arXiv subjects

Vahagn Hovhannisyan

Publications and source records attributed to Vahagn Hovhannisyan.

3 recordsLinked to original sources

arXiv2026

Metric entropy of Fourier ratio classes on ${\mathbb Z}_N$

We study metric entropy and uniform sampling for classes of signals on ${\mathbb Z}_N$ with prescribed Fourier ratio. The Fourier ratio measures how spread out the Fourier transform of a signal is, interpolating between sparse spectral support and nearly uniform spectral distribution. Our main result gives upper and lower bounds for the metric entropy of a Fourier-ratio layer of size $r.$ At any sufficiently small fixed covering scale, these bounds match in their dependence on $r$ and $N$ and show that $FR(f)^2$ acts as an effective dimension parameter governing the size of the class. We use the entropy estimate to obtain uniform bounds for empirical approximation over Fourier-ratio classes. We also establish a phase-orbit packing result. If a single signal has a flat spectral block of size $k,$ then phase perturbations of that signal generate an exponentially large family with the same Fourier ratio and positive $\ell^2$ separation. Together, these results show that the Fourier ratio governs not only approximation properties of individual signals, but also the geometric size and uniform sampling behavior of entire signal classes.

math.CA↗

arXiv2026

Emergent Misalignment via In-Context Learning: Narrow in-context examples can produce broadly misaligned LLMs

Recent work has shown that narrow finetuning can produce broadly misaligned LLMs, a phenomenon termed emergent misalignment (EM). While concerning, these findings were limited to finetuning and activation steering, leaving out in-context learning (ICL). We therefore ask: does EM emerge in ICL? We find that it does: across four model families (Gemini, Kimi-K2, Grok, and Qwen), narrow in-context examples cause models to produce misaligned responses to benign, unrelated queries. With 16 in-context examples, EM rates range from 1% to 24% depending on model and domain, appearing with as few as 2 examples. Neither larger model scale nor explicit reasoning provides reliable protection, and larger models are typically even more susceptible. Next, we formulate and test a hypothesis, which explains in-context EM as conflict between safety objectives and context-following behavior. Consistent with this, instructing models to prioritize safety reduces EM while prioritizing context-following increases it. These findings establish ICL as a previously underappreciated vector for emergent misalignment that resists simple scaling-based solutions.

cs.CL↗

arXiv2025

Arbitrarily long strings of consecutive primes in special sets

Let $F(x)$ be a function of the form $ \sum_{i=1}^r d_i x^{ρ_i}$ where $d_1,\ldots,d_r\in\mathbb{R}$, $0 \leq ρ_1 < \ldots < ρ_r,$ $ρ_r \not\in \mathbb{Z},ρ_i \in \mathbb{R}$ for $ 1 \leq i \leq r$ and $d_r\not=0$. We prove that sets of the form $\{ n \in \mathbb{N}: \{ F(n) \} \in U \}$ for any non-empty open set $U \subset [0,1)$ contain arbitrarily long strings of consecutive primes.

math.NT↗