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Carla P. Gomes

Publications and source records attributed to Carla P. Gomes.

At least 19 recordsLinked to original sources
arXiv2026

MoRE: Mixture of Reused Experts

Mixture-of-Experts (MoE) architectures decouple model capacity from computational cost, yet incur high memory footprints as parameters grow linearly with the number of experts. Recurrent Transformers achieve parameter efficiency by reusing layer weights, but typically lack the capacity for competitive language modeling. We propose Mixture of Reused Experts (MoRE), a hybrid that shares expert pools across groups of adjacent layers. Each layer retains its own router but selects from a larger shared pool, expanding the diversity of routing combinations without additional parameters. To enable shared experts to distinguish between layers, we introduce lightweight learnable depth embeddings that condition each layer's input before routing. Experiments across three model scales (114M-1.15B parameters) show that MoRE consistently achieves lower perplexity and stronger downstream performance than standard MoEs and state-of-the-art weight-sharing architectures at matched compute and parameter budgets, with only minimal modifications to existing MoE implementations.

cs.LG↗
arXiv2026

A Four-Stage Decomposition of Word-Problem Solving and Mechanistic Fragility in LLM Math Reasoning

Large language models solve grade-school math word problems with high accuracy, yet a single irrelevant clause inserted into the problem can collapse it. We reconcile these observations with a mechanistic account. We show that the model's internal computation decomposes into a four-stage sequential pipeline, Schema Abstraction, Operation Planning, Operand Binding, and Computation, each stage producing a distinct intermediate representation in an identifiable band of layers. Using the same scaffold to diagnose distractor-induced failure, we localize the corruption to a single stage, Operation Planning, implemented by a set of attention heads whose causal role we validate bidirectionally. In short, we provide a mechanistic interpretation of math word problem reasoning in LLMs, and their failure when distracted.

cs.AI↗
arXiv2026

Optimize Your Sampling: Tuned Diffusion Sampling with Bayesian Optimization

Sampling from a diffusion model typically requires many forward passes through a large neural network, making generation computationally expensive. While much work has focused on efficient solvers and samplers, comparatively little attention has been paid to selecting the sampling timesteps themselves. A recent line of work optimizes theoretically derived surrogates for sample quality rather than the quality metric itself. We propose Optimizing Your Sampling (OYS), which instead treats timestep selection as a black-box optimization problem, optimizing the target metric directly with Bayesian optimization. OYS outperforms both the default schedules and those of Align Your Steps on text-to-image generation, and improves over the default schedules on inpainting and other image tasks, in both quantitative and human evaluations. OYS requires no additional training, is applicable even to distilled models, and improves both simple and sophisticated samplers such as Euler and DPM-Solver++. A 5-step OYS schedule retains 89%-94% of the quality of a 50-step schedule while reducing inference cost by 10x.

cs.LG↗
arXiv2026

Agentic Neurosymbolic Collaboration for Mathematical Discovery: A Case Study in Combinatorial Design

We study mathematical discovery through the lens of neurosymbolic reasoning, where an AI agent powered by a large language model (LLM), coupled with symbolic computation tools, and human strategic direction, jointly produced a new result in combinatorial design theory. The main result of this human-AI collaboration is a tight lower bound on the imbalance of Latin squares for the notoriously difficult case $n \equiv 1 \pmod{3}$. We reconstruct the discovery process from detailed interaction logs spanning multiple sessions over several days and identify the distinct cognitive contributions of each component. The AI agent proved effective at uncovering hidden structure and generating hypotheses. The symbolic component consists of computer algebra, constraint solvers, and simulated annealing, which provides rigorous verification and exhaustive enumeration. Human steering supplied the critical research pivot that transformed a dead end into a productive inquiry. Our analysis reveals that multi-model deliberation among frontier LLMs proved reliable for criticism and error detection but unreliable for constructive claims. The resulting human-AI mathematical contribution, a tight lower bound of $4n(n{-}1)/9$, is achieved via a novel class of near-perfect permutations. The bound was formally verified in Lean 4. Our experiments show that neurosymbolic systems can indeed produce genuine discoveries in pure mathematics.

cs.AI↗
arXiv2026

Graph Neural Networks are Heuristics

Graph neural networks are usually treated as auxiliaries for combinatorial optimization: they imitate algorithms, guide search, or supply scores to classical procedures. We show that this auxiliary role is not intrinsic. A GNN can itself be a heuristic. For the Euclidean Travelling Salesman Problem, we train a non-autoregressive GNN with no labels, rewards, sequential decoding, search, or local improvement. A differentiable Hamiltonian-cycle objective is the only supervision. The trained model produces a complete tour in one forward pass, while dropout and snapshots from a single training trajectory provide solution diversity without engineered moves. The heuristic is therefore learned, not programmed. It is also fast: batched inference remains in the millisecond regime on GPUs. Experiments on TSP100, TSP200, and TSP500 show that the model consistently improves over nearest-neighbor greedy baselines. These results identify unsupervised GNNs as a class of fast learned heuristics for combinatorial optimization.

cs.AI↗
arXiv2026

STELLAR: Spatio-Temporal Environmental Learning with Latent Alignment and Refinement for Long-Tailed Species Distribution Modeling

Joint Species Distribution Modeling (JSDM) is a key enabler for biodiversity monitoring and conservation planning. However, accurate JSDM faces two coupled challenges: environmental drivers and species distributions are inherently spatio-temporal, while species co-occurrence patterns exhibit complex non-linear community structure and severe long-tail imbalance driven by rare species. Existing approaches often address these factors in isolation, learning from static covariates or neglecting the historical trajectories of dynamic community structure. To overcome these limitations, we propose STELLAR (Spatio-Temporal Environmental Learning with Latent Alignment and Refinement), a novel framework that learns a shared latent space where dynamic habitat context and community structure are optimized jointly. Our approach integrates three complementary components: (1) a Graph-Temporal Encoder that employs graph attention and recurrent units to aggregate spatial neighborhood effects and capture the co-evolving historical dynamics of environmental context and community structure; (2) a Context-Anchored Latent Alignment mechanism that structures the latent space using a label-activated mixture prior and supervised contrastive learning, actively clustering species based on shared environmental preferences; and (3) an Imbalance-Aware Decoupled Decoding module that utilizes Asymmetric Loss to focus learning on hard, rare species samples, preventing mode collapse in the long tail. Experiments on the large-scale eBird dataset, curated with domain experts, demonstrate that our framework significantly outperforms state-of-the-art baselines, particularly in predicting rare species and revealing interpretable species interactions.

cs.LG↗
arXiv2026

Divergence-Suppressing Couplings for Rectified Flow

The promise of Rectified Flow rests on producing self-generated couplings whose trajectories are straight, or nearly so. In practice, trajectories generated by the base flow model can bend and intertwine, and the resulting coupling inherits this distortion. In this paper, we identify that such trajectory entanglement is often associated with regions of nonzero divergence in the learned velocity field, where local expansion or contraction distorts trajectories and steers particles away from their ideal endpoints. We then propose divergence-suppressing couplings for Rectified Flow, an offline correction that attenuate the divergent component of the learned velocity during coupling generation. The correction is paid only once per coupling pair and amortized over training, so deployment runs plain Euler at identical wall-clock cost to standard Rectified Flow. Empirically, this offline modification yields consistent improvements on 2D synthetic benchmarks and on image generation.

cs.AI↗
arXiv2026

Learning Unbiased Permutations via Flow Matching

Learning permutations is fundamental to sorting, ranking, and matching, but existing differentiable methods based on entropy-regularized Sinkhorn produce a single softened solution and collapse under ambiguity. We present PermFlow, a conditional flow matching framework that operates directly on the affine subspace of matrices with unit row and column sums. A closed-form tangent-space projector preserves these constraints exactly along every trajectory, by construction rather than through iterative correction, and a nearest-target coupling routes distinct noisy initializations toward distinct valid permutations. The result is a model that captures multimodal permutation distributions rather than collapsing them to a single mode. On a visual sorting task with blended-digit ambiguity and a symmetric linear assignment problem, PermFlow achieves high accuracy on unambiguous inputs and recovers both valid permutations under ambiguity, where Sinkhorn-based baselines structurally fail.

cs.LG↗
arXiv2026

Evaluating Large Language Models in Scientific Discovery

Large language models (LLMs) are increasingly applied to scientific research, yet prevailing science benchmarks probe decontextualized knowledge and overlook the iterative reasoning, hypothesis generation, and observation interpretation that drive scientific discovery. We introduce a scenario-grounded benchmark that evaluates LLMs across biology, chemistry, materials, and physics, where domain experts define research projects of genuine interest and decompose them into modular research scenarios from which vetted questions are sampled. The framework assesses models at two levels: (i) question-level accuracy on scenario-tied items and (ii) project-level performance, where models must propose testable hypotheses, design simulations or experiments, and interpret results. Applying this two-phase scientific discovery evaluation (SDE) framework to state-of-the-art LLMs reveals a consistent performance gap relative to general science benchmarks, diminishing return of scaling up model sizes and reasoning, and systematic weaknesses shared across top-tier models from different providers. Large performance variation in research scenarios leads to changing choices of the best performing model on scientific discovery projects evaluated, suggesting all current LLMs are distant to general scientific "superintelligence". Nevertheless, LLMs already demonstrate promise in a great variety of scientific discovery projects, including cases where constituent scenario scores are low, highlighting the role of guided exploration and serendipity in discovery. This SDE framework offers a reproducible benchmark for discovery-relevant evaluation of LLMs and charts practical paths to advance their development toward scientific discovery.

cs.AI↗
arXiv2026

Adaptive Moments are Surprisingly Effective for Plug-and-Play Diffusion Sampling

Guided diffusion sampling relies on approximating often intractable likelihood scores, which introduces significant noise into the sampling dynamics. We propose using adaptive moment estimation to stabilize these noisy likelihood scores during sampling. Despite its simplicity, our approach achieves state-of-the-art results on image restoration and class-conditional generation tasks, outperforming more complicated methods, which are often computationally more expensive. We provide empirical analysis of our method on both synthetic and real data, demonstrating that mitigating gradient noise through adaptive moments offers an effective way to improve alignment.

cs.LG↗
arXiv2026

Accelerating Scientific Discovery with Autonomous Goal-evolving Agents

There has been unprecedented interest in developing agents that expand the boundary of scientific discovery, primarily by optimizing quantitative objective functions specified by scientists. However, for grand challenges in science, these objectives may only be imperfect proxies. We argue that automating objective function design is a central, yet unmet need for scientific discovery agents. In this work, we introduce the Scientific Autonomous Goal-evolving Agent (SAGA) to address this challenge. SAGA employs a bi-level architecture in which an outer loop of LLM agents analyzes optimization outcomes, proposes new objectives, and converts them into computable scoring functions, while an inner loop performs solution optimization under the current objectives. This bi-level design enables systematic exploration of the space of objectives and their trade-offs, rather than treating them as fixed inputs. We demonstrate the framework through a wide range of design applications, including antibiotics, nanobodies, functional DNA sequences, inorganic materials, and chemical processes. Notably, our experimental validation identifies a structurally novel hit with promising potency and safety profiles for E. coli in the antibiotic design task, and three de novo PD-L1 binders in the nanobody design task. These results suggest that automating objective formulation can substantially improve the effectiveness of scientific discovery agents.

cs.AI↗
arXiv2026

Biogeochemistry-Informed Neural Network (BINN) for Improving Accuracy of Model Prediction and Scientific Understanding of Soil Organic Carbon

The increasing availability of large-scale observational data and the rapid development of artificial intelligence (AI) provide unprecedented opportunities to enhance our understanding of the global carbon cycle and other biogeochemical processes. However, retrieving mechanistic knowledge from these large-scale data remains a challenge. Here, we develop a Biogeochemistry-Informed Neural Network (BINN) that seamlessly integrates a vectorized process-based soil carbon cycle model (i.e., Community Land Model version 5, CLM5) into a neural network (NN) structure to examine mechanisms governing soil organic carbon (SOC) storage from big data. BINN demonstrates high accuracy in retrieving biogeochemical parameter values from synthetic data in a parameter recovery experiment. Furthermore, by incorporating Monte Carlo (MC) dropout to generate posterior distributions, we demonstrate that BINN can effectively quantify uncertainty in estimated parameters. We use BINN to predict six major processes (or components in process-based models) regulating the soil carbon cycle from 25,925 observed SOC profiles across the contiguous US and compare them with the same processes previously retrieved by a Bayesian inference-based PROcess-guided deep learning and DAta-driven modeling (PRODA) approach. The good agreement between the spatial patterns retrieved by BINN and PRODA (average correlation coefficient = 0.86) suggests that BINN's ability of capturing mechanistic knowledge is consistent with the established Bayesian-based methods. Additionally, the integration of neural networks and process-based models in BINN improves computational efficiency by more than 50 times over PRODA. We conclude that BINN is an efficient framework that harnesses the power of both AI, large-scale data, and process-based modeling to understand large scale soil carbon cycle.

physics.geo-ph↗
arXiv2026

Learning from Synthetic Data Improves Multi-hop Reasoning

Reinforcement Learning (RL) has been shown to significantly boost reasoning capabilities of large language models (LLMs) in math, coding, and multi-hop reasoning tasks. However, RL fine-tuning requires abundant high-quality verifiable data, often sourced from human annotations, generated from frontier LLMs, or scored by LLM-based verifiers. All three have considerable limitations: human-annotated datasets are small and expensive to curate, LLM-generated data is hallucination-prone and costly, and LLM-based verifiers are inaccurate and slow. In this work, we investigate a cheaper alternative: RL fine-tuning on rule-generated synthetic data for multi-hop reasoning tasks. We discover that LLMs fine-tuned on synthetic data perform significantly better on popular real-world question-answering benchmarks, despite the synthetic data containing only fictional knowledge. On stratifying performance by question difficulty, we find that synthetic data teaches LLMs to compose knowledge -- a fundamental and generalizable reasoning skill. Our work highlights rule-generated synthetic reasoning data as a free and scalable resource to improve LLM reasoning capabilities.

cs.LG↗
arXiv2026

HeuriGym: An Agentic Benchmark for LLM-Crafted Heuristics in Combinatorial Optimization

While Large Language Models (LLMs) have demonstrated significant advancements in reasoning and agent-based problem-solving, current evaluation methodologies fail to adequately assess their capabilities: existing benchmarks either rely on closed-ended questions prone to saturation and memorization, or subjective comparisons that lack consistency and rigor. In this work, we introduce HeuriGym, an agentic framework designed for evaluating heuristic algorithms generated by LLMs for combinatorial optimization problems, characterized by clearly defined objectives and expansive solution spaces. HeuriGym empowers LLMs to propose heuristics, receive evaluative feedback via code execution, and iteratively refine their solutions. We evaluate nine state-of-the-art models on nine problems across domains such as computer systems, logistics, and biology, exposing persistent limitations in tool use, planning, and adaptive reasoning. To quantify performance, we propose the Quality-Yield Index (QYI), a metric that captures both solution pass rate and quality. Even top models like GPT-o4-mini-high and Gemini-2.5-Pro attain QYI scores of only 0.6, well below the expert baseline of 1. Our open-source benchmark aims to guide the development of LLMs toward more effective and realistic problem-solving in scientific and engineering domains.

cs.LG↗
arXiv2026

Scientifically-Interpretable Reasoning Network (ScIReN): Discovering Hidden Relationships in the Carbon Cycle and Beyond

Soils have potential to mitigate climate change by sequestering carbon from the atmosphere, but the soil carbon cycle remains poorly understood. Scientists have developed process-based models of the soil carbon cycle based on existing knowledge, but they contain numerous unknown parameters and often fit observations poorly. On the other hand, neural networks can learn patterns from data, but do not respect known scientific laws, and are too opaque to reveal novel scientific relationships. We thus propose Scientifically-Interpretable Reasoning Network (ScIReN), a fully-transparent framework that combines interpretable neural and process-based reasoning. An interpretable encoder predicts scientifically-meaningful latent parameters, which are then passed through a differentiable process-based decoder to predict labeled output variables. While the process-based decoder enforces existing scientific knowledge, the encoder leverages Kolmogorov-Arnold networks (KANs) to reveal interpretable relationships between input features and latent parameters, using novel smoothness penalties to balance expressivity and simplicity. ScIReN also introduces a novel hard-sigmoid constraint layer to restrict latent parameters into prior ranges while maintaining interpretability. We apply ScIReN on two tasks: simulating the flow of organic carbon through soils, and modeling ecosystem respiration from plants. On both tasks, ScIReN outperforms or matches black-box models in predictive accuracy, while greatly improving scientific interpretability -- it can infer latent scientific mechanisms and their relationships with input features.

cs.LG↗
arXiv2026

LabelKAN -- Kolmogorov-Arnold Networks for Inter-Label Learning: Avian Community Learning

Global biodiversity loss is accelerating, prompting international efforts such as the Kunming-Montreal Global Biodiversity Framework (GBF) and the United Nations Sustainable Development Goals to direct resources toward halting species declines. A key challenge in achieving this goal is having access to robust methodologies to understand where species occur and how they relate to each other within broader ecological communities. Recent deep learning-based advances in joint species distribution modeling have shown improved predictive performance, but effectively incorporating community-level learning, taking into account species-species relationships in addition to species-environment relationships, remains an outstanding challenge. We introduce LabelKAN, a novel framework based on Kolmogorov-Arnold Networks (KANs) to learn inter-label connections from predictions of each label. When modeling avian species distributions, LabelKAN achieves substantial gains in predictive performance across the vast majority of species. In particular, our method demonstrates strong improvements for rare and difficult-to-predict species, which are often the most important when setting biodiversity targets under frameworks like GBF. These performance gains also translate to more confident predictions of the species spatial patterns as well as more confident predictions of community structure. We illustrate how the LabelKAN leads to qualitative and quantitative improvements with a focused application on the Great Blue Heron, an emblematic species in freshwater ecosystems that has experienced significant population declines across the United States in recent years. Using the LabelKAN framework, we are able to identify communities and species in New York that will be most sensitive to further declines in Great Blue Heron populations.

q-bio.QM↗
arXiv2026

FEAT: Free energy Estimators with Adaptive Transport

We present Free energy Estimators with Adaptive Transport (FEAT), a novel framework for free energy estimation -- a critical challenge across scientific domains. FEAT leverages learned transports implemented via stochastic interpolants and provides consistent, minimum-variance estimators based on escorted Jarzynski equality and controlled Crooks theorem, alongside variational upper and lower bounds on free energy differences. Unifying equilibrium and non-equilibrium methods under a single theoretical framework, FEAT establishes a principled foundation for neural free energy calculations. Experimental validation on toy examples, molecular simulations, and quantum field theory demonstrates improvements over existing learning-based methods. Our PyTorch implementation is available at https://github.com/jiajunhe98/FEAT.

stat.ML↗
arXiv2026

Autonomous Materials Exploration by Integrating Automated Phase Identification and AI-Assisted Human Reasoning

Autonomous experimentation holds the potential to accelerate materials development by combining artificial intelligence (AI) with modular robotic platforms to explore extensive combinatorial chemical and processing spaces. Such self-driving laboratories can not only increase the throughput of repetitive experiments, but also incorporate human domain expertise to drive the search towards user-defined objectives, including improved materials performance metrics. We present an autonomous materials synthesis extension to SARA, the Scientific Autonomous Reasoning Agent, utilizing phase information provided by an automated probabilistic phase labeling algorithm to expedite the search for targeted phase regions. By incorporating human input into an expanded SARA-H (SARA with human-in-the-loop) framework, we enhance the efficiency of the underlying reasoning process. Using synthetic benchmarks, we demonstrate the efficiency of our AI implementation and show that the human input can contribute to significant improvement in sampling efficiency. We conduct experimental active learning campaigns using robotic processing of thin-film samples of several oxide material systems, including Bi$_2$O$_3$, SnO$_x$, and Bi-Ti-O, using lateral-gradient laser spike annealing to synthesize and kinetically trap metastable phases. We showcase the utility of human-in-the-loop autonomous experimentation for the Bi-Ti-O system, where we identify extensive processing domains that stabilize $δ$-Bi$_2$O$_3$ and Bi$_2$Ti$_2$O$_7$, explore dwell-dependent ternary oxide phase behavior, and provide evidence confirming predictions that cationic substitutional doping of TiO$_2$ with Bi inhibits the unfavorable transformation of the metastable anatase to the ground-state rutile phase. The autonomous methods we have developed enable the discovery of new materials and new understanding of materials synthesis and properties.

cond-mat.mtrl-sci↗