More Like this

1. Symbolic Rule Extraction From Attention-Guided Sparse Representations in Vision Transformers

   https://doi.org/10.1017/S1471068425100318  

   PADALKAR, PARTH; GUPTA, GOPAL (July 2025, Theory and Practice of Logic Programming)

   Abstract Recentneuro-symbolic approaches have successfully extracted symbolic rule-sets from Convolutional Neural Network-based models to enhance interpretability. However, applying similar techniques to Vision Transformers (ViTs) remains challenging due to their lack of modular concept detectors and reliance on global self-attention mechanisms. We propose a framework for symbolic rule extraction from ViTs by introducing a sparse concept layer inspired by Sparse Autoencoders (SAEs). This linear layer operates on attention-weighted patch representations and learns a disentangled, binarized representation in which individual neurons activate for high-level visual concepts. To encourage interpretability, we apply a combination of L1 sparsity, entropy minimization, and supervised contrastive loss. These binarized concept activations are used as input to the FOLD-SE-M algorithm, which generates a rule-set in the form of a logic program. Our method achieves abetter classification accuracy than the standard ViT while enabling symbolic reasoning. Crucially, the extracted rule-set is not merely post-hoc but acts as a logic-based decision layer that operates directly on the sparse concept representations. The resulting programs are concise and semantically meaningful. This work is the first to extract executable logic programs from ViTs using sparse symbolic representations, providing a step forward in interpretable and verifiable neuro-symbolic AI. 

   more » « less
2. Discovering sparse interpretable dynamics from partial observations

   https://doi.org/10.1038/s42005-022-00987-z  

   Lu, Peter Y.; Ariño Bernad, Joan; Soljačić, Marin (August 2022, Communications Physics)

   Abstract Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. Achieving this kind of interpretable system identification is even more difficult for partially observed systems. We propose a machine learning framework for discovering the governing equations of a dynamical system using only partial observations, combining an encoder for state reconstruction with a sparse symbolic model. The entire architecture is trained end-to-end by matching the higher-order symbolic time derivatives of the sparse symbolic model with finite difference estimates from the data. Our tests show that this method can successfully reconstruct the full system state and identify the equations of motion governing the underlying dynamics for a variety of ordinary differential equation (ODE) and partial differential equation (PDE) systems. 

   more » « less
3. High-performance symbolic-numerics via multiple dispatch

   https://doi.org/10.1145/3511528.3511535  

   Gowda, Shashi; Ma, Yingbo; Cheli, Alessandro; Gwóźzdź, Maja; Shah, Viral B.; Edelman, Alan; Rackauckas, Christopher (September 2021, ACM Communications in Computer Algebra)

   As mathematical computing becomes more democratized in high-level languages, high-performance symbolic-numeric systems are necessary for domain scientists and engineers to get the best performance out of their machine without deep knowledge of code optimization. Naturally, users need different term types either to have different algebraic properties for them, or to use efficient data structures. To this end, we developed Symbolics.jl, an extendable symbolic system which uses dynamic multiple dispatch to change behavior depending on the domain needs. In this work we detail an underlying abstract term interface which allows for speed without sacrificing generality. We show that by formalizing a generic API on actions independent of implementation, we can retroactively add optimized data structures to our system without changing the pre-existing term rewriters. We showcase how this can be used to optimize term construction and give a 113x acceleration on general symbolic transformations. Further, we show that such a generic API allows for complementary term-rewriting implementations. Exploiting this feature, we demonstrate the ability to swap between classical term-rewriting simplifiers and e-graph-based term-rewriting simplifiers. We illustrate how this symbolic system improves numerical computing tasks by showcasing an e-graph ruleset which minimizes the number of CPU cycles during expression evaluation, and demonstrate how it simplifies a real-world reaction-network simulation to halve the runtime. Additionally, we show a reaction-diffusion partial differential equation solver which is able to be automatically converted into symbolic expressions via multiple dispatch tracing, which is subsequently accelerated and parallelized to give a 157x simulation speedup. Together, this presents Symbolics.jl as a next-generation symbolic-numeric computing environment geared towards modeling and simulation. 

   more » « less
4. TinyNS: Platform-Aware Neurosymbolic Auto Tiny Machine Learning

   https://doi.org/10.1145/3603171  

   Saha, Swapnil Sayan; Sandha, Sandeep Singh; Aggarwal, Mohit; Wang, Brian; Han, Liying; Briseno, Julian de; Srivastava, Mani (May 2023, ACM Transactions on Embedded Computing Systems)

   Machine learning at the extreme edge has enabled a plethora of intelligent, time-critical, and remote applications. However, deploying interpretable artificial intelligence systems that can perform high-level symbolic reasoning and satisfy the underlying system rules and physics within the tight platform resource constraints is challenging. In this paper, we introduceTinyNS, the first platform-aware neurosymbolic architecture search framework for joint optimization of symbolic and neural operators.TinyNSprovides recipes and parsers to automatically write microcontroller code for five types of neurosymbolic models, combining the context awareness and integrity of symbolic techniques with the robustness and performance of machine learning models.TinyNSuses a fast, gradient-free, black-box Bayesian optimizer over discontinuous, conditional, numeric, and categorical search spaces to find the best synergy of symbolic code and neural networks within the hardware resource budget. To guarantee deployability,TinyNStalks to the target hardware during the optimization process. We showcase the utility ofTinyNSby deploying microcontroller-class neurosymbolic models through several case studies. In all use cases,TinyNSoutperforms purely neural or purely symbolic approaches while guaranteeing execution on real hardware. 

   more » « less
5. Automatic Differentiation in Machine Learning: a Survey

   Baydin, A.G.; Pearlmutter, B.A.; Radul, A.A; Siskind, J.M (April 2018, Journal of machine learning research)

   Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD), also called algorithmic differentiation or simply ``autodiff'', is a family of techniques similar to but more general than backpropagation for efficiently and accurately evaluating derivatives of numeric functions expressed as computer programs. AD is a small but established field with applications in areas including computational fluid dynamics, atmospheric sciences, and engineering design optimization. Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results. Despite its relevance, general-purpose AD has been missing from the machine learning toolbox, a situation slowly changing with its ongoing adoption under the names ``dynamic computational graphs'' and ``differentiable programming''. We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main implementation techniques. By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of the terms ``autodiff'', ``automatic differentiation'', and ``symbolic differentiation'' as these are encountered more and more in machine learning settings. 

   more » « less