arXiv subjects

Alvaro Velasquez

Publications and source records attributed to Alvaro Velasquez.

At least 19 recordsLinked to original sources

arXiv2026

DeFAb: A Dataset for Grounded Scientific Discovery through Defeasible Abduction

A theory can accommodate a counterexample by adding an exception. The harder problem is deciding how far the exception should extend and which predictions should survive. We present DeFAb, a dataset and symbolic verification framework built from curated biological knowledge in the Gene Ontology. Models fill gaps in a theory or propose exceptions to its rules. A verifier checks the consequences of each edit, allowing different solutions to receive credit. Simple symbolic repairs solve all 336 tasks in the released evaluation panel. This result exposes a limitation of the revision test. An exception tied to one entity can succeed without identifying a pattern that applies to other cases. We develop a contextual task that requires an exception to reach the relevant cases and preserve predictions elsewhere. Two planned studies compare training with verified and rejected examples, and revision with and without feedback about consequences. DeFAb makes the scope of a proposed explanation testable, providing a controlled step toward studying theory revision in scientific reasoning.

cs.AI↗

arXiv2026

Differentiable Repairability & Mutations for Scalable Combinatorial Optimization

Combinatorial optimization problems such as Maximum Independent Set (MIS) and Maximum Cut (MaxCut) arise across a wide range of applications, yet solving large-scale instances remains computationally challenging. While discrete local-search procedures can produce high-quality solutions, their inherently sequential and iterative nature can become increasingly expensive as problem size and density grow. In this paper, we present a differentiable perspective on combinatorial optimization that leverages continuous relaxation with parallelizable gradient-based updates to improve scalability while reducing dependence on discrete local search. More specifically, for MIS, we show that solutions that remain repairable through a discrete (1,2)-swap can nevertheless be fixed points of projected gradient ascent, revealing a fundamental limitation of purely local gradient dynamics. For MaxCut, we develop a new quadratic formulation whose landscape provably allows projected gradient ascent to escape 1-flip-repairable solutions while ensuring binary local maximizers. Building on these insights, and inspired by discrete perturb-and-improve methods, we introduce a framework that combines projected gradient ascent with differentiable mutations (partial resets) to efficiently explore new regions of the solution space}. Experimental results on MIS and MaxCut demonstrate the potential of this approach for scalable combinatorial optimization, particularly in regimes where conventional discrete local search becomes computationally prohibitive.

cs.DM↗

arXiv2026

Parallelizable Gradient-Based Optimization For Multi-Objective MaxCut

Multi-objective combinatorial optimization arises in a wide range of problems and applications, including the canonical multi-objective MaxCut problem. Differentiable single-instance quadratic methods have recently achieved remarkable performance in single-objective combinatorial optimization. In this paper, we develop a differentiable framework for multi-objective MaxCut by combining an adjacency-based quadratic formulation with linear scalarization, thereby reducing the problem to a preference-conditioned single-objective signed-weight MaxCut problem. Theoretically, we characterize projected gradient ascent (PGA) fixed points and their local dynamics under the signed-weight adjacency formulation. We further characterize how these fixed points depend on preferences and establish their connection to Pareto optimality. Computationally, unlike conventional heuristics and branch-and-bound methods, our approach is GPU-parallelizable and can therefore benefit from substantial performance speedups. We term our algorithm Multi-objective QUadratic Combinatorial Optimization (MO-QUCO) and its parallelized variant pMO-QUCO. Empirically, we evaluate our methods on multi-layered graphs with different sizes and edge-weight distributions. Both our CPU-only and GPU-based algorithms outperform state-of-the-art exact and heuristic methods in terms of wall-clock runtime and objective quality. Despite operating under different computational settings, MO-QUCO also outperforms the SOTA quantum method.

cs.DM↗

arXiv2026

Foundation Model-Aided Multi-Agent Reinforcement Learning for Wireless Random Access Network Optimization

Random access (RA) is one of the most foundational medium access control (MAC) layer scheduling schemes for handling unpredictable data traffic from multiple terminals. While multi-agent reinforcement learning (MARL) has been explored to optimize RA-based wireless networks, its reliance on experience-driven, distributed policy learning incurs significant training overhead for each optimization task, limiting its feasibility in real-world applications. In this work, we propose to leverage a foundation model (FM) to improve MARL efficiency across diverse RA network optimization tasks. Specifically, we design an FM-aided actor-critic algorithm within a consensus-based decentralized MARL architecture and provide its convergence analysis under local reward exchanges and nonlinear value function approximations to show that our algorithm achieves the same convergence order as the conventional MARL with critic model exchanges and linear approximations. Our numerical results show that our FM-based approach significantly enhances MARL speed for RA network optimization.

cs.LG↗

arXiv2026

See What I See, Know What I Think: Dense Latent Communication Across Heterogeneous Agents

Language-model agents build internal representations of the information they observe and the reasoning they perform. Sharing these representations offers a way to communicate both source information and reasoning across agents. For agents built from different models, this requires aligning their representations while preserving information useful to the receiver. We study this problem through KV-cache communication, examining how an agent uses internal states shared by other agents, with or without direct access to the information that other agents observed. A controlled self-communication study shows that cache pruning causes substantially greater degradation when the receiving agent lacks access to that information. We use this finding to guide dense cross-model cache alignment, combining positional disentanglement and KV-group transformations with reconstruction followed by generation training. Across six directed Qwen3 pairs, aligned caches improve in-domain accuracy over text communication when both agents observe the same input, with fewer estimated inference FLOPs. Experiments with three-agent document sharing and Mistral-to-Qwen transfer further demonstrate that aligned caches can carry information across both multiple separate observations and different model families.

cs.MA↗

arXiv2026

The Missing Primitive: Diagnosing and Repairing Mathematical Reasoning in Large Language Models

While Large Language Models (LLMs) have demonstrated striking capabilities on frontier mathematical problems, it remains unclear whether they possess the structural mathematical understanding underlying their solutions. In this paper, we take a first step toward systematically studying mathematical understanding in LLMs, from diagnosing its distinct capabilities to leveraging these findings to improve post-training. First, we introduce the notion of Mathematical Primitive to probe structural mathematical understanding and propose \hlei{}, a novel benchmark that evaluates mathematical reasoning along four distinct dimensions: Discovery, Generation, Digestion, and Execution. Second, our systematic diagnosis shows that solution accuracy masks distinct capability profiles, primitives unlock substantial latent execution capacity, and Discovery is the dominant bottleneck in mathematical reasoning. Our post-training analysis further shows that discovery-limited failures are particularly amenable to repair. Finally, building on these findings, we introduce \abs{}, a primitive-privileged self-distillation framework that selectively transfers primitive-guided reasoning into the student model. Extensive experiments demonstrate that \abs{} consistently improves mathematical reasoning over baselines across model scales and challenging benchmarks.

cs.LG↗

arXiv2026

Robust Nash Alignment under Preference Uncertainty

Preference-based alignment methods typically optimize against a single preference model, and can therefore be brittle when pairwise preferences are uncertain: noisy, heterogeneous, or shift after deployment. To address these issues, we propose Robust Nash Alignment, a game-theoretic framework for alignment to uncertain pairwise preferences. Our formulation has a major learner seeking a policy with a large worst-case win rate against both an adversarial competitor and any preference kernel lying in an ambiguity set around a nominal preference. When the ambiguity set captures the uncertainty in preferences, the resulting robust objective of the game directly yields a certified lower bound on worst-case performance. However, we note this problem is computationally challenging to optimize, and to address this, we introduce a four-player primal-dual proxy game involving the leader policy, follower policy, adversarial kernel, and dual variable, and develop a single-loop optimistic mirror descent-ascent algorithm for it. We show that the proxy always lower-bounds the truncated hard-constrained objective, quantify the proxy-to-hard gap, and characterize an exactness condition under which the proxy recovers the robust objective. We then prove an $\mathcal{O}(1/\sqrt{T})$ average-iteration convergence for the proxy-game duality gap, which implies a near-optimal robust policy for the original robust objective. Experiments on controlled tabular games and LLM alignment with uncertain preference further validate the convergence theory and show improved performance over nominal baselines.

cs.AI↗

arXiv2026

DEALS: Decentralized Expertise-Aware Load Serving for Multi-Agent LLM Systems

Multi-agent systems (MAS) have recently emerged as an effective approach for coordinating large language model (LLM)-based agents to solve complex tasks through structured interactions. In practice, MASs often handle a stream of heterogeneous and complex tasks, requiring agents to decompose each task and then self-organize and self-evolve to adapt to incoming tasks while sharing execution resources. However, most early approaches to MASs rely on centralized controllers or fixed coordination patterns, which can limit scalability or adaptability. In contrast, existing decentralized and dynamic MASs often require training dedicated routers or invoking LLMs for agent selection, resulting in substantial computational costs and coordination overhead. To address these challenges and enable efficient task-level self-organization and self-evolution for task- and workload-level collaboration, we propose Decentralized Expertise-Aware Load Serving (DEALS), a decentralized and low-complexity framework that enables agents to self-organize and dynamically route concurrent tasks for processing. Specifically, each agent maintains local queues of incoming tasks, and its router decides whether to process a task locally or forward it to a neighbor based on differences in backlog and success rate. Meanwhile, executors process independent tasks concurrently within and across agents, and partially solved tasks can be resumed by other agents. Experiments show that DEALS not only improves performance along multiple dimensions (e.g., answer accuracy and task throughput) in both homogeneous and heterogeneous agent pools, but also balances agent expertise and workload in a self-organized manner, enabling effective decentralized coordination.

cs.LG↗

arXiv2026

To Solve Bilevel Optimization with Nonconvex Lower Levels, We Need Second-Order Stationarity

Although bilevel optimization (BLO) has emerged as a powerful framework for addressing many complex and nested machine learning problems in recent years, most existing studies are confined to the lower-level strongly convex (LLSC) or lower-level generally convex (LLGC) settings (i.e., the lower-level objective function is assumed to be, at least, convex). While the LLSC/LLGC assumptions render more tractable algorithmic design and theoretical analysis, they are too rigid to encompass many machine learning problems in practice. The limitations of LLSC/LLGC assumptions in BLO motivate us to investigate solving the BLO problem in the general lower-level nonconvex (LLNC) settings, which remains in its infancy. In the literature on LLNC-BLO, most of the existing works either require additional structures in the lower-level objective function for tractable theoretical analysis, or adopt the first-order stationarity reformulation as a lower-level surrogate problem, which is inherited from the LLSC/LLGC settings but could lose their effectiveness in the LLNC setting. To bridge this gap, we propose to reformulate the nonconvex lower-level problem using a second-order stationarity-based surrogate, the solution of which guarantees a local optimal solution at the lower level. Based on this reformulation, we propose the PROBE (Perturbed gradient algorithm for bilevel problem) and show that it overcomes the limitations of prior works by probing and escaping lower-level saddle points. We prove that PROBE achieves a finite-time convergence rate of $O(T^{-2/5})$, where T denotes iterations. To our knowledge, this work is the first to establish the finite-time convergence for achieving lower-level second-order stationary solutions in general LLNC-BLO. Our experiments on both a large language model-based data curation task and a meta-learning task also show that PROBE outperforms SOTA methods.

cs.LG↗

arXiv2026

Neurosymbolic Routing for Reliable Reasoning on Resource-Constrained Edge Devices

Running a language model on edge hardware provides private and low-latency reasoning without a network connection, and yet the small models that fit on such devices are unreliable on the tasks computers are expected to handle well, such as arithmetic, algebra, and formal logic problems. We argue that much of this unreliability is avoidable. Many queries appearing to demand reasoning are in fact structurally deterministic and permit fast and exact symbolic solutions. Therefore, forcing a probabilistic model to approximate them sacrifices accuracy and energy for little benefit. We present a neurosymbolic router that classifies each incoming query and dispatches it to the cheapest correct solver, sending structured tasks to deterministic engines and reserving the small language model (SLM) for open-ended word problems. Instead of hand-coding the routing logic, we learn a deterministic finite automaton (DFA) with the L* grammatical inference algorithm, using the SLM as a membership oracle and labeled data as an equivalence oracle. On a Raspberry Pi 4B (8 GB RAM, no GPU), evaluated on 100 untested prompts from DeepMind Mathematics, GSM8K, and RuleTaker, learned routing attains 100% routing accuracy and 98.3% overall accuracy with a 512-token reasoning budget (93.3% on word problems), compared with 72.0% for the strongest agent baseline, Program-of-Thought, and 58.7% for a tool-calling agent given the same solvers. Since formatted queries never reach the model, the router answers them in 1-11 ms and, in its 30-token configuration, runs 8.8x faster and 2.8x more energy-efficient than Program-of-Thought.

cs.AI↗

arXiv2026

CEDAR: Automata as Verifiable Interfaces for Language-Guided Embodied Action

Natural-language tasking of embodied agents is rarely just goal specification: users also impose constraints that must persist while the world changes. Code-generating LLM agents can produce plausible behaviors for such instructions, but their free-form programs provide no stable object to verify, compose with new constraints, or repair from a failing trace. We present CEDAR, a counterexample-guided framework that grounds instructions as regular languages over environment event traces. CEDAR uses a language model for semantic judgments and execution traces for correction, then represents both skills and specifications as deterministic finite automata. This turns constraints into executable finite-state objects: a learned skill can be intersected with a learned sleep at night or stay in this biome specification, yielding a controller that enforces the learned constraint by construction rather than by repeated prompting. In Minecraft, with the same simulator/API observations available to a program-generating baseline, CEDAR maintains temporal and spatial constraints that the baseline fails to preserve and amortizes reuse of learned skills, reducing cumulative LLM queries. These results suggest that regular languages offer a practical verification layer between natural-language instructions and embodied-agent policies.

cs.AI↗

arXiv2026

A Scalable Lift-and-Project Differentiable Approach For the Maximum Cut Problem

We propose a scalable framework for solving the Maximum Cut (MaxCut) problem in large graphs using projected gradient ascent on quadratic objectives. Our approach is differentiable and leverages GPUs for gradient-based optimization. It is not a machine learning method and does not require training data. Starting from a continuous relaxation of the classical quadratic binary formulation, we present a parallelized strategy that explores multiple initialization vectors in batch. We analyze the relaxed objective, showing it is convex and has fixed-points corresponding to local optima, particularly at boundary points, highlighting a key challenge in non-convex optimization. To improve exploration, we introduce a lifted quadratic formulation that over-parameterizes the solution space. We also provide a theoretical characterization of these lifted fixed-points. Finally, we propose DECO, a dimension-alternating algorithm that switches between the unlifted and lifted formulations, combined with importance-based degree initialization and a population-based evolutionary hyper-parameter search. Experiments on diverse graph families show that our methods attain comparable or superior performance relative to recent neural networks and GPU-accelerated sampling approaches.

cs.DM↗

arXiv2026

ANSR-DT: A Neuro-Symbolic Framework for Adaptive and Explainable Digital Twins

Digital twins are increasingly used to monitor and optimize industrial systems, yet many existing frameworks remain difficult to interpret, slow to adapt, and limited in their ability to incorporate explicit domain knowledge. This paper presents ANSR-DT, an adaptive neuro-symbolic framework that unifies temporal anomaly detection, symbolic reasoning, and reinforcement-learning-based decision support within a single digital twin pipeline. ANSR-DT combines a CNN-LSTM model for multivariate pattern recognition with Prolog-based reasoning that converts learned signals into explicit rules, enabling transparent diagnoses and traceable decision paths. A PPO-based adaptation layer further refines operational responses under changing conditions while preserving interpretability. Experiments against eight baselines show that ANSR-DT delivers competitive predictive performance together with stable rule extraction, scalable symbolic reasoning, and actionable explanations. Additional validation on the Skoltech Anomaly Benchmark (SKAB) further indicates that the framework transfers beyond synthetic settings. These findings position ANSR-DT as a practical foundation for trustworthy, adaptive, and explainable industrial digital twins.

cs.AI↗

arXiv2026

Expected Free Energy as Belief-Dependent Utility for rho-POMDPs

An agent acting under partial observability must decide when to gather information and which observations are worth their cost. Standard POMDPs value information only through its eventual effect on reward. The $ρ$-POMDP framework instead rewards uncertainty reduction directly, through a belief-dependent utility $ρ$, but in practice both the choice of $ρ$ and the weight placed on it are tuned by hand for every task. We show that active inference removes this tuning entirely. Minimizing Expected Free Energy (EFE) is exactly equivalent to solving a $ρ$-POMDP whose utility is expected information gain, and the exploration weight is fixed at $w=1$ because the variational bound expresses pragmatic and epistemic value in the same units (nats). We prove this equivalence for observe-then-commit POMDPs and extend it to factored observation POMDPs, a broader class that covers interleaved observe-act problems such as non-destructive testing and mobile sensing, where gathering information leaves the hidden state unchanged. Experiments support the theory. Across environments ranging from the classic Tiger problem to RockSample and a new Structural Inspection benchmark with over 65,000 states, the untuned weight matches or outperforms reward-only planning at the same horizon, avoids the over-exploration of bonuses tuned per task, and sits near the reward-maximizing knee of the success-reward Pareto frontier. The practical payoff is an exploration objective that works out of the box. In applications such as fault detection and medical screening, where every test has a price and every missed fault has a cost, EFE supplies a belief-dependent utility that is derived rather than tuned.

cs.AI↗

arXiv2026

Narration-of-Thought: Inference-Time Scaffolding for Defeasible Ethical Reasoning in Large Language Models

Standard chain-of-thought on moral dilemmas exhibits two failure modes: stakeholder collapse (the trace names at most one party with a stake in the outcome) and uncertainty suppression (no explicit unknowns or hedges before committing to an action). We introduce narration-of-thought (NoT), a system prompt that structures chain-of-thought into five sections: protagonist, stakeholders, two-step consequences, uncertainty, then commitment. NoT adds no training, parameters, or fine-tuning. On 100 DailyDilemmas scenarios across four generators from three vendors, NoT cuts stakeholder collapse from up to 31% to under 1% and uncertainty suppression from up to 72% to 1-24% on every model. A matched-budget verbose-CoT control rules out token spend as the active ingredient; NoT retains Cliff's delta advantages of +0.79 to +0.90 on stakeholder count and +0.65 to +0.93 on uncertainty score for three of four generators, and a section ablation attributes each shift to its specific sub-instruction. Textual-gradient descent initialised at NoT improves the scaffold further; a cross-family training judge (different vendor from the generator) dominates an in-family one on every measured axis. Extended to a five-round multi-stakeholder debate protocol, the scaffold converts a 6% standoff into 95% full consensus on a calibration set and 100% combined convergence on a DailyDilemmas replication. The resulting traces externalise the stakeholders, consequences, and uncertainty grounding each commitment, providing an auditable substrate for dependable agentic deployment.

cs.AI↗

arXiv2026

Active Causal Experimentalist (ACE): Learning Intervention Strategies via Direct Preference Optimization

Discovering causal relationships requires controlled experiments, but experimentalists face a sequential decision problem: each intervention reveals information that should inform what to try next. Traditional approaches such as random sampling, greedy information maximization, and round-robin coverage treat each decision in isolation, unable to learn adaptive strategies from experience. We propose Active Causal Experimentalist (ACE), which learns experimental design as a sequential policy. Our key insight is that while absolute information gains diminish as knowledge accumulates (making value-based RL unstable), relative comparisons between candidate interventions remain meaningful throughout. ACE exploits this via Direct Preference Optimization, learning from pairwise intervention comparisons rather than non-stationary reward magnitudes. Across synthetic benchmarks, physics simulations, and economic data, ACE achieves 70-71% improvement over baselines at equal intervention budgets (p < 0.001, Cohen's d ~ 2). Notably, the learned policy autonomously discovers that collider mechanisms require concentrated interventions on parent variables, a theoretically-grounded strategy that emerges purely from experience. This suggests preference-based learning can recover principled experimental strategies, complementing theory with learned domain adaptation.

cs.LG↗

arXiv2026

Does Reasoning Preserve Alignment? On the Trustworthiness of Large Reasoning Models

Instruction-tuned LLMs are increasingly converted into reasoning models through post-training to improve multi-step task performance. This conversion is usually optimized for reasoning accuracy, without explicitly preserving the alignment behavior of the instruction-tuned model, such as safe refusal, bias avoidance, and privacy protection. We ask: does this conversion preserve alignment? We study this question through a trustworthiness audit and find that it is not behavior-preserving by default. For a systematic analysis, we compare reasoning models produced via supervised fine-tuning, RL-based post-training, and distillation against matched instruction-tuned baselines across six trustworthiness dimensions: safety, toxicity, stereotyping and bias, machine ethics, privacy, and out-of-distribution robustness. We observe that reasoning models often improve on reasoning benchmarks but exhibit alignment regressions, including increased toxicity, amplified stereotyping, miscalibrated refusal, and contextual privacy leakage. These regressions are consistent with behavioral drift from the instruction-tuned baseline, measured by KL divergence. Overall, our results point to the broader conclusion that trustworthiness metrics are essential for evaluating reasoning models and should be reported alongside gains in reasoning capability.

cs.CL↗

arXiv2026

ANNEAL: Adapting LLM Agents via Governed Symbolic Patch Learning

LLM-based agents can recover from individual execution errors, yet they repeatedly fail on the same fault when the underlying process knowledge--operator schemas, preconditions, and constraints--remains unrepaired. Existing self-evolving approaches address this gap by updating prompts, memory, or model weights, but none directly repair the symbolic structures that encode how tasks are executed, and few provide the governance guarantees required for safe deployment. We introduce ANNEAL, a neuro-symbolic agent that converts recurring failures into governed symbolic edits of a process knowledge graph without modifying foundation model weights. Its core mechanism, Failure-Driven Knowledge Acquisition (FDKA), localizes the responsible operator, synthesizes a typed patch through constrained LLM generation, and validates the proposal via multi-dimensional scoring, symbolic guardrails, and canary testing before commit. Every accepted edit carries full provenance and deterministic rollback capability. Across four domains and 27 multi-seed runs, ANNEAL is the only evaluated system that commits persistent structural repairs--strong baselines such as ReAct and Reflexion achieve high episodic recovery yet retain 72--100% holdout failure rates on recurring faults, whereas ANNEAL reduces these to 0% in the tested recurring-failure settings. Ablation confirms that removing FDKA eliminates all structural repairs and drops success rate by up to 26.7 percentage points. These results suggest that governed symbolic repair offers a complementary paradigm to weight-level and prompt-level adaptation for persistent fault elimination.

cs.AI↗