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arXiv

ML-Based Hierarchical Prediction for Practical Energy Scheduling in Dynamic NTN-WPT Systems

Zhanyu Ju, Wenchi Cheng

With advancements in long-distance wireless power transfer (WPT) and space-based energy technologies, integrating WPT into non-terrestrial networks (NTNs), referred to as NTN-WPT, is emerging as a promising approach for next-generation wireless networks. This paper proposes an energy-scheduling approach that jointly optimizes energy efficiency, task completion rate, and task waiting time for power transfer from low Earth orbit satellites to terrestrial mobile user devices (UDs). To address scheduling challenges caused by satellite and UD mobility and channel uncertainty from stochastic propagation effects, we decompose the problem into three subproblems within a three-layer predictive framework: 1) a state prediction layer forecasts UD and satellite states; 2) an interaction mapping layer uses a graph neural network (GNN) to model energy transfer efficiency; and 3) a decision-making layer determines the energy allocation plan. Distinct machine learning (ML) methods are tailored to each layer. To balance the competing objectives, we adopt a multi-objective reinforcement learning (MORL) technique that scalarizes them into a weighted-sum reward, transforming the multi-objective problem into a tractable single-objective problem. We further introduce a multi-agent deep learning model integrating self-attention with multi-agent proximal policy optimization (MAPPO) to improve objective balancing. Simulation results show that the proposed approach achieves a better overall trade-off than baseline methods, maintaining competitive task completion rates and energy efficiency while reducing task waiting times, and remains robust under highly variable conditions.

arXiv

End-to-End Neural Decomposition with Koopman Operators for Time-Series Forecasting

De-Yan Lu, Xugang Lu, Yu Tsao, Jian-Jiun Ding

Koopman theory offers a linear-operator view of nonlinear sequence dynamics by lifting observations into a space where evolution is governed by a linear time-invariant Koopman operator. While the Koopman operator provides a linear representation of nonlinear dynamics, it is generally infinite dimensional and defined under time-invariant assumptions. To model non-stationary signals with frequency-dependent behavior, a frequency-varying extension is required. In recent years, deep learning has been increasingly employed to exploit its powerful function-approximation ability for learning the Koopman operator. In this study, we propose a novel approach called neural decomposition Koopman (NDKoop), an end-to-end architecture that integrates a learnable signal decomposition module with both frequency-independent and frequency-dependent Koopman based networks for sequence forecasting. To the best of our knowledge, this is the first work to jointly realize end-to end Koopman modeling and signal decomposition within a unified neural framework. We demonstrate that decomposing a signal into a frequency-independent trend component and a frequency-dependent periodic component, each governed by a corresponding Koopman operator, improves prediction accuracy when perfect linearization is unattainable. Numerical experiments across several forecasting benchmarks indicate that the proposed NDKoop provides strong performance.

arXiv

Quantum-Classical Physics-Informed Kolmogorov-Arnold Networks for Solving Fuzzy Differential Equations

Xiang Rao, Yuxuan Shen

In this study, we propose a quantum-classical physics-informed Kolmogorov-Arnold network (QCPIKAN) dedicated to the solution of fuzzy differential equations. The network takes the spatiotemporal coordinates and membership level as joint inputs and employs ChebyKAN modules and a parameterized quantum circuit to construct a hybrid function approximator. It simultaneously approximates the lower and upper endpoint functions associated with the α-cuts and incorporates the governing equations, initial-boundary conditions, and fuzzy-structural constraints into the training objective. Theoretically, a unified error-analysis framework is established for QCPIKAN and PIKAN, in which the endpoint-solution error is decomposed into approximation, sampling, optimization, and fuzzy-structure constraint errors. Under the assumptions of well-posedness and residual stability, it is proved that QCPIKAN has a smaller a priori error bound when the representational gain introduced by quantum entanglement features exceeds the additional computational error. Numerical experiments are conducted for elliptic, parabolic, and hyperbolic equations in an ideal quantum-simulation environment. The results show that QCPIKAN captures the overall contraction of the solution interval as increases. At most tested membership levels, the mean relative L2 error of PIKAN is approximately 1.1-2.7 times that of QCPIKAN. In the fuzzy convection example, the mean wavefront-position error of PIKAN is approximately 1.77 times that of QCPIKAN. Nevertheless, both models still exhibit local fuzzy-structure violations near boundaries, in high-gradient regions, and around the wavefront. These results indicate that QCPIKAN provides a quantum-classical hybrid physics-informed computational framework with comparatively high predictive accuracy for solving fuzzy partial differential equations represented by α-cuts.

arXiv

A Mean-Field Framework for Inference-Time Distributional Control of Diffusion Models

Samuel Howard, Nikolas Nüsken

Diffusion models are increasingly used as controllable samplers, whose generations can be steered at inference time according to a chosen reward function. While such rewards are typically defined on individual samples, for many applications it is desirable to steer according to distribution-level rewards, for example to calibrate with population-level information or to encourage diversity. In both cases, simply incorporating the reward gradient into the dynamics, while often effective, comes with few theoretical guarantees on the sampled distribution. For pointwise rewards, recent work has therefore sought to develop a principled framework for targeting a prescribed tilted distribution using particle reweighting. However, an analogous theoretically-grounded approach for distributional rewards is currently lacking. In this work, we formulate inference-time distributional control as targeting a tilted measure under a mean-field framework, and derive a weighted interacting particle scheme to target it in a principled manner. Our framework recovers pointwise-reward steering as a special case, while providing a theoretical foundation for existing batch-level steering methods. Empirically, we verify that the procedure correctly targets the prescribed distribution in tractable low-dimensional settings, and investigate its behaviour in higher-dimensional protein conformation tasks.

arXiv

Scaling Audio Models Efficiently: A Joint Study of Compute Constraints and Optimization Behavior

Vyom Agarwal, Mokshda Gangrade, Siddharth Pal, Jerry Wu

In this paper, we investigate the tradeoffs between compute allocation and model performance for two speech processing tasks: Automatic Speech Recognition (ASR) and Speech Emotion Recognition (SER). We propose a unified framework that analyzes three fundamental compute dimensions: model size ($x_N$), input length ($x_T$), and representation resolution ($x_V$). Motivated by recent advances in compute optimal scaling for multimodal models, we systematically vary these dimensions to examine their influence on task performance under fixed computational budgets. Our study provides insights into how compute resources can be optimally distributed across model capacity, temporal context, and representational granularity, offering practical guidelines for the design of efficient speech models. Through experiments on LibriSpeech and CREMA-D datasets, we demonstrate non-linear scaling behavior and identify optimal operating points. Our results show that (1) increasing model size yields diminishing returns: scaling Tiny (39M) to Small (244M) reduces WER by 8.22%, whereas Small to Medium (769M) reduces WER by only 2.35%; (2) an optimal audio duration of approximately 4 seconds exists for SER; and (3) reducing encoder token resolution provides an effective mechanism for lowering inference cost, Large-v3 (1540M) with 750 frames requires 2572 GFLOPS whereas with 1500 frames requires 5228 GFLOPS, with less than 3% relative increase in WER. Additionally, LoRA-based adaptation enables efficient finetuning with minimal performance degradation.

arXiv

Learning from Consensus and Disagreement: Unsupervised On-Policy Self-Distillation with Minority-Trajectory Contrast

Jiaxin Guo, Yanwei Yue, Xuanbo Fan, Chunyu Yang, Yan Zhang

On-policy self-distillation improves language-model reasoning by querying a teacher on states actually visited by the student. Recent methods create a powerful information asymmetry by exposing the teacher to privileged context, yet they fundamentally rely on external supervision---such as gold solutions or verifiers---to construct this advantage. We introduce CoDA (Consensus and Disagreement Alignment), a fully unsupervised framework that creates reliable privileged information entirely from the latent uncertainty structure of a model's own unlabeled rollouts. CoDA extracts two complementary signals. In the positive branch, answer-level consensus identifies a stable reasoning mode, which conditions a frozen self-teacher to provide dense distributional guidance on fresh student trajectories. However, because agreement does not guarantee correctness, positive-only distillation risks amplifying correlated errors into a false consensus. To break this harmful feedback loop, CoDA incorporates a negative branch that exploits disagreement: minority trajectories are treated as unstable alternatives and gently penalized via a reference-anchored, KTO-style calibration objective. This unpaired binary feedback provides robust regularization without requiring the strong assumption that the consensus is the absolute ground truth. Empirical evaluations on competition-level mathematical benchmarks demonstrate that CoDA significantly improves reasoning, outperforming self-generated baselines and effectively stabilizing training against erroneous consensus.

arXiv

A Distribution Mapping Approach to Counterfactually Fair Reinforcement Learning

Jianhan Zhang, Jitao Wang, John D. Piette, Donglin Zeng, Chengchun Shi, Zhenke Wu

Reinforcement learning (RL) seeks to optimize sequential decisions to maximize population-level benefits over time. However, when deployed in high-stakes settings such as healthcare, RL decisions might systematically restrict some subpopulation's access to valuable services in a manner contrary to the values and goals of stakeholders. Counterfactual fairness (CF) offers a promising framework to address this problem based on causal reasoning. This paper develops a data preprocessing algorithm that, when used in tandem with policy learning, enables CF in RL. Our algorithm relies on a novel quantile distribution mapping method for sequentially estimating the counterfactual states and rewards in the data preprocessing step, subsuming common additivity assumptions used for counterfactual prediction as a special case. We theoretically prove that the per-step level of counterfactual unfairness and infinite-horizon suboptimality gap can be bounded under mild regularity conditions. We also empirically test our algorithm in numerical experiments as well as in application to a real-world interventional digital health dataset.

arXiv

Memory-Efficient Activation Checkpointing with Sliding Window and Hirschberg's Algorithm for 0/1 Knapsack Solving in PyTorch

Jędrzej Maczan

Activation checkpointing minimizes the runtime of neural networks under a given memory budget, by selecting which intermediate tensors to store and which to recompute. PyTorch solves this as a 0/1 knapsack problem, where operations from a joint forward-backward computation graph are items with a memory cost (weight) and a runtime saving (value). The default solver, dp_knapsack, allocates a full dynamic programming (DP) table of shape $(n+1) \times (W+1)$, where $n$ is the number of operations and $W$ is the quantized memory budget. This method is resource-hungry and crashes at $n = 100$ items on a machine with 64 GB RAM. In this paper, we introduce dp_knapsack_sliding_hirschberg, which combines the sliding window trick and Hirschberg's algorithm to reduce peak memory from $O(nW)$ to $O(W)$ while preserving the exact optimal solution. Our experiments show successful knapsack execution at $n = 2000$, where dp_knapsack fails at $n = 100$, a 20$\times$ increase in computable problem size. In addition, our benchmarks show a consistent 25-28\% runtime speedup over dp_knapsack. The implementation is merged into PyTorch and released in version 2.10.

arXiv

PAST: Privileged Adaptation from Complete Student Trajectories for On-Policy Self-Distillation

Yangyang Feng, Zhuoyan Feng, Junlan Chen

On-policy self-distillation (OPSD) uses a privileged teacher to supervise a reasoning model on prefixes sampled from its own rollouts. Yet each rollout also reveals how the student's response unfolds and whether it succeeds, student-specific hindsight that standard OPSD does not use to form the teacher. We introduce Privileged Adaptation from Student Trajectories (PAST), which treats each completed student trajectory as additional privileged information for the OPSD teacher while leaving the student's distillation prefixes unchanged. PAST preserves the student's next-token distribution on correct trajectories and uses failed trajectories to adapt the teacher toward verified success under student-proximity regularization. We characterize what such a trajectory-conditioned teacher can transfer to a prefix-only student. Forward-KL distillation projects the teacher distributions to their conditional arithmetic mean given the prefix. This projection separates trajectory-specific variation that remains privileged from the mean policy shift available to the student. For correct trajectories, the unclipped population objective also has the frozen student as an ideal distributional fixed point. Across three mathematical reasoning benchmarks, PAST improves the Avg@12 macro average over Vanilla OPSD by 5.6 percentage points. A $2\times2$ factorial study shows gains from both complete-trajectory access and teacher adaptation, while trajectory removal and shuffling confirm that the adapted teacher uses the matching hindsight context.

arXiv

Towards a Bridge Layer Between Bibliographic and Formalized Mathematical Knowledge

A. Mayeux

Mathematical knowledge is split between bibliographic databases (e.g., MathSciNet, zbMATH Open) and formal proof libraries (e.g., Lean's mathlib), preventing unified access to published results and their formalizations. We propose a relational bridge-database that aligns publication metadata with formal artifacts, providing an interoperability layer between mathematical literature and machine-verifiable proofs. We introduce a paper-level formalization score that measures how much of a publication is covered in formal systems, together with a correctness profile recording what machine verification has established about each printed statement: certified, corrected, uncorrected, open, or untested. As a feasibility study, we show how such scores can be estimated via cross-document alignment between informal texts and Lean formalizations, enabling large-scale analysis of formalization coverage. We further outline a concrete construction pathway: multi-source scoring over heterogeneous formalization artifacts, an agentic collection workflow with direct author submission, a dual validation policy, algorithmic then human, and a global formalization score of indexed mathematics. This framework is a step toward integrating bibliographic and formal mathematical ecosystems.

arXiv

Gaming Without an Attacker: Benchmark Fingerprinting in LLM-Driven Search Under Selection Pressure

Víctor Gallego

Benchmarks for systems that are optimized against the evaluation signal measure something different from what they claim. We document this concretely in two GPU-kernel-optimization suites with held-out generalization gates: Metal-Sci (10 scientific-compute tasks) and Metal-ZK (12 zero-knowledge/cryptographic tasks), in which three frontier LLMs (Opus 4.7, Gemini 3.1 Pro, GPT-5.5) propose Metal kernels inside a $(1{+}1)$ evolutionary loop with rich feedback. Although no model is prompted to act adversarially, the promoted winners repeatedly fingerprint the evaluation configuration: they branch on the identity of runtime parameters, tune the measured branch maximally, and leave the unmeasured branch slow or silently wrong. Across the pooled suites, $16/53$ ($30\%$) of in-distribution wins fail to transfer to held-out configurations. We give a four-mode taxonomy of these failures, from configuration fingerprints to gate leakage. We distill design guidance for measurement under strategic optimization: held-out probes retain validity only on non-enumerable axes; gates must measure held-out performance, not just correctness; and a transfer rate is interpretable only with per-failure mechanism grades: ours decomposes into gamed, overfit, and benign. Code and research artifacts: https://github.com/vicgalle/kernel-fingerprinting

arXiv

Multi-kernel spectral clustering: Entrywise eigenvector perturbation bounds and exact recovery

Zeqin Lin, Guangming Pan, Zhixiang Zhang, Yinbing Zhou

Kernel spectral clustering with a single bandwidth can be inadequate for data exhibiting multiple characteristic pairwise-distance scales, a problem particularly prevalent in the high-dimensional regime. We address this issue through a multi-kernel formulation that aggregates kernels with different bandwidths. The bandwidths are selected as prescribed empirical quantiles of the pairwise squared distances, thereby capturing the relevant distance scales without requiring prior population-scale information. We develop a rigorous theoretical analysis of the resulting method under a general high-dimensional, multi-scale mixture model with heterogeneous cluster centers and covariance geometries. We construct a blockwise constant, low-rank informative approximation to the empirical multi-kernel matrix and establish row-wise $\ell_{2,\infty}$ perturbation bounds for its leading spectral components, as well as for the associated normalized Laplacian matrix. These bounds yield observation-level control of the spectral embedding, which is more informative than conventional global eigenspace perturbation estimates. Under suitable eigen-gap and cluster-separation conditions, we show that approximate $K$-means applied to the multi-kernel spectral embedding achieves exact recovery with high probability.

arXiv

Loss-Resilient Wireless Video Token Communication over Block Fading Channels

Bingyan Xie, Yongjeong Oh, Zihan Chen, Jihong Park, Yongpeng Wu, Wenjun Zhang

Video token communication represents video content as discrete tokens that differ in their importance to reconstruction and exhibit temporal dependencies. When these tokens are packetized for wireless transmission, block fading can cause multiple important or correlated tokens to be lost together, severely degrading video reconstruction. To address this issue, we propose a loss-resilient wireless video token communication (WVTC) framework. WVTC evaluates token importance from the intrinsic predictive structure of video tokens, assigning high priority to structural I-tokens and measuring P-token importance by temporal neighborhood novelty. A shuffled mixed I/P-token packetization scheme disperses structural anchors and correlated temporal regions across packets. Using only current block channel state information, an online scheduler jointly considers packet importance density, MCS-dependent decoding reliability, block capacity, and importance concentration when allocating packets to fading blocks. At the receiver, a fine-tuned detokenizer reconstructs missing content from surviving tokens without retransmission. Numerical results demonstrate improved perceptual quality and more graceful degradation under increasing packet error rates.

arXiv

SearchSwarm: Towards Delegation Intelligence in Agentic LLMs for Long-Horizon Deep Research

Xiaochong Lan, Quan Chen, Kun Tao, Xinyu Tang, Tianshu Wang, Qianggang Cao, XinYu KONG, zujie wen, Zhiqiang Zhang, JUN ZHOU

Large language models are increasingly expected to handle complex, long-horizon real-world tasks whose context demands can grow without bound, yet model context windows remain inherently finite. Recent work explores a paradigm where a main agent decomposes tasks and dispatches subtasks to subagents, which execute and return only summarized results, conserving the main agent's context budget. However, performing this well requires delegation intelligence: the ability to decompose complex tasks, determine when and what to delegate, and integrate returned results into the ongoing workflow. Training data for this capability is scarce in naturally occurring text, and to our knowledge, how to synthesize such data and train models to acquire this capability remains largely unexplored in the open-source community. To bridge this gap, we present a preliminary exploration targeting deep research, a representative long-horizon agent task. Specifically, we design a harness that guides the model toward high-quality task decomposition and delegation, while constraining subagents to return results properly to support the main agent's workflow. The harness-guided trajectories naturally encode correct delegation decisions, which we use as supervised fine-tuning data to internalize delegation intelligence into model weights. Our resulting model, SearchSwarm-30B-A3B, achieves 68.1 on BrowseComp and 73.3 on BrowseComp-ZH, the best results among all models of comparable scale. We will release our harness, model weights, and training data to facilitate future research.

arXiv

RippleKV: Cross-Layer KV Cache Allocation via Perturbation Propagation

Dongjie Xu, Kai Qian, Julius, Weijie Shi, Yuxuan Sun, Minghua Tang, Fenglei Jin, Hanchi Dong, Jiajie Xu

Long-context LLM inference is bottlenecked by KV cache memory, yet distributing a limited cache budget across layers remains challenging. Existing methods rely on proxies such as layer depth, attention statistics, or representation change. These proxies do not measure how perturbations at each layer propagate to the output and may therefore cause sensitive layers to be underallocated while tolerant layers are overallocated. To address this issue, we propose RippleKV, which allocates cache across layers by estimating how perturbations to each layer's value cache affect the final predictive distribution. RippleKV independently injects norm-adaptive perturbations into each layer's value cache and measures the induced KL divergence at the model output over a small calibration set. Averaging these responses yields a sensitivity profile specific to the model that need not vary monotonically with depth. RippleKV then converts the sensitivity profile into layer budget multipliers by normalizing the sensitivity scores and applying an exponential mapping. A ratio parameter controls the allocation disparity between sensitive and tolerant layers, while a final normalization preserves the KV cache budget. Experiments on LongBench demonstrate that RippleKV achieves the highest average performance among the evaluated KV cache compression methods under matched cache budgets.

arXiv

Efficient Test-Time Scaling for LLM-based Time Series Forecasting

Xuan-May Le, Minh-Tuan Tran, Ling Luo, Uwe Aickelin, Dinh Phung, Trung Le

Long-term time series forecasting benefits from preserving global structure such as trends and seasonality. Recent LLM-based forecasters often improve accuracy through test-time scaling (e.g., iterative refinement), but these methods are computationally expensive and increasingly prone to global-shape mismatch as the prediction horizon extends. We propose SCALER, a coarse-to-fine forecasting framework that first employs a lightweight Transformer tailored to long-term shape modeling to predict a coarse representation of future dynamics. This predicted shape then serves as a compact guide for an LLM to perform test-time scaling via iterative coarse-to-fine residual token refinement, while processing substantially fewer tokens at each step. By guiding refinement with an explicit future-shape prediction, SCALER reduces reliance on long description prompts, and its fixed-step refinement avoids costly reward-model-based selection, further lowering computational overhead. Experimental results demonstrate that SCALER outperforms strong forecasting baselines in long-term, short-term and zero-shot forecasting while significantly reducing the inference cost associated with scaled LLM for time series forecasting. Code: https://github.com/xuanmay2701/SCALER.

arXiv

Catastrophic Forgetting in Continual Reinforcement Learning

Emma Graham

This work explores the relationship between task similarity and catastrophic forgetting in reinforcement learning. Catastrophic forgetting, the phenomenon in machine learning of losing the ability to effectively perform on previous tasks, is a significant impediment to continual learning. This study aims to understand the extent to which the similarity of a new task influences the performance on the previous task. Interpretable reinforcement learning, specifically Q-learning, is employed on graph-based tasks with the objective of minimising the number of steps to reach a goal. The study investigates the performance on a previously learned task after training on a new task, for tasks of varying relative levels of complexity. The experimental results reveal a complex dynamic between task similarity and forgetting, with significant fluctuations in forgetting severity observed across degrees of task similarities and task complexities, and are suggestive of an interdependence of forgetting on the similarity and complexity of tasks. The observations were accompanied by observations of high degrees of variability in forgetting and an uneven distribution of task similarity measures. The relationship between these variables remains unclear and no evidence of statistical significance that task similarity has an effect, independently, on forgetting is found in continual reinforcement learning. Further research is warranted to gain a comprehensive understanding of the potential interplay between task similarity and catastrophic forgetting.

arXiv

Kernel Methods for Refined Prophet Inequalities

Patrick Loiseau, Mathieu Molina, Vianney Perchet, Sebastian Perez-Salazar, Victor Verdugo

The single-selection prophet inequality is a canonical Bayesian online selection problem in which independent nonnegative values arrive sequentially and the decision-maker must irrevocably select at most one. Classical single-threshold guarantees are tight in the worst case, but the hard instances that prove tightness are highly irregular: the prophet's advantage is driven by rare, very large realizations of the maximum. We refine this worst-case picture by imposing a bound on the relative variance of the prophet's value, $\mathrm{Var}(\max_{i\in[n]}X_i)/\mathbb E[\max_{i\in[n]}X_i]^2$. This yields a nonparametric complexity measure that interpolates between deterministic instances, where the full prophet value can be recovered, and the unrestricted worst-case regime. Our main technical contribution is a general kernel method for single-threshold prophet inequalities. The method represents an instance by the quantile function of the maximum and rewrites the payoff of a threshold as a linear kernel functional of this quantile. This turns the worst-case analysis into an infinite-dimensional convex program, restores strong minimax duality in quantile space, and reduces the bounded-variance adversary's problem to a one-parameter variational family. Applying this framework, we obtain an exact characterization of the IID bounded-variance curve and asymptotically optimal finite-horizon thresholds, a closed-form expression for the fixed-order non-identical model, and a prophet-secretary lower-bound program together with a strict separation from the IID benchmark at every positive finite variance constraint. As a further application of the same kernel viewpoint, we derive an exact formula for IID random horizons under a convexity condition on the horizon pgf, which includes monotone-hazard-rate horizons, highlighting the broad applicability of this new technique for single threshold settings.

arXiv

LegoLM: Structured Weight Sharing for Large Language Models

Joseph Bingham

We present \LegoLM{}, a structured weight-sharing compression framework for large language models grounded in a systematic study of why global weight sharing fails and how to fix it. We identify two distinct failure modes. Distributional mismatch: for vector blocks of dimension d <= 2, transformer layers with heterogeneous weight scales impose a scale-mismatch penalty that grows linearly with d and cannot be resolved by increasing K, producing perplexity in the millions.Outlier dominance: for scalar blocks, a fraction ~1/K of weights lies beyond the outermost Lloyd-Max decision threshold and cannot be represented by any centroid; their misrepresentation accumulates across layers, causing catastrophic quality loss. \LegoLM{} resolves both failure modes via three data-free adaptations: 1 scalar-block encoding to eliminate the $d$-linear mismatch component, 2 percentile-selective replacement that identifies and preserves outlier weights verbatim, and 3 boundary-layer protection for the first and last transformer blocks. Across GPT-2 small (124M) and Mistral-7B, \LegoLM{} achieves +0.03% PPL degradation at 4.41X compression on Mistral-7B - outperforming PTQ-8bit in both quality and compression ratio - and -0.02% at 2.67X. Downstream evaluation on LAMBADA and HellaSwag confirms that \LegoLM{} at K=64, p=99% preserves accuracy within noise at 5.12 X compression, exceeding PTQ-8bit's compression ratio while matching its accuracy. We further discover that outlier dominance grows with model scale: full replacement at K=128 degrades GPT-2 small by only +23% but catastrophically degrades Mistral-7B by +1,134,279%, while selective replacement at p=99% rescues both models to under +15%. A controlled ablation confirms that selective replacement is the dominant mechanism: adding it to per-layer K-means also yields near-lossless quality, matching \LegoLM{} within 0.02%.

arXiv

Exact Rank-Space KL Projection for Shared-Marginal Low-Rank Factors: Application to Doubly Stochastic Clustering

Enliang Hu

We study exact Kullback--Leibler (KL) projection for low-rank factorizations whose two nonnegative factors have prescribed row marginals and a shared, learned column marginal. For arbitrary positive row marginals of equal total mass, the joint KL projection reduces exactly to a strictly convex gauge-fixed dual with only $r-1$ effective variables; its Hessian is a sum of categorical covariance terms and admits $O((n+m)r)$ matrix-free Hessian--vector products. The projection theorem is objective-independent. We then specialize this geometry to doubly stochastic (DS) graph learning through $W=U\operatorname{Diag}(g)^{-1}V^\top$, where row-simplex factors with a common column mass induce an exactly DS graph without materializing an $n\times n$ optimization variable. Combined with observed-edge sparse fitting, a stochastic anchor-reduced manifold regularizer, and Bregman backtracking, the resulting mirror-descent method preserves exact feasibility at every accepted step. Under a nonvanishing latent-mass condition, it satisfies sufficient decrease and an $O(1/N)$ mirror-stationarity bound, while strictly positive accumulation points are KKT stationary. Matched clustering experiments show competitive accuracy, feasibility residuals near numerical precision, and favorable anytime behavior without a dense learned graph.

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