradient-based methods are the most effective when the reward is differentiable and its gradient is affordable; otherwise DiffusionNFT-style methods generally reach high rewards in relatively few iterations despite a sometimes higher per-iteration cost. Extra inference steps show no systematic aggregate benefit in our experiments, although selected outputs visibly improve with two to four times as many sampling steps as in training.

We investigate the optimal asymptotic rate $R_q$ of perfect $q$-hash codes, a fundamental extremal problem in combinatorics, information theory, and computer science. Let $B_q=-\log_2(1-q!/q^q)/(q-1)$ denote the classical probabilistic lower bound. We prove that $R_q=B_q$ if and only if $q=2$, establishing an explicit strict improvement for every $q\ge3$ and settling the first assertion of a conjecture of Xing and Yuan (Combinatorica 43 (2023), 347--366). More significantly, we show that, for every $η>0$, $R_q\ge B_q+\exp(-(2+η)q)$ for all sufficiently large integers $q$. This improves the previously known increments of scale $\exp(-3q+O(\ln q))$ by an exponential factor. We also establish a structural limitation of the concatenation method. For pairwise uniform inner codes of subexponential length, the resulting rate bound exceeds $B_q$ by at most $\exp(-3q+o(q))$. Thus, exponentially long inner codes are necessary to achieve the new improvement scale within this framework. Our proofs combine Fourier analysis, high-dimensional simplex codes, additive permutation counts, and entropy bounds for hypergraph matchings. We further strengthen lower bounds from short inner codes and improve several known numerical estimates.

Multi-modal large language models (MLLMs) with impressive perception and understanding capabilities will enable a range of downstream applications. However, their substantial computational and memory requirements hinder the real-world implementation, particularly for resource-constrained edge devices. Quantization has emerged as an effective solution for deploying large models. While post-training quantization (PTQ) successfully retains the performance at moderate bit-width (e.g., W8A8), it suffers from severe performance degradation under low-bit quantization (e.g., W4A8), especially for small-scale models that are more suitable for edge deployment. In this paper, we propose ProQuant, a novel weight-activation quantization-aware training (QAT) framework tailored for low-bit MLLMs. First, to align the limited finetuning dataset distribution with the pretrained dataset distribution, we propose a self-relabeling (SRL) scheme to resample the responses of the open-source multimodal dataset. Second, we are the first to take a decoupled view of multi-modal (MM) understanding and language modeling abilities. We propose a progressive block activation (PBA) mechanism to prioritize the MM understanding recovery. We also introduce a vision-sensitive factor $\vecτ$ that effectively identifies the MM-critical layers. Extensive experiments across various benchmarks, covering models with 2B-8B parameters, show that ProQuant significantly outperforms existing methods. For example, our W4A8 Qwen3-VL-2B-Instruct improves average accuracy by impressively 6.6% and achieves performance comparable to full precision counterparts with only approximately 1% performance drop. Code is available at https://github.com/yufeixue-ai/ProQuant/.