Methods and Open Problems in Differentiable Social Choice: Learning Mechanisms, Decisions, and Alignment

Social choice is no longer a peripheral concern of political theory or economics-it has become a foundational component of modern machine learning systems. From auctions and resource allocation to federated learning, participatory governance, and the alignment of large language models, machine learning pipelines increasingly aggregate heterogeneous preferences, incentives, and judgments into collective decisions. In effect, many contemporary machine learning systems already implement social choice mechanisms, often implicitly and without explicit normative scrutiny. This Review surveys differentiable social choice: an emerging paradigm that formulates voting rules, mechanisms, and aggregation procedures as learnable, differentiable models optimized from data. We synthesize work across auctions, voting, budgeting, liquid democracy, decentralized aggregation, and inverse mechanism learning, showing how classical axioms and impossibility results reappear as objectives, constraints, and optimization trade-offs. We conclude by identifying 36 open problems defining a new research agenda at the intersection of machine learning, economics, and democratic theory.

Representational Homomorphism Predicts and Improves Compositional Generalization In Transformer Language Model

Compositional generalization-the ability to interpret novel combinations of familiar components-remains a persistent challenge for neural networks. Behavioral evaluations reveal when models fail but offer limited insight into why failures arise at the representational level. We introduce Homomorphism Error (HE), a structural metric that quantifies deviations from approximate homomorphisms between the expression algebra and a model's hidden-state space. We instantiate HE for two compositional operators in SCAN-style tasks: modifier HE for unary composition and sequence HE for binary composition, measured by learning representation-level operators that predict composed representations from their parts. Across controlled experiments with small decoder-only Transformers, HE predicts out-of-distribution (OOD) compositional generalization under noise injection, achieving R^2 = 0.73 correlation between modifier HE and OOD accuracy. Ablations show that model depth has minimal effect on either HE or OOD accuracy, training data coverage exhibits threshold effects (insufficient coverage sharply increases HE and degrades OOD performance), and randomly inserted noise tokens systematically increase HE. Finally, we test if HE-regularized training improves OOD accuracy. Experiment shows that explicitly enforcing low modifier HE during training significantly reduces modifier HE (p = 1.1x10-4) and sequence HE (p = 0.001) and yields a statistically significant improvement in OOD accuracy (p = 0.023). Together, these results indicate the potential of HE to be both a diagnostic and an actionable training signal for improving compositional generalization. Code to reproduce our experiments is open-sourced.

Differential Voting: Loss Functions For Axiomatically Diverse Aggregation of Heterogeneous Preferences

Reinforcement learning from human feedback (RLHF) implicitly aggregates heterogeneous human preferences into a single utility function, even though the underlying utilities of the participants are in practice diverse. Hence, RLHF can be viewed as a form of voting, where the aggregation mechanism is defined by the loss function. Although Arrow's Impossibility Theorem suggests that different mechanisms satisfy different sets of desirable axioms, most existing methods rely on a single aggregation principle, typically the Bradley-Terry-Luce (BTL) model, which corresponds to Borda count voting. This restricts the axiomatic properties of the learned reward and obscures the normative assumptions embedded in optimization. In this work, we introduce Differential Voting, a unifying framework that constructs instance-wise, differentiable loss functions whose population-level optima provably correspond to distinct classical voting rules. We develop differentiable surrogates for majority-based aggregation (BTL), Copeland, and Kemeny rules, and formally analyze their calibration properties, gradient fields, and limiting behavior as smoothing parameters vanish. For each loss, we establish consistency with the corresponding social choice rule and characterize the axioms it satisfies or violates. Our analysis shows how design choices in loss geometry-such as margin sensitivity and boundary concentration-directly translate into normative aggregation behavior. Differential Voting makes preference aggregation an explicit and controllable design choice in RLHF, enabling principled trade-offs between axiomatic guarantees and optimization stability. Code to reproduce our experiments is open-sourced.

DIML: Differentiable Inverse Mechanism Learning from Behaviors of Multi-Agent Learning Trajectories

We study inverse mechanism learning: recovering an unknown incentive-generating mechanism from observed strategic interaction traces of self-interested learning agents. Unlike inverse game theory and multi-agent inverse reinforcement learning, which typically infer utility/reward parameters inside a structured mechanism, our target includes unstructured mechanism -- a (possibly neural) mapping from joint actions to per-agent payoffs. Unlike differentiable mechanism design, which optimizes mechanisms forward, we infer mechanisms from behavior in an observational setting. We propose DIML, a likelihood-based framework that differentiates through a model of multi-agent learning dynamics and uses the candidate mechanism to generate counterfactual payoffs needed to predict observed actions. We establish identifiability of payoff differences under a conditional logit response model and prove statistical consistency of maximum likelihood estimation under standard regularity conditions. We evaluate DIML with simulated interactions of learning agents across unstructured neural mechanisms, congestion tolling, public goods subsidies, and large-scale anonymous games. DIML reliably recovers identifiable incentive differences and supports counterfactual prediction, where its performance rivals tabular enumeration oracle in small environments and its convergence scales to large, hundred-participant environments. Code to reproduce our experiments is open-sourced.

MoralReason: Generalizable Moral Decision Alignment For LLM Agents Using Reasoning-Level Reinforcement Learning

Large language models are increasingly influencing human moral decisions, yet current approaches focus primarily on evaluating rather than actively steering their moral decisions. We formulate this as an out-of-distribution moral alignment problem, where LLM agents must learn to apply consistent moral reasoning frameworks to scenarios beyond their training distribution. We introduce Moral-Reason-QA, a novel dataset extending 680 human-annotated, high-ambiguity moral scenarios with framework-specific reasoning traces across utilitarian, deontological, and virtue ethics, enabling systematic evaluation of moral generalization in realistic decision contexts. Our learning approach employs Group Relative Policy Optimization with composite rewards that simultaneously optimize decision alignment and framework-specific reasoning processes to facilitate learning of the underlying moral frameworks. Experimental results demonstrate successful generalization to unseen moral scenarios, with softmax-normalized alignment scores improving by +0.757 for utilitarian and +0.450 for deontological frameworks when tested on out-of-distribution evaluation sets. The experiments also reveal training challenges and promising directions that inform future research. These findings establish that LLM agents can be systematically trained to internalize and apply specific moral frameworks to novel situations, providing a critical foundation for AI safety as language models become more integrated into human decision-making processes.

SoilX: Calibration-Free Comprehensive Soil Sensing Through Contrastive Cross-Component Learning

Precision agriculture demands continuous and accurate monitoring of soil moisture (M) and key macronutrients, including nitrogen (N), phosphorus (P), and potassium (K), to optimize yields and conserve resources. Wireless soil sensing has been explored to measure these four components; however, current solutions require recalibration (i.e., retraining the data processing model) to handle variations in soil texture, characterized by aluminosilicates (Al) and organic carbon (C), limiting their practicality. To address this, we introduce SoilX, a calibration-free soil sensing system that jointly measures six key components: {M, N, P, K, C, Al}. By explicitly modeling C and Al, SoilX eliminates texture- and carbon-dependent recalibration. SoilX incorporates Contrastive Cross-Component Learning (3CL), with two customized terms: the Orthogonality Regularizer and the Separation Loss, to effectively disentangle cross-component interference. Additionally, we design a novel tetrahedral antenna array with an antenna-switching mechanism, which can robustly measure soil dielectric permittivity independent of device placement. Extensive experiments demonstrate that SoilX reduces estimation errors by 23.8% to 31.5% over baselines and generalizes well to unseen fields.

Towards VM Rescheduling Optimization Through Deep Reinforcement Learning

Modern industry-scale data centers need to manage a large number of virtual machines (VMs). Due to the continual creation and release of VMs, many small resource fragments are scattered across physical machines (PMs). To handle these fragments, data centers periodically reschedule some VMs to alternative PMs, a practice commonly referred to as VM rescheduling. Despite the increasing importance of VM rescheduling as data centers grow in size, the problem remains understudied. We first show that, unlike most combinatorial optimization tasks, the inference time of VM rescheduling algorithms significantly influences their performance, due to dynamic VM state changes during this period. This causes existing methods to scale poorly. Therefore, we develop a reinforcement learning system for VM rescheduling, VM2RL, which incorporates a set of customized techniques, such as a two-stage framework that accommodates diverse constraints and workload conditions, a feature extraction module that captures relational information specific to rescheduling, as well as a risk-seeking evaluation enabling users to optimize the trade-off between latency and accuracy. We conduct extensive experiments with data from an industry-scale data center. Our results show that VM2RL can achieve a performance comparable to the optimal solution but with a running time of seconds. Code and datasets are open-sourced: https://github.com/zhykoties/VMR2L_eurosys, https://drive.google.com/drive/folders/1PfRo1cVwuhH30XhsE2Np3xqJn2GpX5qy.

Disentangling Uncertainties by Learning Compressed Data Representation

We study aleatoric and epistemic uncertainty estimation in a learned regressive system dynamics model. Disentangling aleatoric uncertainty (the inherent randomness of the system) from epistemic uncertainty (the lack of data) is crucial for downstream tasks such as risk-aware control and reinforcement learning, efficient exploration, and robust policy transfer. While existing approaches like Gaussian Processes, Bayesian networks, and model ensembles are widely adopted, they suffer from either high computational complexity or inaccurate uncertainty estimation. To address these limitations, we propose the Compressed Data Representation Model (CDRM), a framework that learns a neural network encoding of the data distribution and enables direct sampling from the output distribution. Our approach incorporates a novel inference procedure based on Langevin dynamics sampling, allowing CDRM to predict arbitrary output distributions rather than being constrained to a Gaussian prior. Theoretical analysis provides the conditions where CDRM achieves better memory and computational complexity compared to bin-based compression methods. Empirical evaluations show that CDRM demonstrates a superior capability to identify aleatoric and epistemic uncertainties separately, achieving AUROCs of 0.8876 and 0.9981 on a single test set containing a mixture of both uncertainties. Qualitative results further show that CDRM's capability extends to datasets with multimodal output distributions, a challenging scenario where existing methods consistently fail. Code and supplementary materials are available at https://github.com/ryeii/CDRM.

GWRF: A Generalizable Wireless Radiance Field for Wireless Signal Propagation Modeling

We present Generalizable Wireless Radiance Fields (GWRF), a framework for modeling wireless signal propagation at arbitrary 3D transmitter and receiver positions. Unlike previous methods that adapt vanilla Neural Radiance Fields (NeRF) from the optical to the wireless signal domain, requiring extensive per-scene training, GWRF generalizes effectively across scenes. First, a geometry-aware Transformer encoder-based wireless scene representation module incorporates information from geographically proximate transmitters to learn a generalizable wireless radiance field. Second, a neural-driven ray tracing algorithm operates on this field to automatically compute signal reception at the receiver. Experimental results demonstrate that GWRF outperforms existing methods on single scenes and achieves state-of-the-art performance on unseen scenes.

See Behind Walls in Real-time Using Aerial Drones and Augmented Reality

This work presents ARD2, a framework that enables real-time through-wall surveillance using two aerial drones and an augmented reality (AR) device. ARD2 consists of two main steps: target direction estimation and contour reconstruction. In the first stage, ARD2 leverages geometric relationships between the drones, the user, and the target to project the target's direction onto the user's AR display. In the second stage, images from the drones are synthesized to reconstruct the target's contour, allowing the user to visualize the target behind walls. Experimental results demonstrate the system's accuracy in both direction estimation and contour reconstruction.