Related papers: Generation-by-Generation Dissection of the Respons…
We study the linear response to an external perturbation of a renewal process, in an aging condition that, with no perturbation, would yield super-diffusion. We use the phenomenological approach to the linear response adopted in earlier…
The scalability of large language models for long-context reasoning is severely constrained by the linear growth of their Transformer key-value cache, which incurs significant memory and computational costs. We posit that as a model…
Large language models (LLMs) have demonstrated remarkable capabilities across a wide range of tasks, yet exhibit critical limitations in knowledge-intensive tasks, often generating hallucinations when faced with questions requiring…
Consider first a memoryless population model described by the usual branching process with a given mean reproduction matrix on a finite space of types. Motivated by the consequences of atavism in Evolutionary Biology, we are interested in a…
Many driven systems alternate between bursts of activity and quiescence and can become trapped in an absorbing state, such as complete inactivity in reaction-diffusion processes or extinction in predator-prey dynamics. It is generally…
\emph{Resistive memories}, such as \emph{phase change memories} and \emph{resistive random access memories} have attracted significant attention in recent years due to their better scalability, speed, rewritability, and yet non-volatility.…
We observe non-monotonic aging and memory effects, two hallmarks of glassy dynamics, in two disordered mechanical systems: crumpled thin sheets and elastic foams. Under fixed compression, both systems exhibit monotonic non-exponential…
Traditional studies of memory for meaningful narratives focus on specific stories and their semantic structures but do not address common quantitative features of recall across different narratives. We introduce a statistical ensemble of…
We monitor the relaxation of internal stresses in a fractal colloidal gel on cessation of flow and find a weak power law decay, $\sigma_i \sim t^{-\alpha}$ over 5 decades of time where $\alpha \approx 0.07$. The system exhibits physical…
I hypothesize that re-occurring prior experience of complex systems mobilizes a fast response, whose attractor is encoded by their strongly connected network core. In contrast, responses to novel stimuli are often slow and require the…
Lifelong sequence generation (LSG), a problem in continual learning, aims to continually train a model on a sequence of generation tasks to learn constantly emerging new generation patterns while avoiding the forgetting of previous…
A central challenge in continual learning is forgetting, the loss of performance on previously learned tasks induced by sequential adaptation to new ones. While forgetting has been extensively studied empirically, rigorous theoretical…
We present a detailed discussion of the role played by memory, and the nature of self-induced shocks, in an evolutionary population competing for limited resources. Our study builds on a previously introduced multi-agent system [Phys. Rev.…
Recent studies of cortical neurons driven by fluctuating currents revealed cutoff frequencies for action potential encoding of several hundred Hz. Theoretical studies of biophysical neuron models have predicted a much lower cutoff frequency…
Sinai's model of diffusion in one-dimension with random local bias is studied by a real space renormalization group which yields exact results at long times. The effects of an additional small uniform bias force are also studied. We obtain…
Large Reasoning Models (LRMs) demonstrate remarkable capabilities on complex tasks, exhibiting emergent, human-like thinking patterns. Despite their advances, we identify a fundamental limitation: current LRMs lack a dedicated meta-level…
It has been proposed (Phys. Rev. E {\bf 71}, 026121 (2005)) that unlike the short range contact process, a long-range counterpart may lead to the existence a discontinuous phase transition in one dimension. Aiming at exploring such link,…
The time evolution of systems relaxing towards thermal equilibrium is examined near the critical temperature $T_c$, with special attention paid to the role of the initial value $m_i$ of the order parameter $\phi$. To this end, the…
Masked Diffusion Models (MDMs) significantly accelerate inference by trading off sequential determinism. However, the theoretical mechanisms governing generation order and the risks inherent in parallelization remain under-explored. In this…
We introduce a family of synthetic languages with hierarchical structure -- generated by a broadcast process on trees -- for which the role of context length and reasoning in autoregressive generation can be analyzed precisely. At the heart…