arXiv subjects

Muhammad Umer

Publications and source records attributed to Muhammad Umer.

At least 19 recordsLinked to original sources

arXiv2026

Small Models Scout Bottleneck Order for Large-Model Data Control

Small proxy models are commonly used to identify data mixtures for larger-scale training. We ask whether their training trajectories reveal another transferable structure: the order in which larger models should resolve skill bottlenecks. We formulate first-passage skill training, where each monitored skill has a target floor and the objective is to minimize the tokens required to reach all floors. We introduce LogFloor, a closed-loop controller that directs each round toward current bottlenecks, producing phase-ordered resolution trajectories. Across five bAbI skill slices on Qwen2.5-1.5B, LogFloor reduces token cost by 56.2% on average. In 70M-to-12B transfer, three-round replay of a 70M scout path reaches every floor in all eight target runs, saving 30.9% by pair mean, 39.4% in pooled training tokens, and 37.6% under source-cost accounting. On MMLU-control, a frozen scout path succeeds across all eight 12B runs. Collapsing a path to its static marginal mixture or reversing its phase order removes most benefits, while bottleneck labels alone remain partially useful. These results identify phase-ordered bottleneck resolution as a transferable curriculum structure for monitored skill-targeted training.

cs.AI↗

arXiv2026

Refining Over Resampling: Test-Time Self-Correction for LLM Reasoning

Test-time scaling improves LLM reasoning by using additional inference compute, but wider sampling alone can suffer from diminishing returns: new rollouts often repeat existing answer patterns instead of adding useful reasoning diversity. Verifier-based selection offers an alternative, but its performance depends on the calibration of an external reward model. We propose a verifier-free breadth--depth refinement framework that uses test-time compute to both explore and improve candidate solutions. The method samples multiple independent reasoning rollouts, refines each rollout through iterative self-critique and self-correction, and aggregates the refined answers by majority voting. Breadth preserves diverse initial attempts, while depth repairs local reasoning errors before aggregation. Across AIME24, AIME25, AMC, OlympiadBench, and MATH500, our method consistently improves over greedy decoding, majority voting, verifier-based best-of-$N$, beam search, and lookahead decoding across multiple open-weight models. For instance, with Qwen2.5-1.5B, accuracy increases from the strongest verifier-based baseline to $58.0\%$ on MATH500, and from $25.0\%$ to $32.5\%$ on AMC. These results show that test-time compute can be more effective when used to refine sampled trajectories rather than only to sample more candidates or rely on verifier-guided selection.

cs.AI↗

arXiv2026

Circuit Design Informed Adaptive Variational Quantum Algorithms

Resource-efficient computation is of central importance in the noisy intermediate-scale quantum (NISQ) era, where decoherence, gate errors, and restricted qubit connectivity severely limit the reliable execution of quantum algorithms. In this work, we demonstrate that incorporating circuit design considerations is crucial for developing resource-efficient variational quantum algorithms. By focusing on the Hadamard test circuit architecture, hardware-aware qubit connectivity, and problem-specific adaptive framework, we analyze how circuit design constraints can systematically reduce the measurement overhead associated with repeated evaluations of the candidate gate pool in adaptive algorithms. Specifically, we demonstrate reductions in the required measurement resources ranging from at least 25% to as high as 50% - 55%. To assess the effectiveness of our approach, we investigate the ground state problem of the nonlinear Schr\"{o}dinger equation. Overall, our work contributes to resource-friendly strategies for quantum computation and underscores that algorithmic frameworks should systematically integrate circuit design constraints with hardware-aware and problem-specific structures to enhance the practical feasibility of quantum devices in the NISQ era.

quant-ph↗

arXiv2026

General Preference Reinforcement Learning

Post-training has split large language model (LLM) alignment into two largely disconnected tracks. Online reinforcement learning (RL) with verifiable rewards drives emergent reasoning on math and code but depends on a programmatic verifier that cannot reach open-ended tasks, while preference optimization handles open-ended generation yet forgoes the continuous exploration that powers online RL. Closing this gap requires a verifier for open-ended quality, but a scalar reward model is the wrong shape for the job. Quality is multi-dimensional, and any scalar score is an incomplete proxy that lets online RL collapse onto whichever axis the score is most sensitive to. We turn instead to the General Preference Model (GPM), which embeds responses into $k$ skew-symmetric subspaces and represents preference as a structured, intransitivity-aware comparison. Building on this, we propose General Preference Reinforcement Learning (GPRL), which carries the $k$-way structure through to the policy update. GPRL computes per-dimension group-relative advantages, normalizes each on its own scale so no axis can dominate, and aggregates them with context-dependent eigenvalues. The same structure powers a closed-loop drift monitor that detects single-axis exploitation and corrects it on the fly by reweighting dimensions and tightening the trust region. Starting from $\texttt{Llama-3-8B-Instruct}$, GPRL reaches a length-controlled win rate of $56.51\%$ on AlpacaEval~2.0 while also outperforming SimPO and SPPO on Arena-Hard, MT-Bench, and WildBench by resisting reward hacking across extended training runs.

cs.LG↗

arXiv2026

Epistemic Uncertainty for Test-Time Discovery

Automated scientific discovery using large language models relies on identifying genuinely novel solutions. Standard reinforcement learning penalizes high-variance mutations, which leads the policy to prioritize familiar patterns. As a result, the maximum reward plateaus even as the average reward increases. Overcoming this limitation requires a signal that distinguishes unexplored regions from intrinsically difficult problems. This necessitates measuring disagreement across independently adapted weight hypotheses rather than relying on a single network's confidence. UG-TTT addresses this challenge by maintaining a small ensemble of low-rank adapters over a frozen base model. The per-token disagreement, quantified as the mutual information between ensemble predictions and weight hypotheses, isolates epistemic uncertainty and identifies positions where insufficient coverage leads to adapter divergence rather than intrinsic problem difficulty. This measure is incorporated as an exploration bonus into the policy gradient, directing the policy toward positions where persistent adapter disagreement signals low training coverage, the same frontier where genuine discovery is possible. A nuclear norm regularizer ensures the adapters remain distinct from one another, thereby preserving the exploration signal throughout training. Across four scientific discovery benchmarks, UG-TTT increases the maximum reward on three tasks, maintains substantially higher solution diversity, and an ablation study confirms that the regularizer is essential for sustaining this behavior.

cs.LG↗

arXiv2026

Canonical Optimization for MIMO MAC Design

Resource allocation in the multiple-input multiple-output (MIMO) multiple access channel (MAC) is a fundamental problem in multiuser communications, yet it is increasingly treated as non-convex and computationally intractable. This has motivated a large body of heuristic machine learning and successive-approximation methods. Results here show that the MIMO MAC admits canonical convex formulations and present four solvers that together characterize its capacity region. maxRMAC performs weighted sum-rate maximization under per-user energy constraints, minPMAC finds the minimum weighted energy required to support target rates, maxRESMAC performs weighted sum-rate maximization under a total energy constraint, and admMAC tests rate-region feasibility. The solvers exploit the polymatroid structure of the MAC rate region and the separability of the dual Lagrangian across frequency tones, which reduces the problem to parallel per-tone covariance optimizations solved via limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) over Cholesky-like covariance factors. Experiments on spatially correlated MIMO orthogonal frequency-division multiplexing (OFDM) channels show that the proposed solvers match a commercial convex solver in solution quality while running up to two orders of magnitude faster and scaling to regimes where the commercial solver times out. Through broadcast channel (BC) to MAC duality, the same solvers also enable optimal precoder design for the MIMO BC. All solvers are open-sourced and available at https://github.com/muhd-umer/canonical-mac.

eess.SP↗

arXiv2026

Minimum Toffoli depth for the multi-controlled Toffoli gate via teleportation

The decomposition of complex quantum operations into experimentally feasible gate sets has been a central challenge since the early development of quantum computing. The multi-controlled Toffoli (MCT) gate is a key example, with applications across a wide range of quantum algorithms, whose decomposition into smaller gates, however, typically leads to deep circuits. In this work, we introduce a teleportation-based decomposition that implements an MCT gate. This decomposition has unit Toffoli depth, independent of the number of controls, while achieving the lowest Toffoli count among existing approaches for more than five controls at the cost of a linear overhead in ancilla qubits. We also investigate the parameter regimes in which the teleportation-based decomposition is preferable by analyzing the relative quality of distributed entanglement and Toffoli gates. We further demonstrate the advantages of this implementation in circuits that rely on MCT gates, such as the adder operator, quantum read-only memory, quantum neurons, and quantum decision trees.

quant-ph↗

arXiv2026

Pressure, What Pressure? Sycophancy Disentanglement in Language Models via Reward Decomposition

Large language models exhibit sycophancy, the tendency to shift their stated positions toward perceived user preferences or authority cues regardless of evidence. Standard alignment methods fail to correct this because scalar reward models conflate two distinct failure modes into a single signal: pressure capitulation, where the model changes a correct answer under social pressure, and evidence blindness, where the model ignores the provided context entirely. We operationalise sycophancy through formal definitions of pressure independence and evidence responsiveness, serving as a working framework for disentangled training rather than a definitive characterisation of the phenomenon. We propose the first approach to sycophancy reduction via reward decomposition, introducing a multi-component Group Relative Policy Optimisation (GRPO) reward that decomposes the training signal into five terms: pressure resistance, context fidelity, position consistency, agreement suppression, and factual correctness. We train using a contrastive dataset pairing pressure-free baselines with pressured variants across three authority levels and two opposing evidence contexts. Across five base models, our two-phase pipeline consistently reduces sycophancy on all metric axes, with ablations confirming that each reward term governs an independent behavioural dimension. The learned resistance to pressure generalises beyond our training methodology and prompt structure, reducing answer-priming sycophancy by up to 17 points on SycophancyEval despite the absence of such pressure forms during training.

cs.AI↗

arXiv2026

$S^3$: Stratified Scaling Search for Test-Time in Diffusion Language Models

Test-time scaling investigates whether a fixed diffusion language model (DLM) can generate better outputs when given more inference compute, without additional training. However, naive best-of-$K$ sampling is fundamentally limited because it repeatedly draws from the same base diffusion distribution, whose high-probability regions are often misaligned with high-quality outputs. We propose $S^3$ (Stratified Scaling Search), a classical verifier-guided search method that improves generation by reallocating compute during the denoising process rather than only at the final output stage. At each denoising step, $S^3$ expands multiple candidate trajectories, evaluates them with a lightweight reference-free verifier, and selectively resamples promising candidates while preserving diversity within the search frontier. This procedure effectively approximates a reward-tilted sampling distribution that favors higher-quality outputs while remaining anchored to the model prior. Experiments with LLaDA-8B-Instruct on MATH-500, GSM8K, ARC-Challenge, and TruthfulQA demonstrate that $S^3$ consistently improves performance across benchmarks, achieving the largest gains on mathematical reasoning tasks while leaving the underlying model and decoding schedule unchanged. These results show that classical search over denoising trajectories provides a practical mechanism for test-time scaling in DLMs.

cs.LG↗

arXiv2026

What If We Allocate Test-Time Compute Adaptively?

Test-time compute scaling allocates inference computation uniformly, uses fixed sampling strategies, and applies verification only for reranking. In contrast, we propose a verifier-guided adaptive framework treating reasoning as iterative trajectory generation and selection. For each problem, the agent runs multiple inference iterations. In each iteration, it optionally produces a high-level plan, selects a set of reasoning tools and a compute strategy together with an exploration parameter, and then generates a candidate reasoning trajectory. A process reward model (PRM) serves as a unified control signal: within each iteration, step-level PRM scores are aggregated to guide pruning and expansion during generation, and across iterations, aggregated trajectory rewards are used to select the final response. Across datasets, our dynamic, PRM-guided approach consistently outperforms direct test-time scaling, yielding large gains on MATH-500 and several-fold improvements on harder benchmarks such as AIME24 and AMO-Bench. We characterize efficiency using theoretical FLOPs and a compute intensity metric penalizing wasted generation and tool overhead, demonstrating that verification-guided allocation concentrates computation on high-utility reasoning paths.

cs.CL↗

arXiv2026

Continuous-Utility Direct Preference Optimization

Large language model reasoning is often treated as a monolithic capability, relying on binary preference supervision that fails to capture partial progress or fine-grained reasoning quality. We introduce Continuous Utility Direct Preference Optimization (CU-DPO), a framework that aligns models to a portfolio of prompt-based cognitive strategies by replacing binary labels with continuous scores that capture fine-grained reasoning quality. We prove that learning with K strategies yields a Theta(K log K) improvement in sample complexity over binary preferences, and that DPO converges to the entropy-regularized utility-maximizing policy. To exploit this signal, we propose a two-stage training pipeline: (i) strategy selection, which optimizes the model to choose the best strategy for a given problem via best-vs-all comparisons, and (ii) execution refinement, which trains the model to correctly execute the selected strategy using margin-stratified pairs. On mathematical reasoning benchmarks, CU-DPO improves strategy selection accuracy from 35-46 percent to 68-78 percent across seven base models, yielding consistent downstream reasoning gains of up to 6.6 points on in-distribution datasets with effective transfer to out-of-distribution tasks.

cs.LG↗

arXiv2025

On the Fundamental Limits of LLMs at Scale

Large Language Models (LLMs) have benefited enormously from scaling, yet these gains are bounded by five fundamental limitations: (1) hallucination, (2) context compression, (3) reasoning degradation, (4) retrieval fragility, and (5) multimodal misalignment. While existing surveys describe these phenomena empirically, they lack a rigorous theoretical synthesis connecting them to the foundational limits of computation, information, and learning. This work closes that gap by presenting a unified, proof-informed framework that formalizes the innate theoretical ceilings of LLM scaling. First, computability and uncomputability imply an irreducible residue of error: for any computably enumerable model family, diagonalization guarantees inputs on which some model must fail, and undecidable queries (e.g., halting-style tasks) induce infinite failure sets for all computable predictors. Second, information-theoretic and statistical constraints bound attainable accuracy even on decidable tasks, finite description length enforces compression error, and long-tail factual knowledge requires prohibitive sample complexity. Third, geometric and computational effects compress long contexts far below their nominal size due to positional under-training, encoding attenuation, and softmax crowding. We further show how likelihood-based training favors pattern completion over inference, how retrieval under token limits suffers from semantic drift and coupling noise, and how multimodal scaling inherits shallow cross-modal alignment. Across sections, we pair theorems and empirical evidence to outline where scaling helps, where it saturates, and where it cannot progress, providing both theoretical foundations and practical mitigation paths like bounded-oracle retrieval, positional curricula, and sparse or hierarchical attention.

cs.LG↗

arXiv2025

Depth optimization of CNOT ladder circuits

The increasing depth of quantum circuits presents a major limitation for the execution of quantum algorithms, as the limited coherence time of physical qubits leads to noise that manifests as errors during computation. In this work, we focus on CNOT ladder circuits, which find applications in several quantum computing tasks, including the preparation of GHZ states, the implementation of fan-out and long-range CNOT gates, fermionic simulations, and the construction of ansatz circuits for variational quantum computing. The linearly increasing depth of a CNOT ladder circuit can be exchanged for constant CNOT depth at the expense of wider circuits that rely on mid-circuit measurements and classically controlled operations. Our error analysis shows that the choice between these two constructions depends on the relative difference between CNOT and idling error rates. Overall, the technique developed in this work enables low-depth implementations of circuits that are ubiquitous in quantum computing algorithms.

quant-ph↗

arXiv2025

Transformer-Based Sparse CSI Estimation for Non-Stationary Channels

Accurate and efficient estimation of Channel State Information (CSI) is critical for next-generation wireless systems operating under non-stationary conditions, where user mobility, Doppler spread, and multipath dynamics rapidly alter channel statistics. Conventional pilot aided estimators incur substantial overhead, while deep learning approaches degrade under dynamic pilot patterns and time varying fading. This paper presents a pilot-aided Flash-Attention Transformer framework that unifies model-driven pilot acquisition with data driven CSI reconstruction through patch-wise self-attention and a physics aware composite loss function enforcing phase alignment, correlation consistency, and time frequency smoothness. Under a standardized 3GPP NR configuration, the proposed framework outperforms LMMSE and LSTM baselines by approximately 13 dB in phase invariant normalized mean-square error (NMSE) with markedly lower bit-error rate (BER), while reducing pilot overhead by 16 times. These results demonstrate that attention based architectures enable reliable CSI recovery and enhanced spectral efficiency without compromising link quality, addressing a fundamental bottleneck in adaptive, low-overhead channel estimation for non-stationary 5G and beyond-5G networks.

cs.DC↗

arXiv2025

6G Twin: Hybrid Gaussian Radio Fields for Channel Estimation and Non-Linear Precoder Design for Radio Access Networks

This work introduces 6G Twin, the first end-to-end artificial intelligence (AI)-native radio access network (RAN) design that unifies (i) neural Gaussian Radio Fields (GRF) for compressed channel state information (CSI) acquisition, (ii) continual channel prediction with handover persistence, and (iii) an energy-optimal nonlinear precoder (minPMAC). GRF replaces dense pilots with a sparse Gaussian field, cutting pilot overhead by about 100x while delivering 1.1 ms inference and less than 2 minutes on-site training, thus enabling millisecond-scale closed-loop operation. A replay-driven continual learner sustains accuracy under mobility and cell transitions, improving channel normalized mean square error (NMSE) by more than 10 dB over frozen predictors and an additional 2-5 dB over uniform replay, thereby stabilizing performance across UMi/UMa handovers. Finally, minPMAC solves a convex, order-free MAC precoder design that recovers the globally optimal order from Broadcast Channel (BC) duals and minimizes transmit energy subject to minimum-rate guarantees, achieving 4-10 times lower energy (scenario dependent) with monotonically increasing bits per joule as SNR grows. This translates to up to 5 times higher data rate at comparable power or the same rates at substantially lower power. Together, these components form a practical, GPU-ready framework that attains real-time CSI, robust tracking in dynamic networks with efficient handovers, and state-of-the-art throughput-energy tradeoffs under 3GPP-style settings.

cs.DC↗

arXiv2025

Conditional Prior-based Non-stationary Channel Estimation Using Accelerated Diffusion Models

Wireless channels in motion-rich urban microcell (UMi) settings are non-stationary; mobility and scatterer dynamics shift the distribution over time, degrading classical and deep estimators. This work proposes conditional prior diffusion for channel estimation, which learns a history-conditioned score to denoise noisy channel snapshots. A temporal encoder with cross-time attention compresses a short observation window into a context vector, which captures the channel's instantaneous coherence and steers the denoiser via feature-wise modulation. In inference, an SNR-matched initialization selects the diffusion step whose marginal aligns with the measured input SNR, and the process follows a shortened, geometrically spaced schedule, preserving the signal-to-noise trajectory with far fewer iterations. Temporal self-conditioning with the previous channel estimate and a training-only smoothness penalty further stabilizes evolution without biasing the test-time estimator. Evaluations on a 3GPP benchmark show lower NMSE across all SNRs than LMMSE, GMM, LSTM, and LDAMP baselines, demonstrating stable performance and strong high SNR fidelity.

cs.DC↗

arXiv2025

Channel Prediction under Network Distribution Shift Using Continual Learning-based Loss Regularization

Modern wireless networks face critical challenges when mobile users traverse heterogeneous network configurations with varying antenna layouts, carrier frequencies, and scattering statistics. Traditional predictors degrade under distribution shift, with NMSE rising by 37.5\% during cross-configuration handovers. This work addresses catastrophic forgetting in channel prediction by proposing a continual learning framework based on loss regularization. The approach augments standard training objectives with penalty terms that selectively preserve network parameters essential for previous configurations while enabling adaptation to new environments. Two prominent regularization strategies are investigated: Elastic Weight Consolidation (EWC) and Synaptic Intelligence (SI). Across 3GPP scenarios and multiple architectures, SI lowers the high-SNR NMSE floor by up to 1.8 dB ($\approx$32--34\%), while EWC achieves up to 1.4 dB ($\approx$17--28\%). Notably, standard EWC incurs $\mathcal{O}(MK)$ complexity (storing $M$ Fisher diagonal entries and corresponding parameter snapshots across $K$ tasks) unless consolidated, whereas SI maintains $\mathcal{O}(M)$ memory complexity (storing $M$ model parameters), independent of task sequence length, making it suitable for resource-constrained wireless infrastructure

cs.DC↗

arXiv2025

Neural Gaussian Radio Fields for Channel Estimation

Accurate channel state information (CSI) is a critical bottleneck in modern wireless networks, with pilot overhead consuming 11\% to 21\% of transmission bandwidth and feedback delays causing severe throughput degradation under mobility. Addressing this requires rethinking how neural fields represent coherent wave phenomena. This work introduces \textit{neural Gaussian radio fields (\textcolor{stanfordred}{nGRF})}, a physics-informed framework that fundamentally reframes neural field design by replacing view-dependent rasterization with direct complex-valued aggregation in 3D space. This approach natively models wave superposition rather than visual occlusion. The architectural shift transforms the learning objective from function-fitting to source-recovery, a well-posed inverse problem grounded in electromagnetic theory. While demonstrated for wireless channel estimation, the core principle of explicit primitive-based fields with physics-constrained aggregation extends naturally to any coherent wave-based domain, including acoustic propagation, seismic imaging, and ultrasound reconstruction. Evaluations show that the inductive bias of \textcolor{stanfordred}{nGRF} achieves 10.9 dB higher prediction SNR than state-of-the-art methods with 220$\times$ faster inference (1.1 ms vs. 242 ms), 18$\times$ lower measurement density, and 180$\times$ faster training. For large-scale outdoor environments where implicit methods fail, \textcolor{stanfordred}{nGRF} achieves 28.32 dB SNR, demonstrating that structured representations supplemented by domain physics can fundamentally outperform generic deep learning architectures.

eess.SP↗