arXiv subjects

Luke Miller

Publications and source records attributed to Luke Miller.

3 recordsLinked to original sources

arXiv2026

QuIC: A Training-Free Quantum Graph Embedding from Ideal Analysis to Practical Hardware Evaluation

We introduce QuIC, a training-free quantum graph embedding that maps graphs to sorted output distributions via a fixed parameterized circuit. In the ideal one-repetition setting, we prove that the resulting sorted distribution is permutation-invariant and injective on labeled graphs under an irrational-angle condition, yielding completeness on isomorphism classes for the ideal one-repetition exact-arithmetic embedding. We then use those ideal structural properties to motivate a practical embedding pipeline and study how much of that behavior survives under finite-shot estimation, truncation, realistic noise, transpilation, and hardware execution. The sorted distribution concentrates discriminative signal in a compact head, making fixed-length head truncation an effective practical operating point in the tested regimes. Under noise-model simulation, all tested graph pairs satisfied the study's operational separation criterion, including strongly regular graph pairs that are standard 2-WL stress tests and CFI families used as hard instances for fixed-k WL methods. A hardware study comprising 14,800 transpiled circuits across 37 CFI families on IBM Heron (ibm_fez, 156 qubits), including paired one- and two-repetition evaluations, reports empirical separation up to 66 qubits for the tested families under the reported execution protocol, identifies a device-dependent depth limit near 210-250 layers, and characterizes the current practical boundary of the method under the reported execution protocol.

quant-ph↗

arXiv2022

Training language models to follow instructions with human feedback

Making language models bigger does not inherently make them better at following a user's intent. For example, large language models can generate outputs that are untruthful, toxic, or simply not helpful to the user. In other words, these models are not aligned with their users. In this paper, we show an avenue for aligning language models with user intent on a wide range of tasks by fine-tuning with human feedback. Starting with a set of labeler-written prompts and prompts submitted through the OpenAI API, we collect a dataset of labeler demonstrations of the desired model behavior, which we use to fine-tune GPT-3 using supervised learning. We then collect a dataset of rankings of model outputs, which we use to further fine-tune this supervised model using reinforcement learning from human feedback. We call the resulting models InstructGPT. In human evaluations on our prompt distribution, outputs from the 1.3B parameter InstructGPT model are preferred to outputs from the 175B GPT-3, despite having 100x fewer parameters. Moreover, InstructGPT models show improvements in truthfulness and reductions in toxic output generation while having minimal performance regressions on public NLP datasets. Even though InstructGPT still makes simple mistakes, our results show that fine-tuning with human feedback is a promising direction for aligning language models with human intent.

cs.CL↗

arXiv2016

The hydrodynamic limit of beta coalescents that come down from infinity

We quantify the manner in which the beta coalescent $\Pi=\{ \Pi(t), t\geq 0\},$ with parameters $a\in (0, 1),$ $b>0,$ comes down from infinity. Approximating $\Pi$ by its restriction $\Pi^n$ to $[n]\:= \{1, \ldots, n\},$ the suitably rescaled block counting process $n^{-1}\#\Pi^n(tn^{a-1})$ has a deterministic limit, $c(t)$, as $n\to\infty.$ An explicit formula for $c(t)$ is provided in Theorem 1. The block size spectrum $(\mathfrak{c}_{1}\Pi^n(t), \ldots, \mathfrak{c}_{n}\Pi^n(t)),$ where $\mathfrak{c}_{i}\Pi^n(t)$ counts the number of blocks of size $i$ in $\Pi^n(t),$ captures more refined information about the coalescent tree corresponding to $\Pi$. Using the corresponding rescaling, the block size spectrum also converges to a deterministic limit as $n\to\infty.$ This limit is characterized by a system of ordinary differential equations whose $i$th solution is a complete Bell polynomial, depending only on $c(t)$ and $a,$ that we work out explicitly, see Corollary 1.

math.PR↗