Hilal AlQuabeh

Ahmed Oumar El-Shangiti, Tatsuya Hiraoka, Hilal AlQuabeh et al.

This paper investigates whether large language models (LLMs) utilize numerical attributes encoded in a low-dimensional subspace of the embedding space when answering questions involving numeric comparisons, e.g., Was Cristiano born before Messi? We first identified, using partial least squares regression, these subspaces, which effectively encode the numerical attributes associated with the entities in comparison prompts. Further, we demonstrate causality, by intervening in these subspaces to manipulate hidden states, thereby altering the LLM's comparison outcomes. Experiments conducted on three different LLMs showed that our results hold across different numerical attributes, indicating that LLMs utilize the linearly encoded information for numerical reasoning.

Ruben Solozabal, Velibor Bojkovic, Hilal AlQuabeh et al.

Current methods for initializing state space models (SSMs) parameters mainly rely on the \textit{HiPPO framework}, which is based on an online approximation of orthogonal polynomials. Recently, diagonal alternatives have shown to reach a similar level of performance while being significantly more efficient due to the simplification in the kernel computation. However, the \textit{HiPPO framework} does not explicitly study the role of its diagonal variants. In this paper, we take a further step to investigate the role of diagonal SSM initialization schemes from the frequency perspective. Our work seeks to systematically understand how to parameterize these models and uncover the learning biases inherent in such diagonal state-space models. Based on our observations, we propose a diagonal initialization on the discrete Fourier domain \textit{S4D-DFouT}. The insights in the role of pole placing in the initialization enable us to further scale them and achieve state-of-the-art results on the Long Range Arena benchmark, allowing us to train from scratch on very large datasets as PathX-256.

Muhammad Cendekia Airlangga, Hilal AlQuabeh, Munachiso S Nwadike et al.

We study memory in state-space language models using primacy and recency effects as behavioral tools to uncover how information is retained and forgotten over time. Applying structured recall tasks to the Mamba architecture, we observe a consistent U-shaped accuracy profile, indicating strong performance at the beginning and end of input sequences. We identify three mechanisms that give rise to this pattern. First, long-term memory is supported by a sparse subset of channels within the model's selective state space block, which persistently encode early input tokens and are causally linked to primacy effects. Second, short-term memory is governed by delta-modulated recurrence: recent inputs receive more weight due to exponential decay, but this recency advantage collapses when distractor items are introduced, revealing a clear limit to memory depth. Third, we find that memory allocation is dynamically modulated by semantic regularity: repeated relations in the input sequence shift the delta gating behavior, increasing the tendency to forget intermediate items. We validate these findings via targeted ablations and input perturbations on two large-scale Mamba-based language models: one with 1.4B and another with 7B parameters.

H. V. AlquBoj, Hilal AlQuabeh, Velibor Bojkovic et al.

Grokking, a delayed generalization in neural networks after perfect training performance, has been observed in Transformers and MLPs, but the components driving it remain underexplored. We show that embeddings are central to grokking: introducing them into MLPs induces delayed generalization in modular arithmetic tasks, whereas MLPs without embeddings can generalize immediately. Our analysis identifies two key mechanisms: (1) Embedding update dynamics, where rare tokens stagnate due to sparse gradient updates and weight decay, and (2) Bilinear coupling, where the interaction between embeddings and downstream weights introduces saddle points and increases sensitivity to initialization. To confirm these mechanisms, we investigate frequency-aware sampling, which balances token updates by minimizing gradient variance, and embedding-specific learning rates, derived from the asymmetric curvature of the bilinear loss landscape. We prove that an adaptive learning rate ratio, \(\frac{η_E}{η_W} \propto \frac{σ_{\max}(E)}{σ_{\max}(W)} \cdot \frac{f_W}{f_E}\), mitigates bilinear coupling effects, accelerating convergence. Our methods not only improve grokking dynamics but also extend to broader challenges in Transformer optimization, where bilinear interactions hinder efficient training.

H. V. AlquBoj, Hilal AlQuabeh, Velibor Bojkovic et al.

Humans are believed to perceive numbers on a logarithmic mental number line, where smaller values are represented with greater resolution than larger ones. This cognitive bias, supported by neuroscience and behavioral studies, suggests that numerical magnitudes are processed in a sublinear fashion rather than on a uniform linear scale. Inspired by this hypothesis, we investigate whether large language models (LLMs) exhibit a similar logarithmic-like structure in their internal numerical representations. By analyzing how numerical values are encoded across different layers of LLMs, we apply dimensionality reduction techniques such as PCA and PLS followed by geometric regression to uncover latent structures in the learned embeddings. Our findings reveal that the model's numerical representations exhibit sublinear spacing, with distances between values aligning with a logarithmic scale. This suggests that LLMs, much like humans, may encode numbers in a compressed, non-uniform manner.