arXiv subjects

Michelle Xu

Publications and source records attributed to Michelle Xu.

5 recordsLinked to original sources

arXiv2026

LLM Router: Rethinking Routing with Prefill Activations

Existing routers rely on semantic query features or handcrafted features, which often fail to capture model-specific failures or intrinsic task difficulty. We instead route using internal LLM activations, specifically the residual stream. Our key idea, Encoder-Target Decoupling, separates the model that produces the predictive signal (the Encoder) from the model whose correctness is being estimated (the Target), allowing open-weight encoders to predict the performance of closed-source target models. We evaluate layerwise geometric probes, finding that Fisher Separability ($J$) effectively identifies informative layers, supported by Effective Dimensionality ($d_{\mathrm{eff}}$) diagnostics. We then utilize a SharedTrunkNet, a joint multi-output MLP that predicts simultaneous correctness probabilities across candidate models using concatenated prefill features. In our experiments, SharedTrunkNet consistently outperforms semantic baselines. At its best, SharedTrunkNet closes 45.58% of the gap between the strongest standalone model and the oracle while achieving 74.31% cost savings relative to the most expensive model. These results demonstrate that prefill activations provide a robust routing signal, establishing activation-based routing as a high-performance alternative to purely semantic selection.

cs.CL↗

arXiv2025

Design boosters: from constant-time quantum chaos to $\infty$-designs and beyond

We study a counterintuitive property of 'conditioning' on the result of measuring a subsystem of a quantum state: such conditioning can boost design quality, at the cost of increased system size. We work in the setting of deep thermalization from many-body physics: starting from a bipartite state on a global system $(A,B)$ drawn from a $k$-design, we measure system $B$ in the computational basis, keep the outcome and examine the state that remains in system $A$, approximating the overall ensemble (the 'projected ensemble') by a $k'$-design. We ask: how does the design quality change due to this procedure, or how does $k'$ compare to $k$? We give the first rigorous example of unitary dynamics generating a state such that, projection at very early (constant) times can boost design randomness. These dynamics are those of quantum chaos, modeled by the evolution of a Hamiltonian drawn from the Gaussian Unitary Ensemble (GUE). We show that, even though a state generated by such dynamics at constant time only forms a $k=\mathcal{O}(1)$ design, the projected ensemble is Haar-random (or a $k'=\infty$ design) in the thermodynamic limit (i.e. when $N_B=\infty$). This phenomenon persists even with weaker and more physically realistic assumptions; our results can be appropriately applied to non-GUE Hamiltonians that nevertheless show likely chaotic signatures in their eigenbases. Moreover, we show that with no assumption on how the global state was generated, a $k$-design experiences a degradation in design quality to $k' = \lfloor k/2 \rfloor$. This improves upon best prior results on the deep thermalization of designs. Together, our contributions argue for design boosting as a result of chaos and showcase a novel mechanism to generate good designs.

quant-ph↗

arXiv2024

Cryptographic tests of the python's lunch conjecture

In the AdS/CFT correspondence, a subregion of the CFT allows for the recovery of a corresponding subregion of the bulk known as its entanglement wedge. In some cases, an entanglement wedge contains a locally but not globally minimal surface homologous to the CFT subregion, in which case it is said to contain a python's lunch. It has been proposed that python's lunch geometries should be modelled by tensor networks that feature projective operations where the wedge narrows. This model leads to the python's lunch (PL) conjecture, which asserts that reconstructing information from past the locally minimal surface is computationally difficult. In this work, we use cryptographic tools related to a primitive known as the Conditional Disclosure of Secrets (CDS) to develop consequences of the projective tensor network model that can be checked directly in AdS/CFT. We argue from the tensor network picture that the mutual information between appropriate CFT subregions is lower bounded linearly by an area difference associated with the geometry of the lunch. Recalling that the mutual information is also computed by bulk extremal surfaces, this gives a checkable geometrical consequence of the tensor network model. We prove weakened versions of this geometrical statement in asymptotically AdS$_{2+1}$ spacetimes satisfying the null energy condition, and confirm it in some example geometries, supporting the tensor network model and by proxy the PL conjecture.

hep-th↗

arXiv2024

Efficient Unitary T-designs from Random Sums

Unitary $T$-designs play an important role in quantum information, with diverse applications in quantum algorithms, benchmarking, tomography, and communication. Until now, the most efficient construction of unitary $T$-designs for $n$-qudit systems has been via random local quantum circuits, which have been shown to converge to approximate $T$-designs in the diamond norm using $O(T^{5+o(1)} n^2)$ quantum gates. In this work, we provide a new construction of $T$-designs via random matrix theory using $\tilde{O}(T^2 n^2)$ quantum gates. Our construction leverages two key ideas. First, in the spirit of central limit theorems, we approximate the Gaussian Unitary Ensemble (GUE) by an i.i.d. sum of random Hermitian matrices. Second, we show that the product of just two exponentiated GUE matrices is already approximately Haar random. Thus, multiplying two exponentiated sums over rather simple random matrices yields a unitary $T$-design, via Hamiltonian simulation. A central feature of our proof is a new connection between the polynomial method in quantum query complexity and the large-dimension ($N$) expansion in random matrix theory. In particular, we show that the polynomial method provides exponentially improved bounds on the high moments of certain random matrix ensembles, without requiring intricate Weingarten calculations. In doing so, we define and solve a new type of moment problem on the unit circle, asking whether a finite number of equally weighted points, corresponding to eigenvalues of unitary matrices, can reproduce a given set of moments.

quant-ph↗

arXiv2023

Non-local computation and the black hole interior

In a two sided black hole, systems falling in from opposite asymptotic regions can meet inside the black hole and interact. This is the case even while the two CFTs describing each asymptotic region are non-interacting. Here, we relate these behind the horizon interactions to non-local quantum computations. This gives a quantum circuit perspective on these interactions, which applies whenever the interaction occurs in the past of a certain extremal surface that sits inside the black hole and in arbitrary dimension. Whenever our perspective applies, we obtain a boundary signature for these interior collisions which is stated in terms of the mutual information. We further revisit the connection discussed earlier between bulk interactions in one sided AdS geometries and non-local computation, and recycle some of our techniques to offer a new perspective on making that connection precise.

hep-th↗