Language model systems often enable LLMs to generate code for arithmetic operations to achieve accurate calculations.

To achieve accurate calculations, language model systems often enable LLMs to generate code for arithmetic operations. However, this approach compromises speed and security and, if finetuning is involved, risks the language model losing prior capabilities. We propose a framework that enables exact arithmetic in a single autoregressive step, providing faster, more secure, and more interpretable LLM systems with arithmetic capabilities. We use the hidden states of an LLM to control a symbolic architecture which performs arithmetic. Our implementation using Llama 3 8B Instruct with OccamNet as a symbolic model (OccamLlama) achieves 100% accuracy on single arithmetic operations (+,,,, sin, cos, log, exp,), outperforming GPT 4o and on par with GPT 4o using a code interpreter. OccamLlama also outperforms GPT 4o both with and without a code interpreter on mathematical problem solving benchmarks involving challenging arithmetic, thus enabling small LLMs to match the arithmetic performance of even much larger models. We will make our code public shortly.

In social science, formal and quantitative models, such as ones describing economic growth and collective action, are used to formulate mechanistic explanations, provide predictions, and uncover questions about observed phenomena. Here, we demonstrate the use of a machine learning system to aid the discovery of symbolic models that capture nonlinear and dynamical relationships in social science datasets. By extending neuro-symbolic methods to find compact functions and differential equations in noisy and longitudinal data, we show that our system can be used to discover interpretable models from real-world data in economics and sociology. Augmenting existing workflows with symbolic regression can help uncover novel relationships and explore counterfactual models during the scientific process. We propose that this AI-assisted framework can bridge parametric and non-parametric models commonly employed in social science research by systematically exploring the space of nonlinear models and enabling fine-grained control over expressivity and interpretability.

Dataset bias and spurious correlations can significantly impair generalization in deep neural networks. Many prior efforts have addressed this problem using either alternative loss functions or sampling strategies that focus on rare patterns. We propose a new direction: modifying the network architecture to impose inductive biases that make the network robust to dataset bias. Specifically, we propose OccamNets, which are biased to favor simpler solutions by design. OccamNets have two inductive biases. First, they are biased to use as little network depth as needed for an individual example. Second, they are biased toward using fewer image locations for prediction. While OccamNets are biased toward simpler hypotheses, they can learn more complex hypotheses if necessary. In experiments, OccamNets outperform or rival state-of-the-art methods run on architectures that do not incorporate these inductive biases. Furthermore, we demonstrate that when the state-of-the-art debiasing methods are combined with OccamNets results further improve.

A key factor in the modern success of deep learning is the astonishing expressive power of neural networks. However, this comes at the cost of complex, black-boxed models that are unable to extrapolate beyond the domain of the training dataset, conflicting with goals of expressing physical laws or building human-readable programs. In this paper, we introduce OccamNet, a neural network model that can find interpretable, compact and sparse solutions for fitting data, \`{a} la Occam's razor. Our model defines a probability distribution over a non-differentiable function space, and we introduce an optimization method that samples functions and updates the weights based on cross-entropy matching in an evolutionary strategy: we train by biasing the probability mass towards better fitting solutions. We demonstrate that we can fit a variety of algorithms, ranging from simple analytic functions through recursive programs to even simple image classification. Our method takes minimal memory footprint, does not require AI accelerators for efficient training, fits complicated functions in minutes of training on a single CPU, and demonstrates significant performance gains when scaled on GPU. Our implementation, demonstrations and instructions for reproducing the experiments are available at https://github.com/AllanSCosta/occam-net.