Neural Fields for NV-Center Inverse Sensing

Inverse problems in scientific sensing are often solved with either hand-designed regularizers or supervised networks trained on simulated labels, yet both can fail when the forward model is nonlinear, spectrally coupled, and physically delicate. We study this issue for noise sensing based on nitrogen-vacancy (NV) centers in diamond, where a quantum sensor measures magnetic-noise spectra generated by sparse spin sources. We show that replacing a common scalar/coherent forward approximation with a tensor power-summed dipolar operator changes the inverse landscape and exposes a center-collapse failure mode in free-density optimization. We propose NeTMY, an amortization-free coordinate neural field coupled to the differentiable NV forward model, with annealed positional encoding, multiscale optimization, sparsity/gating, and spectrum-fidelity losses. Across sparse synthetic reconstructions generated by the corrected operator, NeTMY achieves the best localization and distributional metrics in the tested benchmark. Mechanism experiments show that NeTMY does not directly execute the raw density-space gradient; its parameterization smooths and redistributes updates, mitigating the center-collapse pathology. These results position NV quantum sensing as a useful testbed for physics-faithful neural inverse problems.

Topology-Preserving Neural Operator Learning via Hodge Decomposition

In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective. We reveal that Hodge orthogonality fundamentally resolves spectral interference by isolating unlearnable topological degrees of freedom from learnable geometric dynamics, enabling an additive approximation confined to structure-preserving subspaces. Building on Hodge theory and operator splitting, we derive a principled operator-level decomposition. The result is a Hybrid Eulerian-Lagrangian architecture with an algebraic-level inductive bias we call Hodge Spectral Duality (HSD). In our framework, we use discrete differential forms to capture topology-dominated components and an orthogonal auxiliary ambient space to represent complex local dynamics. Our method achieves superior accuracy and efficiency on geometric graphs with enhanced fidelity to physical invariants. Our code is available at https://github.com/ContinuumCoder/Hodge-Spectral-Duality

HodgeCover: Higher-Order Topological Coverage Drives Compression of Sparse Mixture-of-Experts

Sparse Mixture-of-Experts (MoE) layers route tokens through a handful of experts, and learning-free compression of these layers reduces inference cost without retraining. A subtle obstruction blocks every existing compressor in this family: three experts can each be pairwise compatible yet form an irreducible cycle when merged together, so any score that ranks experts on pairwise signals is structurally blind to which triples are jointly mergeable. We show the obstruction is a precise mathematical object, the harmonic kernel of the simplicial Laplacian on a 2-complex whose vertices are experts, whose edges carry KL merge barriers, and whose faces carry triplet barriers; Hodge-decomposing the edge-barrier signal isolates the kernel exactly. We turn the diagnostic into a selection objective: HodgeCover greedily covers the harmonic-critical edges and triplet-critical triangles, and a hybrid variant of HodgeCover pairs it with off-the-shelf weight pruning on survivors. On three open-weight Sparse MoE backbones under aggressive expert reduction, HodgeCover matches state-of-the-art learning-free baselines on the expert-reduction axis, leads on the aggressive-compression frontier of the hybrid axis, and uniquely balances retained mass across all four Hodge components. These results show that exposing the harmonic kernel of a learned MoE structure changes which compressor wins at the regime that matters most.

Neural Field Thermal Tomography: A Differentiable Physics Framework for Non-Destructive Evaluation

We propose Neural Field Thermal Tomography (NeFTY), a differentiable physics framework for the quantitative 3D reconstruction of material properties from transient surface temperature measurements. While traditional thermography relies on pixel-wise 1D approximations that neglect lateral diffusion, and soft-constrained Physics-Informed Neural Networks (PINNs) often fail in transient diffusion scenarios due to gradient stiffness, NeFTY parameterizes the 3D diffusivity field as a continuous neural field optimized through a rigorous numerical solver. By leveraging a differentiable physics solver, our approach enforces thermodynamic laws as hard constraints while maintaining the memory efficiency required for high-resolution 3D tomography. Our discretize-then-optimize paradigm effectively mitigates the spectral bias and ill-posedness inherent in inverse heat conduction, enabling the recovery of subsurface defects at arbitrary scales. Experimental validation on synthetic data demonstrates that NeFTY significantly improves the accuracy of subsurface defect localization over baselines. Additional details at https://cab-lab-princeton.github.io/nefty/

Privacy-Preserving End-to-End Full-Duplex Speech Dialogue Models

End-to-end full-duplex speech models feed user audio through an always-on LLM backbone, yet the speaker privacy implications of their hidden representations remain unexamined. Following the VoicePrivacy 2024 protocol with a lazy-informed attacker, we show that the hidden states of SALM-Duplex and Moshi leak substantial speaker identity across all transformer layers. Layer-wise and turn-wise analyses reveal that leakage persists across all layers, with SALM-Duplex showing stronger leakage in early layers while Moshi leaks uniformly, and that Linkability rises sharply within the first few turns. We propose two streaming anonymization setups using Stream-Voice-Anon: a waveform-level front-end (Anon-W2W) and a feature-domain replacement (Anon-W2F). Anon-W2F raises EER by over 3.5x relative to the discrete encoder baseline (11.2% to 41.0%), approaching the 50% random-chance ceiling, while Anon-W2W retains 78-93% of baseline sBERT across setups with sub-second response latency (FRL under 0.8 s).

RIFT: Repurposing Negative Samples via Reward-Informed Fine-Tuning

While Supervised Fine-Tuning (SFT) and Rejection Sampling Fine-Tuning (RFT) are standard for LLM alignment, they either rely on costly expert data or discard valuable negative samples, leading to data inefficiency. To address this, we propose Reward Informed Fine-Tuning (RIFT), a simple yet effective framework that utilizes all self-generated samples. Unlike the hard thresholding of RFT, RIFT repurposes negative trajectories, reweighting the loss with scalar rewards to learn from both the positive and negative trajectories from the model outputs. To overcome the training collapse caused by naive reward integration, where direct multiplication yields an unbounded loss, we introduce a stabilized loss formulation that ensures numerical robustness and optimization efficiency. Extensive experiments on mathematical benchmarks across various base models show that RIFT consistently outperforms RFT. Our results demonstrate that RIFT is a robust and data-efficient alternative for alignment using mixed-quality, self-generated data.

Local-Canonicalization Equivariant Graph Neural Networks for Sample-Efficient and Generalizable Swarm Robot Control

Multi-agent reinforcement learning (MARL) has emerged as a powerful paradigm for coordinating swarms of agents in complex decision-making, yet major challenges remain. In competitive settings such as pursuer-evader tasks, simultaneous adaptation can destabilize training; non-kinetic countermeasures often fail under adverse conditions; and policies trained in one configuration rarely generalize to environments with a different number of agents. To address these issues, we propose the Local-Canonicalization Equivariant Graph Neural Networks (LEGO) framework, which integrates seamlessly with popular MARL algorithms such as MAPPO. LEGO employs graph neural networks to capture permutation equivariance and generalization to different agent numbers, canonicalization to enforce E(n)-equivariance, and heterogeneous representations to encode role-specific inductive biases. Experiments on cooperative and competitive swarm benchmarks show that LEGO outperforms strong baselines and improves generalization. In real-world experiments, LEGO demonstrates robustness to varying team sizes and agent failure.

Constraint Matters: Multi-Modal Representation for Reducing Mixed-Integer Linear programming

Model reduction, which aims to learn a simpler model of the original mixed integer linear programming (MILP), can solve large-scale MILP problems much faster. Most existing model reduction methods are based on variable reduction, which predicts a solution value for a subset of variables. From a dual perspective, constraint reduction that transforms a subset of inequality constraints into equalities can also reduce the complexity of MILP, but has been largely ignored. Therefore, this paper proposes a novel constraint-based model reduction approach for the MILP. Constraint-based MILP reduction has two challenges: 1) which inequality constraints are critical such that reducing them can accelerate MILP solving while preserving feasibility, and 2) how to predict these critical constraints efficiently. To identify critical constraints, we first label these tight-constraints at the optimal solution as potential critical constraints and design a heuristic rule to select a subset of critical tight-constraints. To learn the critical tight-constraints, we propose a multi-modal representation technique that leverages information from both instance-level and abstract-level MILP formulations. The experimental results show that, compared to the state-of-the-art methods, our method improves the quality of the solution by over 50\% and reduces the computation time by 17.47\%.

Beyond Standard MoE: Mixture of Latent Experts for Resource-Efficient Language Models

Mixture of Experts (MoE) has emerged as a pivotal architectural paradigm for efficient scaling of Large Language Models (LLMs), operating through selective activation of parameter subsets for each input token. Nevertheless, conventional MoE architectures encounter substantial challenges, including excessive memory utilization and communication overhead during training and inference, primarily attributable to the proliferation of expert modules. In this paper, we introduce Mixture of Latent Experts (MoLE), a novel parameterization methodology that facilitates the mapping of specific experts into a shared latent space. Specifically, all expert operations are systematically decomposed into two principal components: a shared projection into a lower-dimensional latent space, followed by expert-specific transformations with significantly reduced parametric complexity. This factorized approach substantially diminishes parameter count and computational requirements. Beyond the pretraining implementation of the MoLE architecture, we also establish a rigorous mathematical framework for transforming pre-trained MoE models into the MoLE architecture, characterizing the sufficient conditions for optimal factorization and developing a systematic two-phase algorithm for this conversion process. Our comprehensive theoretical analysis demonstrates that MoLE significantly enhances computational efficiency across multiple dimensions while preserving model representational capacity. Empirical evaluations corroborate our theoretical findings, confirming that MoLE achieves performance comparable to standard MoE implementations while substantially reducing resource requirements.

Unlocking Efficient Long-to-Short LLM Reasoning with Model Merging

The transition from System 1 to System 2 reasoning in large language models (LLMs) has marked significant advancements in handling complex tasks through deliberate, iterative thinking. However, this progress often comes at the cost of efficiency, as models tend to overthink, generating redundant reasoning steps without proportional improvements in output quality. Long-to-Short (L2S) reasoning has emerged as a promising solution to this challenge, aiming to balance reasoning depth with practical efficiency. While existing approaches, such as supervised fine-tuning (SFT), reinforcement learning (RL), and prompt engineering, have shown potential, they are either computationally expensive or unstable. Model merging, on the other hand, offers a cost-effective and robust alternative by integrating the quick-thinking capabilities of System 1 models with the methodical reasoning of System 2 models. In this work, we present a comprehensive empirical study on model merging for L2S reasoning, exploring diverse methodologies, including task-vector-based, SVD-based, and activation-informed merging. Our experiments reveal that model merging can reduce average response length by up to 55% while preserving or even improving baseline performance. We also identify a strong correlation between model scale and merging efficacy with extensive evaluations on 1.5B/7B/14B/32B models. Furthermore, we investigate the merged model's ability to self-critique and self-correct, as well as its adaptive response length based on task complexity. Our findings highlight model merging as a highly efficient and effective paradigm for L2S reasoning, offering a practical solution to the overthinking problem while maintaining the robustness of System 2 reasoning. This work can be found on Github https://github.com/hahahawu/Long-to-Short-via-Model-Merging.