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Abstract The search for Kitaev’s quantum spin liquid in real materials has recently expanded with the prediction that honeycomb lattices of divalent, high-spin cobalt ions could host the dominant bond-dependent exchange interactions required to stabilize the elusive entangled quantum state. The layered honeycomb Na₃Co₂SbO₆has been singled out as a leading candidate provided that the trigonal crystal field acting on Co 3dorbitals, which enhances non-Kitaev exchange interactions between$${J}_{{{\rm{eff}}}}=\frac{1}{2}$$ $J_{\mathrm{eff}}=\frac{1}{2}$spin-orbital pseudospins, is reduced. Here we show that applied pressure leads to anisotropic compression of the layered structure, significantly reducing the trigonal distortion of CoO₆octahedra. Ferromagnetic correlations between pseudospins are enhanced in the spin-polarized (3 Tesla) phase up to about 60 GPa. Higher pressures drive a high-spin to low-spin transition destroying the$${J}_{{{\rm{eff}}}}=\frac{1}{2}$$ $J_{\mathrm{eff}}=\frac{1}{2}$moments required to map the spin Hamiltonian into Kitaev’s model. The spin transition strongly suppresses the low-temperature magnetic susceptibility and appears to stabilize a paramagnetic phase driven by frustration. The possible emergence of frustrated magnetism of localized$$S=\frac{1}{2}$$ $S=\frac{1}{2}$moments opens the door for exploration of novel magnetic quantum states in compressed honeycomb lattices of divalent cobaltates. 

We study the differentially private (DP) empirical risk minimization (ERM) problem under the semi-sensitive DP setting where only some features are sensitive. This generalizes the Label DP setting where only the label is sensitive. We give improved upper and lower bounds on the excess risk for DP-ERM. In particular, we show that the error only scales polylogarithmically in terms of the sensitive domain size, improving upon previous results that scale polynomially in the sensitive domain size (Ghazi et al., 2021). 

We introduce VampNet, a masked acoustic token modeling approach to music synthesis, compression, inpainting, and variation. We use a variable masking schedule during training which allows us to sample coherent music from the model by applying a variety of masking approaches (called prompts) during inference. VampNet is non-autoregressive, leveraging a bidirectional transformer architecture that attends to all tokens in a forward pass. With just 36 sampling passes, VampNet can generate coherent high-fidelity musical waveforms. We show that by prompting VampNet in various ways, we can apply it to tasks like music compression, inpainting, outpainting, continuation, and looping with variation (vamping). Appropriately prompted, VampNet is capable of maintaining style, genre, instrumentation, and other high-level aspects of the music. This flexible prompting capability makes VampNet a powerful music co-creation tool. Code andaudio samples are available online.