Santiago Gonzalez

Santiago Gonzalez, Alireza Amiri Bavandpour, Peter Ye et al.

As Large Language Models (LLMs) saturate elementary benchmarks, the research frontier has shifted from generation to the reliability of automated evaluation. We demonstrate that standard "LLM-as-a-Judge" protocols suffer from a systematic Alignment Gap when applied to upper-undergraduate to early graduate level mathematics. To quantify this, we introduce QEDBench, the first large-scale dual-rubric alignment benchmark to systematically measure alignment with human experts on university-level math proofs by contrasting course-specific rubrics against expert common knowledge criteria. By deploying a dual-evaluation matrix (7 judges x 5 solvers) against 1,000+ hours of human evaluation, we reveal that certain frontier evaluators like Claude Opus 4.5, DeepSeek-V3, Qwen 2.5 Max, and Llama 4 Maverick exhibit significant positive bias (up to +0.18, +0.20, +0.30, +0.36 mean score inflation, respectively). Furthermore, we uncover a critical reasoning gap in the discrete domain: while Gemini 3.0 Pro achieves state-of-the-art performance (0.91 average human evaluation score), other reasoning models like GPT-5 Pro and Claude Sonnet 4.5 see their performance significantly degrade in discrete domains. Specifically, their average human evaluation scores drop to 0.72 and 0.63 in Discrete Math, and to 0.74 and 0.50 in Graph Theory. In addition to these research results, we also release QEDBench as a public benchmark for evaluating and improving AI judges. Our benchmark is publicly published at https://github.com/qqliu/Yale-QEDBench.

Santiago Gonzalez, Mohak Kant, Risto Miikkulainen

Generative Adversarial Networks (GANs) have extended deep learning to complex generation and translation tasks across different data modalities. However, GANs are notoriously difficult to train: Mode collapse and other instabilities in the training process often degrade the quality of the generated results, such as images. This paper presents a new technique called TaylorGAN for improving GANs by discovering customized loss functions for each of its two networks. The loss functions are parameterized as Taylor expansions and optimized through multiobjective evolution. On an image-to-image translation benchmark task, this approach qualitatively improves generated image quality and quantitatively improves two independent GAN performance metrics. It therefore forms a promising approach for applying GANs to more challenging tasks in the future.

Santiago Gonzalez, Xin Qiu, Risto Miikkulainen

Evolutionary computation can be used to optimize several different aspects of neural network architectures. For instance, the TaylorGLO method discovers novel, customized loss functions, resulting in improved performance, faster training, and improved data utilization. A likely reason is that such functions discourage overfitting, leading to effective regularization. This paper demonstrates theoretically that this is indeed the case for TaylorGLO. Learning rule decomposition reveals that evolved loss functions balance two factors: the pull toward zero error, and a push away from it to avoid overfitting. This is a general principle that may be used to understand other regularization techniques as well (as demonstrated in this paper for label smoothing). The theoretical analysis leads to a constraint that can be utilized to find more effective loss functions in practice; the mechanism also results in networks that are more robust (as demonstrated in this paper with adversarial inputs). The analysis in this paper thus constitutes a first step towards understanding regularization, and demonstrates the power of evolutionary neural architecture search in general.

Olivier Francon, Santiago Gonzalez, Babak Hodjat et al.

There is now significant historical data available on decision making in organizations, consisting of the decision problem, what decisions were made, and how desirable the outcomes were. Using this data, it is possible to learn a surrogate model, and with that model, evolve a decision strategy that optimizes the outcomes. This paper introduces a general such approach, called Evolutionary Surrogate-Assisted Prescription, or ESP. The surrogate is, for example, a random forest or a neural network trained with gradient descent, and the strategy is a neural network that is evolved to maximize the predictions of the surrogate model. ESP is further extended in this paper to sequential decision-making tasks, which makes it possible to evaluate the framework in reinforcement learning (RL) benchmarks. Because the majority of evaluations are done on the surrogate, ESP is more sample efficient, has lower variance, and lower regret than standard RL approaches. Surprisingly, its solutions are also better because both the surrogate and the strategy network regularize the decision-making behavior. ESP thus forms a promising foundation to decision optimization in real-world problems.

Jason Liang, Santiago Gonzalez, Hormoz Shahrzad et al.

Metalearning of deep neural network (DNN) architectures and hyperparameters has become an increasingly important area of research. At the same time, network regularization has been recognized as a crucial dimension to effective training of DNNs. However, the role of metalearning in establishing effective regularization has not yet been fully explored. There is recent evidence that loss-function optimization could play this role, however it is computationally impractical as an outer loop to full training. This paper presents an algorithm called Evolutionary Population-Based Training (EPBT) that interleaves the training of a DNN's weights with the metalearning of loss functions. They are parameterized using multivariate Taylor expansions that EPBT can directly optimize. Such simultaneous adaptation of weights and loss functions can be deceptive, and therefore EPBT uses a quality-diversity heuristic called Novelty Pulsation as well as knowledge distillation to prevent overfitting during training. On the CIFAR-10 and SVHN image classification benchmarks, EPBT results in faster, more accurate learning. The discovered hyperparameters adapt to the training process and serve to regularize the learning task by discouraging overfitting to the labels. EPBT thus demonstrates a practical instantiation of regularization metalearning based on simultaneous training.

Santiago Gonzalez, Risto Miikkulainen

Metalearning of deep neural network (DNN) architectures and hyperparameters has become an increasingly important area of research. Loss functions are a type of metaknowledge that is crucial to effective training of DNNs, however, their potential role in metalearning has not yet been fully explored. Whereas early work focused on genetic programming (GP) on tree representations, this paper proposes continuous CMA-ES optimization of multivariate Taylor polynomial parameterizations. This approach, TaylorGLO, makes it possible to represent and search useful loss functions more effectively. In MNIST, CIFAR-10, and SVHN benchmark tasks, TaylorGLO finds new loss functions that outperform functions previously discovered through GP, as well as the standard cross-entropy loss, in fewer generations. These functions serve to regularize the learning task by discouraging overfitting to the labels, which is particularly useful in tasks where limited training data is available. The results thus demonstrate that loss function optimization is a productive new avenue for metalearning.

Santiago Gonzalez, Risto Miikkulainen

As the complexity of neural network models has grown, it has become increasingly important to optimize their design automatically through metalearning. Methods for discovering hyperparameters, topologies, and learning rate schedules have lead to significant increases in performance. This paper shows that loss functions can be optimized with metalearning as well, and result in similar improvements. The method, Genetic Loss-function Optimization (GLO), discovers loss functions de novo, and optimizes them for a target task. Leveraging techniques from genetic programming, GLO builds loss functions hierarchically from a set of operators and leaf nodes. These functions are repeatedly recombined and mutated to find an optimal structure, and then a covariance-matrix adaptation evolutionary strategy (CMA-ES) is used to find optimal coefficients. Networks trained with GLO loss functions are found to outperform the standard cross-entropy loss on standard image classification tasks. Training with these new loss functions requires fewer steps, results in lower test error, and allows for smaller datasets to be used. Loss-function optimization thus provides a new dimension of metalearning, and constitutes an important step towards AutoML.