Path Integral Value Matching for Linear Quadratic Stochastic Optimal Control

Linear Quadratic Stochastic Optimal Control (LQ-SOC) establishes a fundamental framework for steering noisy dynamical systems and has recently gained renewed interest in the machine learning community. However, current state-of-the-art policy-based methods suffer from prohibitive computational costs and instability due to their heavy reliance on full-trajectory simulation. To overcome these limitations, we propose a paradigm shift toward a value-based approach by revisiting Path Integral Control (PIC). Although standard PIC suffers from the same high-variance bottleneck as policy-based methods, we discover that by truncating and marginalizing the original path integral formulation, we can derive a temporal recursive form of the value function. Building upon this theoretical foundation, we propose the Path Integral Value Matching (PI-VM) algorithm. Specifically, we employ temporal-difference learning to approximate the recursive value dynamics, and further integrate the Girsanov theorem with experience replay to enable off-policy training. We benchmark PI-VM against SOTA policy-based methods across various SOC benchmarks and sampling tasks. Empirical results demonstrate that PI-VM matches SOTA precision with an order-of-magnitude efficiency gain in low-dimensional settings, while effectively mitigating mode collapse in high-dimensional scenarios. Consequently, PI-VM offers a scalable solution for solving complex SOC problems.

A Finite E-Group of Nilpotency Class Three

A group is an E-group if every element commutes with each of its endomorphic images. Caranti asked whether a finite E-group can have nilpotency class three. We prove that the $3$-group of order $3^{84}$ introduced by Abdollahi, Faghihi, and Mohammadi Hassanabadi, and later shown by Abdollahi, Faghihi, Linton, and O'Brien to have the corresponding automorphism property, is an E-group. Let $P$ denote this group and put $V=P/Φ(P)\cong \mathbb{F}_3^9$. The nine power relations of $P$ determine a linear map $q:V\longrightarrowΛ^2 V$. We prove that $q$ has no nonzero proper subspace $U$ satisfying $q(U)\subseteqΛ^2 U$. Since the image induced by any endomorphism of $P$ on $V$ has precisely this closure property, every endomorphism acts on $V$ either invertibly or trivially. The invertible case is the known A-group case. In the trivial case the image first lies in $Φ(P)=P'$, and the power relations then force it into $Ω_1(P')=Z(P)$. Thus every element commutes with every endomorphic image. The tensor rigidity is reduced to an exact finite calculation on the $9841$ points of $\mathrm{PG}(8,3)$.

Kimi K3: Open Frontier Intelligence

We introduce Kimi K3, a 2.8T parameter Mixture-of-Experts model with 104 billion activated parameters, native vision capabilities, and a 1-million-token context window. Kimi K3 is built on Kimi Delta Attention and Attention Residuals, which improve information flow across sequence length and model depth. Together with Stable LatentMoE, which effectively activates 16 of 896 routed experts per token, and refined training and data recipes, these advances yield an approximately 2.5x improvement in overall scaling efficiency over Kimi K2. Post-training highlights reinforcement learning across general, agentic, and coding domains and multiple reasoning-effort levels, enabling compositional generalization and robust long-horizon execution. At 2.8T scale, Kimi K3 is supported by infrastructure advances in multiple areas: algorithm-system co-design for KDA, perfectly balanced expert-parallel training with efficient memory management, million-token agentic RL with persistent rollout and sandbox states, and deployment innovations. Extensive evaluations show that Kimi K3 achieves frontier-level performance across long-horizon coding, agentic, knowledge, reasoning, and vision tasks. While its overall performance still trails the most powerful proprietary models, namely Claude Fable 5 and GPT-5.6 Sol, Kimi K3 consistently outperforms other open and proprietary models evaluated in our suite. We release the full Kimi K3 model weights to facilitate future research and accelerate the broader deployment and adoption of frontier intelligence.

An Exact Counterexample to Carlson's Associated-Prime Depth Conjecture from a Group of Order 128

In Question~3.1 of his 1995 paper on depth and transfer, Carlson asked whether the depth of a finite-group cohomology ring is always realized by the dimension of one of its associated primes. We give a negative answer. Let \[ G=\SG{128}{859},\qquad k=\kbar. \] An exact presentation certificate proves that $\depth H^*(G;k)=2$. Okuyama's associated-prime theorem would convert an associated prime of dimension two into a rank-two elementary abelian subgroup $E\leq G$ satisfying $\depth H^*(C_G(E);k)=2$. We enumerate all $75$ rank-two elementary abelian subgroups of $G$ and obtain six centralizer types. Duflot's theorem gives depth at least three for four types, while exact ideal-quotient certificates exhibit regular sequences of length three for the remaining two. Hence every rank-two centralizer has cohomological depth at least three, so $H^*(G;k)$ has no associated prime of dimension two. The finite group presentation, the three cohomology-ring presentations, the enumeration summary, and the exact algebraic certificates are included for independent verification.

An Explicit Counterexample to Stanley's Rankwise Lower-Bound Conjecture for Differential Posets

In Problem~6 of his 1988 paper on differential posets, Stanley asked for the least possible cardinality of a fixed rank of an $r$-differential poset and suggested that the minimum should be attained by $Y^r$, the $r$-fold Cartesian power of Young's lattice. We disprove the resulting universal coefficientwise lower bound. For every $r\geq 3$, we construct an infinite $r$-differential poset $P^{(r)}$ satisfying \[ \card{P^{(r)}_4} =\card{(Y^r)_4}-\left\lfloor\frac r3\right\rfloor. \] For $r=3$, the construction replaces thirteen rank-four lower-cover blocks of $Y^3$ by twelve blocks with the same point and pair incidence multiplicities, producing the initial rank sequence $1,3,9,22,50$ instead of $1,3,9,22,51$. A reflection extension then yields an infinite differential poset. The construction does not address the cases $r=1$ and $r=2$.

HijackKV: New Threat in Position-Independent KV Cache Reuse

Key-Value (KV) cache reduces inference latency in large language models (LLMs). Traditional prefix-based reuse has low cache hit rates across inference requests because it requires exact token and position matches. To improve efficiency, recent system optimizations introduce position-independent KV reuse, allowing KV cache to be reused whenever identical text chunks appear, regardless of their position in the sequence. We show this design introduces a new threat, KV Cache Hijacking. Since KV caches are retrieved by token match but encode the context in which they were originally computed, the KV tied to a benign-looking token chunk may encode an attacker-controlled prefix. When later reused in a victim query, this contaminated KV silently hijacks the model's behavior, even if no attacker-controlled text appears in the input. We introduce HIJACKKV, the first attack framework that systematically exploits this vulnerability, demonstrating its severity and practicality. HIJACKKV optimizes an attacker-controlled prefix, so that the KV computed for a subsequent common benign text encodes the attacker's goal, while the text remains unchanged for future cache hits. HIJACKKV achieves an average 94% success rate in a single attempt, remains effective under realistic constraints including low hit rates (10%) and frequent recomputation (50%), persists over multi-turn interactions, and transfers across models in black-box settings. We further provide design insights for building secure KV reuse systems.

PagedWeight: Efficient MoE LLM Serving with Dynamic Quality-Aware Weight Quantization

Mixture-of-Experts (MoE) is a popular class of large language models (LLMs), offering high efficiency and accuracy. However, in KV-cache-intensive serving scenarios, MoEs often exhibit a tension between the GPU memory requirements of the model weights and the growing KV cache. We propose PagedWeight, a novel management method for MoE LLM serving that dynamically quantizes MoE model's weights at runtime and balances expert-weight precision with the KV cache sizes. PagedWeight exposes and effectively navigates the complex tradeoff between the model's task accuracy, memory consumption, and throughput/latency. Across several memory-sensitive MoE serving scenarios, PagedWeight improves the quality-memory tradeoff over several existing quantization baselines. PagedWeight achieves FP16-equivalent accuracy with up to 72.0% GPU memory savings and 1.94$\times$ throughput improvement, and improves quality over quantization methods by up to 39.3% at a similar memory budget with at most 4.1% throughput loss.

Rethinking Forgery Attacks on Semantic Watermarks in Black-Box Settings: A Geometric Distortion Perspective

Recent studies have shown that semantic watermarks, which embed information into the initial noise of latent diffusion models (LDMs), are vulnerable to black-box forgery attacks. However, existing methods primarily rely on empirical evidence and lack a rigorous theoretical understanding of the conditions under which such attacks succeed or fail. To bridge this gap, we rethink the nature of such attacks through the lens of rate-distortion in the latent space. Our analysis identifies an irreducible distortion floor due to structural mismatches between proxy and target models, which fundamentally limits the fidelity of forged watermarks. We further characterize this distortion as structured geometric deviations on the latent manifold, in the form of global drift and local deformation rather than stochastic noise. Leveraging these insights, we propose a scheme-agnostic detection method that distinguishes forged samples before watermark verification. Extensive experiments demonstrate the effectiveness of our method across diverse black-box scenarios, while preserving robustness to common distortions.

AOR-Bench: Do Large Audio Language Models Over-Refuse Pseudo-Harmful Queries?

Large Audio Language Models (LALMs) have demonstrated strong performance across a wide range of audio tasks. As they are increasingly deployed in real-world applications, ensuring their safety alignment has become more important. Although refusal mechanisms serve as a key safeguard by preventing LALMs from responding to harmful requests, they can also lead to {\em over-refusal}, where models incorrectly reject benign queries. This issue is especially challenging in the audio domain because speech that appears harmful in isolation may become benign when interpreted together with the surrounding acoustic context, such as background sounds. To study this problem, we introduce \textbf{AOR-Bench} (\textbf{A}udio \textbf{O}ver-\textbf{R}efusal \textbf{Bench}mark), the first benchmark for over-refusal specifically designed for LALMs. AOR-Bench contains 3,000 pseudo-harmful audio samples across six scenario categories. Evaluating 12 representative LALMs from six major model families, we find that over-refusal is widespread (Figure~\ref{fig:overall_performance}) and uncover several important patterns in their safety judgments. As a preliminary effort to mitigate this issue, we further explore two lightweight strategies (e.g., Chain-of-Thought and activation steering) to reduce over-refusal.

D^2SD: Accelerating Speculative Decoding with Dual Diffusion Draft Models

Speculative decoding accelerates autoregressive large language model inference by drafting multiple tokens and verifying them in a single target-model forward pass. Recent diffusion-based drafters generate an entire block of tokens in parallel but usually commit to a single draft sequence per verification: once the first mismatch occurs, all subsequent draft tokens are discarded, resulting in a limited acceptance rate. Naively batching more draft candidate sequences only introduces a marginal improvement, as redundant or poorly placed branches increase the cost of drafting and verification without proportionally increasing the number of accepted tokens. We propose D^2SD, a dual diffusion draft speculative decoding framework that organizes candidates into a confidence-guided prefix tree, where the first diffusion drafter generates a block along with per-position confidence scores that are used to identify the most likely rejection boundary and select the top-K prefix ranges for recovery; the second variable-prefix diffusion drafter re-anchors at each selected prefix and proposes alternative continuations in one batched pass; the resulting shared-prefix candidates are jointly verified via cascade attention. Empirically, D^2SD shows clear improvements over both the underlying diffusion approach and strong autoregressive speculative decoding baselines.