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Ning Su

Publications and source records attributed to Ning Su.

At least 19 recordsLinked to original sources

Echo-LoRA: Parameter-Efficient Fine-Tuning via Cross-Layer Representation Injection

Parameter-efficient fine-tuning (PEFT) has become a practical route for adapting large language models to downstream tasks, with LoRA-style methods being particularly attractive because they are inexpensive to train and easy to deploy. Most LoRA variants, however, revise the update rule within the weight space of each layer and leave the intermediate representations formed by deeper layers largely unused. We propose Echo-LoRA, a cross-layer representation injection method for parameter-efficient fine-tuning. During training, Echo-LoRA collects boundary hidden states from deeper source layers, aggregates them into a sample-level echo representation, and uses lightweight projection and gating networks to inject the resulting signal into shallow LoRA or DoRA modules. Answer-only masking, masked distillation, and stochastic routing are used to keep this auxiliary path stable and to reduce the gap between training and inference. On eight commonsense reasoning benchmarks, Echo-LoRA exceeds the reported LoRA baselines by 5.7 percentage points on average across LLaMA-7B, LLaMA2-7B, and LLaMA3-8B. Under reproduced LoRA baselines in our unified implementation, the average gain is 3.0 points; when combined with DoRA, the gain is 2.7 points. The Echo path is discarded after training, so the deployed model keeps the original low-rank LoRA/DoRA form and adds neither inference-time parameters nor inference computation.

cs.LG

Discovering Hidden Algebraic Structures via Transformers with Rank-Aware Beam GRPO

Recent efforts have extended the capabilities of transformers in logical reasoning and symbolic computations. In this work, we investigate their capacity for non-linear latent pattern discovery in the context of functional decomposition, focusing on the challenging algebraic task of multivariate polynomial decomposition. This problem, with widespread applications in science and engineering, is proved to be NP-hard, and demands both precision and insight. Our contributions are threefold: First, we develop a synthetic data generation pipeline providing fine-grained control over problem complexity. Second, we train transformer models via supervised learning and evaluate them across four key dimensions involving scaling behavior and generalizability. Third, we propose Beam Grouped Relative Policy Optimization (BGRPO), a rank-aware reinforcement learning method suitable for hard algebraic problems. Finetuning with BGRPO improves accuracy while reducing beam width by up to half, resulting in approximately 75% lower inference compute. Additionally, our model demonstrates competitive performance in polynomial simplification, outperforming Mathematica in various cases.

cs.LG

Which maximal subgroups are perfect codes?

A perfect code in a graph $\Gamma=(V, E)$ is a subset $C$ of $V$ such that no two vertices in $C$ are adjacent and every vertex in $V \setminus C$ is adjacent to exactly one vertex in $C$. A subgroup $H$ of a group $G$ is called a subgroup perfect code of $G$ if it is a perfect code in some Cayley graph of $G$. In this paper, we undertake a systematic study of which maximal subgroups of a group can be perfect codes. Our approach highlights a characterization of subgroup perfect codes in terms of their ``local'' complements.

math.CO

Bootstrapping the Simplest Deconfined Quantum Critical Point

We study the $N=3$ case of the $CP^{N-1}$ model, which is a field theory of $N$ complex scalars in $3d$ coupled to an Abelian gauge field with $SU(N) \times U(1)$ global symmetry. Recent evidence suggests the $N=2$ theory is not critical, which makes the $N=3$ theory the simplest possibility of deconfined quantum criticality. We apply the conformal bootstrap to correlators of charge $q=0,1,2$ scalar operators under the $U(1)$ symmetry, which gives us access also to $q=3,4$ operators. After imposing that only the lowest $q=0,1,2$ scalar operators are relevant, we find that the bootstrap bounds are saturated by the large $N$ prediction for $q=1,2,3,4$ scalar monopole operator scaling dimensions, which were shown earlier to be accurate even for small $N$, as well as a lattice prediction for the $q=0$ non-monopole scalar operator. We also predict the scaling dimensions of the lowest spinning monopole operators, which we match to the large charge prediction for spinning operators. This suggests that the critical $CP^{2}$ model is described by this bootstrap bound.

hep-th

PANDA: Parkinson's Assistance and Notification Driving Aid

Parkinson's Disease (PD) significantly impacts driving abilities, often leading to early driving cessation or accidents due to reduced motor control and increasing reaction times. To diminish the impact of these symptoms, we developed PANDA (Parkinson's Assistance and Notification Driving Aid), a multi-modality real-time alert system designed to monitor driving patterns continuously and provide immediate alerts for irregular driving behaviors, enhancing driver safety of individuals with PD. The system was developed through a participatory design process with 9 people with PD and 13 non-PD individuals using a driving simulator, which allowed us to identify critical design characteristics and collect detailed data on driving behavior. A user study involving individuals with PD evaluated the effectiveness of PANDA, exploring optimal strategies for delivering alerts and ensuring they are timely and helpful. Our findings demonstrate that PANDA has the potential to enhance the driving safety of individuals with PD, offering a valuable tool for maintaining independence and confidence behind the wheel.

cs.HC

From data to the analytic S-matrix: A Bootstrap fit of the pion scattering amplitude

We propose a novel strategy to fit experimental data using a UV complete amplitude ansatz satisfying the constraints of Analyticity, Crossing, and Unitarity. We focus on $\pi\pi$ scattering combining both experimental and lattice data. The fit strategy requires using S-matrix Bootstrap methods and non-convex Particle Swarm Optimization techniques. Using this procedure, we numerically construct a full-fledged scattering amplitude that fits the data and contains the known QCD spectrum that couples to $\pi \pi$ states below $1.4$ GeV. The amplitude constructed agrees below the two-particle threshold with the two-loop $\chi$PT prediction. Moreover, we correctly predict the $D_2$ phase shift, the appearance of a spin three state, and the behavior of the high-energy total cross-section. Finally, we find a genuine tetraquark resonance around 2 GeV, which we argue might be detected by looking into the decays of B mesons.

hep-th

New Developments in the Numerical Conformal Bootstrap

The numerical conformal bootstrap has become in the last 15 years an indispensable tool for studying strongly coupled CFTs in various dimensions. Here we review the main developments in the field in the last 5 years, since the appearance of the previous comprehensive review \cite{Poland:2018epd}. We describe developments in the software ({\tt SDPB 2.0}, {\tt scalar\_blocks}, {\tt blocks\_3d}, {\tt autoboot}, {\tt hyperion}, {\tt simpleboot}), and on the algorithmic side (Delauney triangulation, cutting surface, tiptop, navigator function, skydive). We also describe the main physics applications which were obtained using the new technology.

hep-th

From O(3) to Cubic CFT: Conformal Perturbation and the Large Charge Sector

The Cubic CFT can be understood as the O(3) invariant CFT perturbed by a slightly relevant operator. In this paper, we use conformal perturbation theory together with the conformal data of the O(3) vector model to compute the anomalous dimension of scalar bilinear operators of the Cubic CFT. When the $Z_2$ symmetry that flips the signs of $\phi_i$ is gauged, the Cubic model describes a certain phase transition of a quantum dimer model. The scalar bilinear operators are the order parameters of this phase transition. Based on the conformal data of the O(3) CFT, we determine the correction to the critical exponent as $\eta_{*}^{Cubic}-\eta_{*}^{O(3)}\approx -0.0215(49)$. The O(3) data is obtained using the numerical conformal bootstrap method to study all four-point correlators involving the four operators: $v=\phi_i$, $s=\sum_i \phi_i\phi_i$ and the leading scalar operators with O(3) isospin $j=2$ and 4. According to large charge effective theory, the leading operator with charge $Q$ has scaling dimension $\Delta_{Q}=c_{3/2} Q^{3/2}+c_{1/2}Q^{1/2}$. We find a good match with this prediction up to isospin $j=6$ for spin 0 and 2 and measured the coefficients $c_{3/2}$ and $c_{1/2}$.

hep-th

Bootstrapping Deconfined Quantum Tricriticality

The paradigmatic example of deconfined quantum criticality is the Neel-VBS phase transition. The continuum description of this transition is the $N=2$ case of the $CP^{N-1}$ model, which is a field theory of $N$ complex scalars in 3d coupled to an Abelian gauge field with $SU(N)\times U(1)$ global symmetry. Lattice studies and duality arguments suggest the global symmetry of the $CP^1$ model is enhanced to $SO(5)$. We perform a conformal bootstrap study of $SO(5)$ invariant fixed points with one relevant $SO(5)$ singlet operator, which would correspond to two relevant $SU(2)\times U(1)$ singlets, i.e. a tricritical point. We find that the bootstrap bounds are saturated by four different predictions from the large $N$ computation of monopole operator scaling dimensions, which were recently shown to be very accurate even for small $N$. This suggests that the Neel-VBS phase transition is described by this bootstrap bound, which predicts that the second relevant singlet has dimension $\approx 2.36$.

hep-th

Skydiving to Bootstrap Islands

We study families of semidefinite programs (SDPs) that depend nonlinearly on a small number of "external" parameters. Such families appear universally in numerical bootstrap computations. The traditional method for finding an optimal point in parameter space works by first solving an SDP with fixed external parameters, then moving to a new point in parameter space and repeating the process. Instead, we unify solving the SDP and moving in parameter space in a single algorithm that we call "skydiving". We test skydiving on some representative problems in the conformal bootstrap, finding significant speedups compared to traditional methods.

hep-th

Non-Abelian currents bootstrap

We initiate the study of correlation functions of non-Abelian spin-1 conserved current in three dimensional conformal field theories using numerical conformal bootstrap. We discuss the general framework and apply it to the particular cases of $SU(N)$ and $O(N)$ global symmetry. In both cases we obtain general bounds on operator dimensions. In the large-$N$ limit our bounds show features in correspondence of the expected position of fermionic QED$_3$ in three dimensions, as well as other interesting theories. By imposing gaps inspired by the spectrum of QED$_3$ at large-$N$, we manage to restrict the plane of certain operator dimensions to a small island, where QED$_3$ must live.

hep-th

Upper critical dimension of the 3-state Potts model

We consider the 3-state Potts model in $d\geq2$ dimensions. For $d$ less than the upper critical dimension $d_\text{crit}$, the model has a critical and a tricritical fixed point. In $d=2$, these fixed points are described by minimal models, and so are exactly solvable. For $d>2$, however, strong coupling makes them difficult to study and there is no consensus on the value of $d_\text{crit}$. We use the numerical conformal bootstrap to compute critical exponents of both the critical and tricritical fixed points for general $d$. In $d=2$ our results match the expected values, and as we increase $d$ we find that the critical exponents of each fixed point get closer until they merge near $d_\text{crit}\lesssim 2.5$.

hep-th

The Hybrid Bootstrap

Finding a method to combine the numerical bootstrap with the analytic lightcone bootstrap is an important goal to advance the conformal bootstrap program. We propose a hybrid bootstrap method to do just that. The numerical and analytic bootstrap approaches are sensitive to different regions of the spectrum and complement each other. When they are effectively combined, the hybrid bootstrap enjoys the best of both worlds and the prediction for the actual CFT can be significantly improved. In this work, we discuss the general strategy to perform such a hybrid bootstrap, and we make a partial implementation of the strategy for 3D Ising CFT $\{\sigma,\epsilon\}$ system. Even at relatively low derivative order $\Lambda=19$, the hybrid bootstrap predicts very precise values for the scaling dimension $\Delta_\sigma,\Delta_\epsilon$ that are within the previous $\Lambda=43$ rigorous error bars.

hep-th

Precision Bootstrap for the $\mathcal{N}=1$ Super-Ising Model

In this note we report an improved determination of the scaling dimensions and OPE coefficients of the minimal supersymmetric extension of the 3d Ising model using the conformal bootstrap. We also show how this data can be used as input to the Lorentzian inversion formula, finding good agreement between analytic calculations and numerical extremal spectra once mixing effects are resolved.

hep-th

Conformal bootstrap bounds for the $U(1)$ Dirac spin liquid and $N=7$ Stiefel liquid

We apply the conformal bootstrap technique to study the $U(1)$ Dirac spin liquid (i.e. $N_f=4$ QED$_3$) and the newly proposed $N=7$ Stiefel liquid (i.e. a conjectured 3d non-Lagrangian CFT without supersymmetry). For the $N_f=4$ QED$_3$, we focus on the monopole operator and ($SU(4)$ adjoint) fermion bilinear operator. We bootstrap their single correlators as well as the mixed correlators between them. We first discuss the bootstrap kinks from single correlators. Some exponents of these bootstrap kinks are close to the expected values of QED$_3$, but we provide clear evidence that they should not be identified as the QED$_3$. By requiring the critical phase to be stable on the triangular and the kagome lattice, we obtain rigorous numerical bounds for the $U(1)$ Dirac spin liquid and the Stiefel liquid. For the triangular and kagome Dirac spin liquid, the rigorous lower bounds of the monopole operator's scaling dimension are $1.046$ and $1.105$, respectively. These bounds are consistent with the latest Monte Carlo results.

cond-mat.str-el

Navigator Function for the Conformal Bootstrap

Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded. We propose a new method for searching theory space that replaces the binary information "allowed"/"excluded" with a continuous "navigator" function that is negative in the allowed region and positive in the excluded region. Such a navigator function allows one to efficiently explore high-dimensional parameter spaces and smoothly sail towards any islands they may contain. The specific functions we introduce have several attractive features: they are everywhere well-defined, can be computed with standard methods, and evaluation of their gradient is immediate due to an SDP gradient formula that we provide. The latter property allows for the use of efficient quasi-Newton optimization methods, which we illustrate by navigating towards the 3d Ising island.

hep-th

A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions

We propose a roadmap for bootstrapping conformal field theories (CFTs) described by gauge theories in dimensions $d>2$. In particular, we provide a simple and workable answer to the question of how to detect the gauge group in the bootstrap calculation. Our recipe is based on the notion of \emph{decoupling operator}, which has a simple (gauge) group theoretical origin, and is reminiscent of the null operator of $2d$ Wess-Zumino-Witten CFTs in higher dimensions. Using the decoupling operator we can efficiently detect the rank (i.e. color number) of gauge groups, e.g., by imposing gap conditions in the CFT spectrum. We also discuss the physics of the equation of motion, which has interesting consequences in the CFT spectrum as well. As an application of our recipes, we study a prototypical critical gauge theory, namely the scalar QED which has a $U(1)$ gauge field interacting with critical bosons. We show that the scalar QED can be solved by conformal bootstrap, namely we have obtained its kinks and islands in both $d=3$ and $d=2+\epsilon$ dimensions.

hep-th

Bootstrapping Heisenberg Magnets and their Cubic Instability

We study the critical $O(3)$ model using the numerical conformal bootstrap. In particular, we use a recently developed cutting-surface algorithm to efficiently map out the allowed space of CFT data from correlators involving the leading $O(3)$ singlet $s$, vector $\phi$, and rank-2 symmetric tensor $t$. We determine their scaling dimensions to be $(\Delta_{s}, \Delta_{\phi}, \Delta_{t}) = (0.518942(51), 1.59489(59), 1.20954(23))$, and also bound various OPE coefficients. We additionally introduce a new "tip-finding" algorithm to compute an upper bound on the leading rank-4 symmetric tensor $t_4$, which we find to be relevant with $\Delta_{t_4} < 2.99056$. The conformal bootstrap thus provides a numerical proof that systems described by the critical $O(3)$ model, such as classical Heisenberg ferromagnets at the Curie transition, are unstable to cubic anisotropy.

hep-th