The Transformer architecture has emerged as a landmark advancement within the broad field of artificial intelligence, effectively catalyzing the advent of large language models (LLMs). However, despite its remarkable capabilities and the substantial progress it has facilitated, the Transformer architecture still has some limitations. One such intrinsic limitation is its inability to effectively recognize regular expressions or deterministic context-free grammars. Standard Transformers lack an explicit mechanism for recursion and structured state transitions, which can hinder systematic generalization on nested and hierarchical patterns. Drawing inspiration from pushdown automata, which efficiently resolve deterministic context-free grammars using stacks, we equip layers with a differentiable stack and propose STACKTRANS with recursion to address the aforementioned issue within LLMs. Unlike previous approaches that modify the attention computation, STACKTRANS explicitly incorporates hidden state stacks between Transformer layers. This design maintains compatibility with existing frameworks like flash-attention. Specifically, our design features stack operations - such as pushing and popping hidden states - that are differentiable and can be learned in an end-to-end manner.

Modern state-space models (SSMs) often utilize structured transition matrices which enable efficient computation but pose restrictions on the model's expressivity, as measured in terms of the ability to emulate finite-state automata (FSA). While unstructured transition matrices are optimal in terms of expressivity, they come at a prohibitively high compute and memory cost, even for moderate state sizes. We propose a structured sparse parametrization of transition matrices in SSMs that enables FSA state tracking with provably optimal state size and depth, while keeping the computational cost of the recurrence comparable to that of diagonal SSMs.

Recent work has revealed that state space models (SSMs), while efficient for longsequence processing, are fundamentally limited in their ability to represent formal languages--particularly due to time-invariant and real-valued recurrence structures. In this work, we draw inspiration from adaptive and structured dynamics observed in biological neural systems and introduce the Adaptive Unitary State Space Model (AUSSM): a novel class of SSMs that leverages skew-symmetric, input-dependent recurrence to achieve unitary evolution and high expressive power. Using algebraic automata theory, we prove that AUSSM can perform modulo counting and simulate solvable group automata at precision logarithmically bounded in the input length, enabling SSMs to model a broad class of regular languages out of reach for other SSM architectures. To overcome the practical inefficiencies of adaptive recurrence, we develop a separable convolution formulation and a CUDA implementation that enables scalable parallel training. Empirically, we show that AUSSM and its hybrid variant--interleaved with Mamba--outperform prior SSMs on formal algorithmic tasks such as parity and modular arithmetic, and achieve competent performance on real-world long time-series classification benchmarks. Our results demonstrate that adaptive unitary recurrence provides a powerful and efficient inductive bias for both symbolic and continuous sequence modeling.

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The transition rule is usually defined to update the state of each cell as a function of its current state and the state of its neighbours.

Deep neural networks have seen great success in recent years; however, training a deep model is often challenging as its performance heavily depends on the hyper-parameters used. In addition, finding the optimal hyper-parameter configuration, even with state-of-the-art (SOTA) hyper-parameter optimization (HPO) algorithms, can be time-consuming, requiring multiple training runs over the entire datasetfor different possible sets of hyper-parameters. Our central insight is that using an informative subset of the dataset for model training runs involved in hyper-parameter optimization, allows us to find the optimal hyper-parameter configuration significantly faster. In this work, we propose AUTOMATA, a gradient-based subset selection framework for hyper-parameter tuning. We empirically evaluate the effectiveness of AUTOMATA in hyper-parameter tuning through several experiments on real-world datasets in the text, vision, and tabular domains. Our experiments show that using gradient-based data subsets for hyper-parameter tuning achieves significantly faster turnaround times and speedups of 3 -30 while achieving comparable performance to the hyper-parameters found using the entire dataset.

Biological systems exhibit remarkable morphogenetic plasticity, where a single genome can encode various specialized cellular structures triggered by local chemical signals. In the domain of Deep Learning, Differentiable Neural Cellular Automata (NCA) have emerged as a paradigm to mimic this self-organization. However, existing NCA research has predominantly focused on continuous texture synthesis or single-target object recovery, leaving the challenge of class-conditional structural generation largely unexplored. In this work, we propose a novel Conditional Neural Cellular Automata (c-NCA) architecture capable of growing distinct topological structures - specifically MNIST digits - from a single generic seed, guided solely by a spatially broadcasted class vector. Unlike traditional generative models (e.g., GANs, VAEs) that rely on global reception fields, our model enforces strict locality and translation equivariance. We demonstrate that by injecting a one-hot condition into the cellular perception field, a single set of local rules can learn to break symmetry and self-assemble into ten distinct geometric attractors. Experimental results show that our c-NCA achieves stable convergence, correctly forming digit topologies from a single pixel, and exhibits robustness characteristic of biological systems. This work bridges the gap between texture-based NCAs and structural pattern formation, offering a lightweight, biologically plausible alternative for conditional generation.

Automata extraction is a method for synthesising interpretable surrogates for black-box neural models that can be analysed symbolically. Existing techniques assume a finite input alphabet, and thus are not directly applicable to data sequences drawn from continuous domains. We address this challenge with deterministic register automata (DRAs), which extend finite automata with registers that store and compare numeric values. Our main contribution is a framework for robust DRA extraction from black-box models: we develop a polynomial-time robustness checker for DRAs with a fixed number of registers, and combine it with passive and active automata learning algorithms. This combination yields surrogate DRAs with statistical robustness and equivalence guarantees. As a key application, we use the extracted automata to assess the robustness of neural networks: for a given sequence and distance metric, the DRA either certifies local robustness or produces a concrete counterexample. Experiments on recurrent neural networks and transformer architectures show that our framework reliably learns accurate automata and enables principled robustness evaluation. Overall, our results demonstrate that robust DRA extraction effectively bridges neural network interpretability and formal reasoning without requiring white-box access to the underlying network.

Automata learning has many applications in artificial intelligence and software engineering. Central to these applications is the $L^*$ algorithm, introduced by Angluin. The $L^*$ algorithm learns deterministic finite-state automata (DFAs) in polynomial time when provided with a minimally adequate teacher. Unfortunately, the $L^*$ algorithm can only learn DFAs over finite alphabets, which limits its applicability. In this paper, we extend $L^*$ to learn symbolic automata whose transitions use predicates over rational numbers, i.e., over infinite and dense alphabets. Our result makes the $L^*$ algorithm applicable to new settings like (real) RGX, and time series. Furthermore, our proposed algorithm is optimal in the sense that it asks a number of queries to the teacher that is at most linear with respect to the number of transitions, and to the representation size of the predicates.