arXiv subjects

Arjun Karuvally

Publications and source records attributed to Arjun Karuvally.

11 recordsLinked to original sources

arXiv2026

When RL Suppresses Its Own Vocabulary: Recovering Reasoning Diversity in Puzzle-to-Math Transfer

Reinforcement learning using verifiable rewards (RLVR) improves LLM reasoning, but the conditions under which it transfers across domains -- and why it does so -- remain under-explored. We study cross-domain transfer in a 7B model whose SFT and RL post-training stages use only constraint-satisfaction puzzles, with no mathematics problems in the post-training data. To analyze how transfer emerges, we introduce a reasoning primitive-level framework that combines a 9-class span classifier with motif extraction, allowing us to segment chain-of-thought traces into primitive motifs and track their evolution across training stages and domains. We find that puzzle SFT induces a reasoning-primitive vocabulary, yielding a $+7$pp \texttt{pass@32} gain on OlymMATH-Hard. Vanilla GSPO then composes these primitives into longer compute-verify chains, adding a further $+6$pp. However, this RL stage also suppresses exploratory primitives such as \textit{hypothesize} and \textit{backtrack}. To address this, we introduce a novelty bonus that rewards diverse correct rollouts, using perplexity under the reference model as a signal. This restores recovery primitives during RL and adds a further $+7$pp \texttt{pass@32} relative to vanilla GSPO. Finally, the end-to-end recipe raises the hard-math capability ceiling from $16.0\%$ at the OLMo3-7B-Instruct-SFT base to $36.0\%$, without adding any mathematics problems during the SFT or RL stages.

cs.LG↗

arXiv2026

TopoBench: Benchmarking LLMs on Hard Topological Reasoning

Solving topological grid puzzles requires reasoning over global spatial invariants such as connectivity, loop closure, and region symmetry and remains challenging for even the most powerful large language models (LLMs). To study these abilities under controlled settings, we introduce TopoBench, a benchmark of six puzzle families across three difficulty levels. We evaluate strong reasoning LLMs on TopoBench and find that even frontier models solve fewer than one quarter of hard instances, with two families nearly unsolved. To investigate whether these failures stem from reasoning limitations or from difficulty extracting and maintaining spatial constraints, we annotate 750 chain of thought traces with an error taxonomy that surfaces four candidate causal failure modes, then test them with targeted interventions simulating each error type. These interventions show that certain error patterns like premature commitment and constraint forgetting have a direct impact on the ability to solve the puzzle, while repeated reasoning is a benign effect of search. Finally we study mitigation strategies including prompt guidance, cell-aligned grid representations and tool-based constraint checking, finding that the bottleneck lies in extracting constraints from spatial representations and not in reasoning over them. Code and data are available at github.com/mayug/topobench-benchmark.

cs.AI↗

arXiv2025

Exponential Dynamic Energy Network for High Capacity Sequence Memory

The energy paradigm, exemplified by Hopfield networks, offers a principled framework for memory in neural systems by interpreting dynamics as descent on an energy surface. While powerful for static associative memories, it falls short in modeling sequential memory, where transitions between memories are essential. We introduce the Exponential Dynamic Energy Network (EDEN), a novel architecture that extends the energy paradigm to temporal domains by evolving the energy function over multiple timescales. EDEN combines a static high-capacity energy network with a slow, asymmetrically interacting modulatory population, enabling robust and controlled memory transitions. We formally derive short-timescale energy functions that govern local dynamics and use them to analytically compute memory escape times, revealing a phase transition between static and dynamic regimes. The analysis of capacity, defined as the number of memories that can be stored with minimal error rate as a function of the dimensions of the state space (number of feature neurons), for EDEN shows that it achieves exponential sequence memory capacity $O(\gamma^N)$, outperforming the linear capacity $O(N)$ of conventional models. Furthermore, EDEN's dynamics resemble the activity of time and ramping cells observed in the human brain during episodic memory tasks, grounding its biological relevance. By unifying static and sequential memory within a dynamic energy framework, EDEN offers a scalable and interpretable model for high-capacity temporal memory in both artificial and biological systems.

cs.NE↗

arXiv2025

Reservoir Computation with Networks of Differentiating Neuron Ring Oscillators

Reservoir Computing is a machine learning approach that uses the rich repertoire of complex system dynamics for function approximation. Current approaches to reservoir computing use a network of coupled integrating neurons that require a steady current to maintain activity. Here, we introduce a small world graph of differentiating neurons that are active only when there are changes in input as an alternative to integrating neurons as a reservoir computing substrate. We find the coupling strength and network topology that enable these small world networks to function as an effective reservoir. We demonstrate the efficacy of these networks in the MNIST digit recognition task, achieving comparable performance of 90.65% to existing reservoir computing approaches. The findings suggest that differentiating neurons can be a potential alternative to integrating neurons and can provide a sustainable future alternative for power-hungry AI applications.

cs.NE↗

arXiv2025

Bridging Expressivity and Scalability with Adaptive Unitary SSMs

Recent work has revealed that state space models (SSMs), while efficient for long-sequence 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. The code is available at https://github.com/arjunkaruvally/AUSSM

cs.NE↗

arXiv2025

Transient Dynamics in Lattices of Differentiating Ring Oscillators

Recurrent neural networks (RNNs) are machine learning models widely used for learning temporal relationships. Current state-of-the-art RNNs use integrating or spiking neurons -- two classes of computing units whose outputs depend directly on their internal states -- and accordingly there is a wealth of literature characterizing the behavior of large networks built from these neurons. On the other hand, past research on differentiating neurons, whose outputs are computed from the derivatives of their internal states, remains limited to small hand-designed networks with fewer than one-hundred neurons. Here we show via numerical simulation that large lattices of differentiating neuron rings exhibit local neural synchronization behavior found in the Kuramoto model of interacting oscillators. We begin by characterizing the periodic orbits of uncoupled rings, herein called ring oscillators. We then show the emergence of local correlations between oscillators that grow over time when these rings are coupled together into lattices. As the correlation length grows, transient dynamics arise in which large regions of the lattice settle to the same periodic orbit, and thin domain boundaries separate adjacent, out-of-phase regions. The steady-state scale of these correlated regions depends on how the neurons are shared between adjacent rings, which suggests that lattices of differentiating ring oscillator might be tuned to be used as reservoir computers. Coupled with their simple circuit design and potential for low-power consumption, differentiating neural nets therefore represent a promising substrate for neuromorphic computing that will enable low-power AI applications.

cs.NE↗

arXiv2024

Hidden Traveling Waves bind Working Memory Variables in Recurrent Neural Networks

Traveling waves are a fundamental phenomenon in the brain, playing a crucial role in short-term information storage. In this study, we leverage the concept of traveling wave dynamics within a neural lattice to formulate a theoretical model of neural working memory, study its properties, and its real world implications in AI. The proposed model diverges from traditional approaches, which assume information storage in static, register-like locations updated by interference. Instead, the model stores data as waves that is updated by the wave's boundary conditions. We rigorously examine the model's capabilities in representing and learning state histories, which are vital for learning history-dependent dynamical systems. The findings reveal that the model reliably stores external information and enhances the learning process by addressing the diminishing gradient problem. To understand the model's real-world applicability, we explore two cases: linear boundary condition (LBC) and non-linear, self-attention-driven boundary condition (SBC). The model with the linear boundary condition results in a shift matrix plus low-rank matrix currently used in H3 state space RNN. Further, our experiments with LBC reveal that this matrix is effectively learned by Recurrent Neural Networks (RNNs) through backpropagation when modeling history-dependent dynamical systems. Conversely, the SBC parallels the autoregressive loop of an attention-only transformer with the context vector representing the wave substrate. Collectively, our findings suggest the broader relevance of traveling waves in AI and its potential in advancing neural network architectures.

cs.NE↗

arXiv2023

Model Complexity of Program Phases

In resource limited computing systems, sequence prediction models must operate under tight constraints. Various models are available that cater to prediction under these conditions that in some way focus on reducing the cost of implementation. These resource constrained sequence prediction models, in practice, exhibit a fundamental tradeoff between the cost of implementation and the quality of its predictions. This fundamental tradeoff seems to be largely unexplored for models for different tasks. Here we formulate the necessary theory and an associated empirical procedure to explore this tradeoff space for a particular family of machine learning models such as deep neural networks. We anticipate that the knowledge of the behavior of this tradeoff may be beneficial in understanding the theoretical and practical limits of creation and deployment of models for resource constrained tasks.

cs.LG↗

arXiv2023

Episodic Memory Theory for the Mechanistic Interpretation of Recurrent Neural Networks

Understanding the intricate operations of Recurrent Neural Networks (RNNs) mechanistically is pivotal for advancing their capabilities and applications. In this pursuit, we propose the Episodic Memory Theory (EMT), illustrating that RNNs can be conceptualized as discrete-time analogs of the recently proposed General Sequential Episodic Memory Model. To substantiate EMT, we introduce a novel set of algorithmic tasks tailored to probe the variable binding behavior in RNNs. Utilizing the EMT, we formulate a mathematically rigorous circuit that facilitates variable binding in these tasks. Our empirical investigations reveal that trained RNNs consistently converge to the variable binding circuit, thus indicating universality in the dynamics of RNNs. Building on these findings, we devise an algorithm to define a privileged basis, which reveals hidden neurons instrumental in the temporal storage and composition of variables, a mechanism vital for the successful generalization in these tasks. We show that the privileged basis enhances the interpretability of the learned parameters and hidden states of RNNs. Our work represents a step toward demystifying the internal mechanisms of RNNs and, for computational neuroscience, serves to bridge the gap between artificial neural networks and neural memory models.

cs.NE↗

arXiv2022

Energy-based General Sequential Episodic Memory Networks at the Adiabatic Limit

The General Associative Memory Model (GAMM) has a constant state-dependant energy surface that leads the output dynamics to fixed points, retrieving single memories from a collection of memories that can be asynchronously preloaded. We introduce a new class of General Sequential Episodic Memory Models (GSEMM) that, in the adiabatic limit, exhibit temporally changing energy surface, leading to a series of meta-stable states that are sequential episodic memories. The dynamic energy surface is enabled by newly introduced asymmetric synapses with signal propagation delays in the network's hidden layer. We study the theoretical and empirical properties of two memory models from the GSEMM class, differing in their activation functions. LISEM has non-linearities in the feature layer, whereas DSEM has non-linearity in the hidden layer. In principle, DSEM has a storage capacity that grows exponentially with the number of neurons in the network. We introduce a learning rule for the synapses based on the energy minimization principle and show it can learn single memories and their sequential relationships online. This rule is similar to the Hebbian learning algorithm and Spike-Timing Dependent Plasticity (STDP), which describe conditions under which synapses between neurons change strength. Thus, GSEMM combines the static and dynamic properties of episodic memory under a single theoretical framework and bridges neuroscience, machine learning, and artificial intelligence.

cs.NE↗

arXiv2018

A Study into the similarity in generator and discriminator in GAN architecture

One popular generative model that has high-quality results is the Generative Adversarial Networks(GAN). This type of architecture consists of two separate networks that play against each other. The generator creates an output from the input noise that is given to it. The discriminator has the task of determining if the input to it is real or fake. This takes place constantly eventually leads to the generator modeling the target distribution. This paper includes a study into the actual weights learned by the network and a study into the similarity of the discriminator and generator networks. The paper also tries to leverage the similarity between these networks and shows that indeed both the networks may have a similar structure with experimental evidence with a novel shared architecture.

cs.LG↗