arXiv subjects

Liam Smith

Publications and source records attributed to Liam Smith.

10 recordsLinked to original sources

arXiv2026

Building The Ph(ysical)AI Layer Of Machine Intelligence

Foundation models achieve generalization through massive-scale training on diverse data, but have limitations with transfer to truly unseen domains without paired training data. We propose principle-driven foundation models that encode signal-theoretic principles (Fourier decomposition, energy conservation, symmetry) rather than learn untethered statistical correlations. We hypothesize that domains differ not in fundamental physics, but in learnable transformations in time, frequency, magnitude, or phase. Training exclusively on radio-frequency (RF) data with co-designed architecture and losses incorporating these principles, we achieve cross-modal transfer to audio, images, text, and video using only frozen representations learned from RF data, requiring no fine-tuning of the encoder on target domains. Our 1.99M parameter frozen encoder achieves 77.7% average accuracy (91.9% top-3) across 15 diverse tasks via linear probing, with systematic variation: 84.5 on physically-grounded tasks (speaker recognition, seismology, RF fingerprinting) versus 70.0% on semantic tasks (music genre, language recognition). This reveals that principle-driven and scale-driven approaches offer complementary paths: physical principles enable efficient cross-modal transfer while naturally establishing the boundary between physical and semantic understanding.

cs.LG↗

arXiv2024

Auxiliary Field Deformations of (Semi-)Symmetric Space Sigma Models

We generalize the auxiliary field deformations of the principal chiral model (PCM) introduced in arXiv:2405.05899 and arXiv:2407.16338 to sigma models whose target manifolds are symmetric or semi-symmetric spaces, including a Wess-Zumino term in the latter case. This gives rise to a new infinite family of classically integrable $\mathbb{Z}_2$ and $\mathbb{Z}_4$ coset models of the form which are of interest in applications of integrability to worldsheet string theory and holography. We demonstrate that every theory in this infinite class admits a zero-curvature representation for its equations of motion by exhibiting a Lax connection.

hep-th↗

arXiv2024

Auxiliary Field Sigma Models and Yang-Baxter Deformations

We combine the Yang-Baxter (YB) and bi-Yang-Baxter (bi-YB) deformations with higher-spin auxiliary field deformations to construct multi-parameter families of integrable deformations of the principal chiral model on a Lie group $G$ with semi-simple Lie algebra $\mathfrak{g}$. In the YB case, our construction produces one integrable deformation for each pair $(\mathcal{R}, E)$, where $\mathcal{R}$ is an antisymmetric bilinear operator on $\mathfrak{g}$ obeying the modified classical Yang-Baxter equation and $E$ is a function of several variables. In the bi-YB case, the pair becomes a triplet $(\mathcal{R},\tilde{\mathcal{R}}, E)$, where $\tilde{\mathcal{R}}$ is another antisymmetric bilinear operator on $\mathfrak{g}$ and obeys the non-split inhomogeneous modified classical Yang-Baxter equation. We show that every model in these families is (weakly) classically integrable by exhibiting a Lax representation for their equations of motion.

hep-th↗

arXiv2024

Integrable Higher-Spin Deformations of Sigma Models from Auxiliary Fields

We construct a new infinite family of integrable deformations of the principal chiral model (PCM) parameterized by an interaction function of several variables, which extends the formalism of arXiv:2405.05899, and includes deformations of the PCM by functions of both the stress tensor and higher-spin conserved currents. We show in detail that every model in this class admits a Lax representation for its equations of motion, and that the Poisson bracket of the Lax connection takes the Maillet form, establishing the existence of an infinite set of Poisson-commuting conserved charges. We argue that the non-Abelian T-dual of any model in this family is classically integrable, and that T-duality "commutes" with a general deformation in this class, in a sense which we make precise. Finally, we demonstrate that these higher-spin auxiliary field deformations can be extended to accommodate the addition of a Wess-Zumino term, and we exhibit the Lax connection in this case.

hep-th↗

arXiv2024

T-Duality and $T \overline{T}$-like Deformations of Sigma Models

We initiate the study of the interplay between T-duality and classical stress tensor deformations in two-dimensional sigma models. We first show that a general Abelian T-duality commutes with the $T \overline{T}$ deformation, which can be engineered by a gravitational dressing. Then, by using an auxiliary field formulation of stress tensor deformations of the principal chiral model (PCM), we prove that non-Abelian T-duality and arbitrary $T \overline{T}$-like flows also commute for theories in this class. We argue that all such auxiliary field deformations of both the PCM and its T-dual are classically integrable.

hep-th↗

arXiv2024

Infinite Family of Integrable Sigma Models Using Auxiliary Fields

We introduce a class of $2d$ sigma models which are parameterized by a function of one variable. In addition to the physical field $g$, these models include an auxiliary field $v_\alpha$ which mediates interactions in a prescribed way. We prove that every theory in this family is classically integrable, in that it possesses an infinite set of conserved charges in involution, which can be constructed from a Lax representation for the equations of motion. This class includes the principal chiral model (PCM) and all deformations of the PCM by functions of the energy-momentum tensor.

hep-th↗

arXiv2023

Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows

Given a model for self-dual non-linear electrodynamics in four spacetime dimensions, any deformation of this theory which is constructed from the duality-invariant energy-momentum tensor preserves duality invariance. In this work we present new proofs of this known result, and also establish a previously unknown converse: any parameterized family of duality-invariant Lagrangians, all constructed from an Abelian field strength $F_{\mu \nu}$ but not its derivatives, is related by a generalized stress tensor flow, in a sense which we make precise. We establish this and other properties of stress tensor deformations of theories of non-linear electrodynamics using both a conventional Lagrangian representation and using two auxiliary field formulations. We analyze these flows in several examples of duality-invariant models including the Born-Infeld and ModMax theories, and we derive a new auxiliary field representation for the two-parameter family of ModMax-Born-Infeld theories. These results suggest that the space of duality-invariant theories may be characterized as a subspace of theories of electrodynamics with the property that all tangent vectors to this subspace are operators constructed from the stress tensor.

hep-th↗

arXiv2023

Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry

We identify the unique stress tensor deformation which preserves zero-birefringence conditions in non-linear electrodynamics, which is a $4d$ version of the ${T\overline{T}}$ operator. We study the flows driven by this operator in the three Lagrangian theories without birefringence -- Born-Infeld, Plebanski, and reverse Born-Infeld -- all of which admit ModMax-like generalizations using a root-${T\overline{T}}$-like flow that we analyse in our paper. We demonstrate one way of making this root-${T\overline{T}}$-like flow manifestly supersymmetric by writing the deforming operator in $\mathcal{N} = 1$ superspace and exhibit two examples of superspace flows. We present scalar analogues in $d = 2$ with similar properties as these theories of electrodynamics in $d = 4$. Surprisingly, the Plebanski-type theories are fixed points of the classical ${T\overline{T}}$-like flows, while the Born-Infeld-type examples satisfy new flow equations driven by relevant operators constructed from the stress tensor. Finally, we prove that any theory obtained from a classical stress-tensor-squared deformation of a conformal field theory gives rise to a related ``subtracted'' theory for which the stress-tensor-squared operator is a constant.

hep-th↗

arXiv2022

Root-$T \overline{T}$ Deformations in Two-Dimensional Quantum Field Theories

In this letter we introduce a one-parameter deformation of two-dimensional quantum field theories generated by a non-analytic operator which we call Root-$T \overline{T}$. For a conformal field theory, the operator coincides with the square-root of the $T \overline{T}$ operator. More generally, the operator is defined so that classically it is marginal and generates a flow which commutes with the $T \overline{T}$-flow. Intriguingly, the Root-$T \overline{T}$ flow is closely related to the ModMax theory recently constructed by Bandos, Lechner, Sorokin and Townsend.

hep-th↗

arXiv2022

On Current-Squared Flows and ModMax Theories

We show that the recently introduced ModMax theory of electrodynamics and its Born-Infeld-like generalization are related by a flow equation driven by a quadratic combination of stress-energy tensors. The operator associated to this flow is a $4d$ analogue of the $T\bar{T}$ deformation in two dimensions. This result generalizes the observation that the ordinary Born-Infeld Lagrangian is related to the free Maxwell theory by a current-squared flow. As in that case, we show that no analogous relationship holds in any other dimension besides $d=4$. We also demonstrate that the $\mathcal{N}=1$ supersymmetric version of the ModMax-Born-Infeld theory obeys a related supercurrent-squared flow which is formulated directly in $\mathcal{N}=1$ superspace.

hep-th↗