2026-10-23

On-policy self-distillation (OPSD) improves reasoning by training a model on its own trajectories with dense token-level supervision from a privileged copy conditioned on a reference solution. Existing methods typically use a single teacher distribution conditioned on the complete reference. We identify a limitation of this formulation: a reference is only one realization of the reasoning process. Although it provides evidence about the answer, it also encodes an ordering, phrasing, and solution path. Full-reference conditioning can therefore produce correct targets that depend excessively on information unavailable to the student at inference. We show that replacing one valid reference with another, while holding the problem and student state fixed, can substantially alter the teacher distribution, a phenomenon we call reference-induced target instability. To address this instability, we introduce Monte Carlo Privileged Distillation (MCPD), which models privileged context as a distribution over partial reference views and distills the marginal teacher distribution. MCPD evaluates the teacher under multiple views and averages the resulting next-token distributions. We show that this probability-space average is the exact target induced by minimizing the expected teacher-to-student KL divergence over privileged views. Across mathematical and scientific reasoning benchmarks, we show that MCPD produces more reference-consistent supervision and consistently improves over full-reference OPSD.

Space data centers (SpaceDCs) are emerging as platforms for large language models (LLMs), supported by continuous solar-energy harvesting and high-speed interconnections. The mixture-of-experts (MoE) architecture supports distributed LLM inference by deploying experts across satellites. However, skewed expert activation creates uneven computation power demands despite uniform solar-power supply at the dawn-dusk sun-synchronous orbit (SSO). Consequently, active experts remain power-constrained while harvested power at idle experts is underused. These reduce inference efficiency and increase latency. To address this supply-demand mismatch, we propose the SpaceWPT framework, which uses inter-satellite laser-based wireless power transfer (WPT) to redistribute harvested power. The key design challenge is to balance the computation demands of power-donating and power-receiving satellites under WPT losses: transferring more power accelerates computation at the receiver but leaves less power for the donor. After deriving design principles that simplify WPT control, we characterize the resulting latency tradeoff through a tractable surrogate of average inference latency. Minimizing the surrogate yields a novel two-sided water-filling strategy that determines whether each active expert donates, retains, or receives power according to the water level and its WPT link efficiency. Simulations with Mixtral-8x7B and Phi-3.5-MoE show up to 29.25% lower inference latency than without WPT, with larger gains under more compact formations and higher transfer efficiencies.

Online Policy Distillation (OPD) often outperforms offline methods such as Supervised Fine-Tuning (SFT) by training on trajectories sampled directly from the student. However, standard OPD trains the student to follow the teacher at every state of the trajectory, assuming that teacher guidance is always beneficial. We instead distinguish between what the teacher prefers and what actually helps the current student succeed. We introduce Advantage-Based On-Policy Distillation (AOPD), which weights teacher actions by their counterfactual advantage under the student. Teacher actions that improve the student's expected outcome are reinforced, while those that do not are downweighted. Directly computing these advantages requires trying alternative teacher actions at each step and running new rollouts from each. Instead, we show that the AOPD objective can be estimated using only standard student rollouts and their terminal rewards. Our estimator uses teacher importance weights on the student-sampled actions to provide unbiased advantage-weighted supervision, without any additional rollouts or reward evaluations. This allows AOPD to focus teacher supervision on actions that help the current student while preserving the rollout efficiency of standard OPD. Experiments on math, coding, and Medqa show gains over distillation and RL baselines in both external-teacher and self-distillation settings.

Visual mathematical reasoning can fail before reasoning begins: when a vision-language model (VLM) misreads a diagram, subsequent reasoning proceeds from false premises. This perceptual bottleneck is especially pronounced in smaller models, while accurate textual descriptions can substantially narrow the gap to larger models. Because obtaining such descriptions at inference requires additional annotation or model calls, we propose minimal-edit corrective on-policy distillation. Using reference figure descriptions and verified reference solutions as training-only information, a teacher scores incorrect student rollouts under a minimal-edit objective, and only teacher-disfavored tokens contribute to the corrective loss. Correct rollouts receive task-reward reinforcement learning. This preserves on-policy supervision while avoiding full-response imitation. Across model scales, the method requires no descriptions at test time and meets or exceeds the corresponding base model supplied with a reference figure description at inference. It also improves perception-oriented performance, particularly low-level geometric perception, and transfers to external mathematics and perception benchmarks. Because the minimal-edit teacher evaluates corrections rather than generating its own solution, the method remains effective with a frozen same-size teacher, although its gains are smaller than with a larger teacher on most metrics.

Weight-only quantization keeps LLM activations in floating point and stores weights as low-bit integers, turning the dominant workload into floating-point-integer (FP-INT) general matrix multiplication. Recent quantizers reach a 2-3-bit average with mixed precision, but hardware has not kept pace: GPUs dequantize weights to FP16 before the tensor-core multiply-accumulate, and bit-parallel FP-INT accelerators run at a single weight precision, so fewer bits save memory but not computation. In this paper, we present FIGFLEX, an algorithm-hardware co-designed mixed-precision accelerator whose bit-parallel datapath scales throughput as precision falls. FIGFLEX contributes (1) a shift-add, radix-4 reformulation of FP-INT multiplication that fuses the multiply-accumulate into a unified, precision-flexible partial-product reduction and roughly halves the partial products, together with a novel INT3 optimization that reclaims the idle datapath radix-4 leaves at that precision; and (2) a mixed-precision quantizer that assigns each channel group its bit-width according to the error GPTQ cannot compensate, with a per-input-channel column scaling whose power-of-two normalization keeps the scaled activations out of the FP16 subnormal range, so that the quantized model maps directly onto FIGFLEX's datapath with the same accuracy as on a GPU. On LLaMA-2-7B, FIGFLEX attains 5.85 and 8.77 WikiText-2 perplexity at 3- and 2-bit average precision, lower than GPTQ, AWQ, SliM-LLM, AMQ, and QuIP# (without fine-tuning), while delivering 1.56x and 1.42x higher whole-chip throughput per area on the linear GEMMs of a 3-bit mixed-precision model than AxCore and FIGLUT, respectively.

Vector quantization (VQ), in particular lattice-based methods, offer strong rate-distortion trade-offs for low-bit large language models (LLMs), yet their behavior under quantization-aware training (VQ-QAT) remains poorly understood. We scale lattice VQ-QAT to billion-parameter LLMs and multi-billion-token training regimes, and introduce SQuAT, a shape-gain VQ-QAT approach trained with a separate straight-through estimator (STE) for the shape and gain. SQuAT decomposes weights into direction and magnitude: normalized directions are quantized using an $E_8$-derived spherical codebook, while gains are quantized independently with low-bit scalar quantizers. We show that, unlike a standard STE applied to the full quantizer, which ignores the shape-gain structure, these separate STEs induce tangent-space updates for directions, yielding an implicit form of spherical (Riemannian) optimization. To enable scalability, we develop a distributed exact nearest-neighbor assignment scheme, in which workers quantize disjoint weight blocks and communicate only discrete indices, reducing VQ-QAT training time by 12.8$\times$ and allowing us to scale it to 10B tokens. Across instruction-tuned LLaMA-3.2-1B/3B, Qwen3-4B, and base Qwen3-1.7B, SQuAT consistently outperforms standard VQ-QAT STE under identical quantizers and initialization, and achieves SOTA VQ-QAT accuracy.

Depth pruning removes entire transformer layers to make large language models faster, and recent methods recover quality by replacing the removed layers with a training-free linear map. Which layers to remove, however, is chosen with heuristic scores whose distance from the best choice is unknown. We evaluate every subset of layer groups exactly (about 53,000 pruned models across four families, with and without repair) and find that the best layers to remove depend on the repair: linear repair absorbs the interaction among nearby layers and turns the optimum from a split layout into a contiguous block, so methods that choose layers without the repair miss the repaired optimum by up to 189%. We therefore select layers under the repair that will be applied. A greedy search at the cost of SLEB lowers perplexity by 20% to 66% relative to ReplaceMe on five models up to 27B parameters, and with a task objective it is up to 25 points more accurate given the same data. A second-order expansion of the loss yields a score that selects the repaired block from one forward and one backward pass of the intact model.

Sparse attention reads only a small subset of the key-value cache, and how to treat the unread tail remains a key challenge. Discarding the tail biases the output, and sampling it as previous approaches do fails at reads of 5% and below, where the tail likely holds heavy hitters the selector missed. Our key observation is that the simplest possible proxy, one token that folds the entire tail into its count-aware mean, already yields lower output error than a sample at every read behind a practical selector. We further show in closed form that at low reads sampling nearly doubles the weight error of discarding while a single proxy stays below it. Building on these findings, we explore approximating the dense attention distribution with a few proxies that target the tail. We propose OpenAttention, a pipeline of clustering, ErrorGate and top-k selection followed by a count-aware mean proxy. To implement clustering and selection both efficiently and effectively, we design training-free Query-Geometry Clustering (QGC) and a Query-Geometry Selector (QGS), which compress the keys while respecting the query directions. Additionally, unlike prior methods that rank clusters by centroid alone, ErrorGate allocates the exact read by the estimated weight error of each cluster. On RULER-32K HARD with Llama-3.1-8B, OpenAttention retains 99% of dense accuracy at a 1% read. It also achieves state-of-the-art accuracy across models, context lengths and datasets. Our customized attention kernel, OpenAttention.flash, runs the decode attention stage 10$\times$ faster than dense attention at a 1% read.

Looped architectures scale quality while keeping parameter count fixed by repeatedly passing activations through the same block of layers. During inference, each recurrence generates independent KV-caches, causing memory to grow linearly. To address this challenge, prior work has proposed KV-sharing (i.e., sharing KV-caches across depth), finding that, in some cases, the KV-cache of the final recurrence can be shared with the earlier recurrences without quality loss, a property we denote as KV-shareability. However, the mechanisms underlying KV-shareability remain poorly understood, with even identically trained looped architectures not consistently exhibiting it. In this paper, we study how KV-shareability can be enabled in looped models. We propose a two-stage method: in the first stage, we use stochastic depth during pretraining, which induces contractive residual dynamics that drive representations toward a common limit across recurrences. In the second stage, we propose BeNice!, a post-training method that broadcasts the final recurrence's KV-cache into the first recurrence, training it to produce compatible residuals while preserving the original model's quality. As a result, BeNice! enables KV-shareability while matching standard finetuning's unshared validation perplexity. Using BeNice!, we show that KV-sharing is complementary to alternative KV-compression methods, composing with memory-efficient sequence mixers (e.g., multi-latent attention, Kimi delta attention) and low-precision KV-cache quantization (e.g., fp8, mxfp8, nvfp4). Finally, in simulated low-memory, long-context inference, KV-sharing improves cache hit rates by up to 31.4%, increases throughput by up to 23.6%, and reduces p90 time-to-first-token by up to 83.6%.