Large Language Models (LLMs) have recently demonstrated remarkable reasoning ability as in Chain-of-thought prompting, but faithful multi-step reasoning remains a challenge. We specifically focus on backward chaining, where the query is recursively decomposed using logical rules until proven. To address the limitations of current backward chaining implementations, we propose SymBa (Symbolic Backward Chaining). In SymBa, the symbolic top-down solver controls the entire proof process and the LLM is called to generate a single reasoning step only when the solver encounters a dead end. By this novel solver-LLM integration, while being able to produce an interpretable, structured proof, SymBa achieves significant improvement in performance, proof faithfulness, and efficiency in diverse multi-step reasoning benchmarks (ProofWriter, Birds-Electricity, GSM8k, CLUTRR-TF, ECtHR Article 6) compared to backward chaining baselines.

The paper proposes a new algorithm called SymBa that aims to achieve more biologically plausible learning than Back-Propagation (BP). The algorithm is based on the Forward-Forward (FF) algorithm, which is a BP-free method for training neural networks. SymBa improves the FF algorithm's convergence behavior by addressing the problem of asymmetric gradients caused by conflicting converging directions for positive and negative samples. The algorithm balances positive and negative losses to enhance performance and convergence speed. Furthermore, it modifies the FF algorithm by adding Intrinsic Class Pattern (ICP) containing class information to prevent the loss of class information during training. The proposed algorithm has the potential to improve our understanding of how the brain learns and processes information and to develop more effective and efficient artificial intelligence systems. The paper presents experimental results that demonstrate the effectiveness of SymBa algorithm compared to the FF algorithm and BP.

The cross section is one of the most important physical quantities in high-energy physics and the most time consuming to compute. While machine learning has proven to be highly successful in numerical calculations in high-energy physics, analytical calculations using machine learning are still in their infancy. In this work, we use a sequence-to-sequence model, specifically, a transformer, to compute a key element of the cross section calculation, namely, the squared amplitude of an interaction. We show that a transformer model is able to predict correctly 97.6% and 99% of squared amplitudes of QCD and QED processes, respectively, at a speed that is up to orders of magnitude faster than current symbolic computation frameworks. We discuss the performance of the current model, its limitations and possible future directions for this work.