arXiv subjects

Rahul Soni

Publications and source records attributed to Rahul Soni.

22 records · Page 2Linked to original sources

arXiv2020

Adversarial TCAV -- Robust and Effective Interpretation of Intermediate Layers in Neural Networks

Interpreting neural network decisions and the information learned in intermediate layers is still a challenge due to the opaque internal state and shared non-linear interactions. Although (Kim et al, 2017) proposed to interpret intermediate layers by quantifying its ability to distinguish a user-defined concept (from random examples), the questions of robustness (variation against the choice of random examples) and effectiveness (retrieval rate of concept images) remain. We investigate these two properties and propose improvements to make concept activations reliable for practical use. Effectiveness: If the intermediate layer has effectively learned a user-defined concept, it should be able to recall --- at the testing step --- most of the images containing the proposed concept. For instance, we observed that the recall rate of Tiger shark and Great white shark from the ImageNet dataset with "Fins" as a user-defined concept was only 18.35% for VGG16. To increase the effectiveness of concept learning, we propose A-CAV --- the Adversarial Concept Activation Vector --- this results in larger margins between user concepts and (negative) random examples. This approach improves the aforesaid recall to 76.83% for VGG16. For robustness, we define it as the ability of an intermediate layer to be consistent in its recall rate (the effectiveness) for different random seeds. We observed that TCAV has a large variance in recalling a concept across different random seeds. For example, the recall of cat images (from a layer learning the concept of tail) varies from 18% to 86% with 20.85% standard deviation on VGG16. We propose a simple and scalable modification that employs a Gram-Schmidt process to sample random noise from concepts and learn an average "concept classifier". This approach improves the aforesaid standard deviation from 20.85% to 6.4%.

cs.LG↗

arXiv2020

BCS-BEC crossover in a $(t_{2g})^4$ Excitonic Magnet

The condensation of spin-orbit-induced excitons in $(t_{2g})^4$ electronic systems is attracting considerable attention. In the large Hubbard U limit, antiferromagnetism was proposed to emerge from the Bose-Einstein Condensation (BEC) of triplons ($J_{\textrm{eff}} = 1$). In this publication, we show that even for the weak and intermediate U regimes, the spin-orbit exciton condensation is possible leading also to staggered magnetic order. The canonical electron-hole excitations (excitons) transform into local triplon excitations at large U , and this BEC strong coupling regime is smoothly connected to the intermediate U excitonic insulator region. We solved the degenerate three-orbital Hubbard model with spin-orbit coupling ($λ$) in one-dimensional geometry using the Density Matrix Renormalization Group, while in two-dimensional square clusters we use the Hartree-Fock approximation (HFA). Employing these techniques, we provide the full $λ$ vs U phase diagrams for both one- and two- dimensional lattices. Our main result is that at the intermediate Hubbard U region of our focus, increasing $λ$ at fixed U the system transitions from an incommensurate spin-density-wave metal to a Bardeen-Cooper-Schrieffer (BCS) excitonic insulator, with coherence length r coh of O(a) and O(10a) in 1d and 2d, respectively, with a the lattice spacing. Further increasing $λ$, the system eventually crosses over to the BEC limit (with r coh << a).

cond-mat.str-el↗

arXiv2020

Fine-grained Uncertainty Modeling in Neural Networks

Existing uncertainty modeling approaches try to detect an out-of-distribution point from the in-distribution dataset. We extend this argument to detect finer-grained uncertainty that distinguishes between (a). certain points, (b). uncertain points but within the data distribution, and (c). out-of-distribution points. Our method corrects overconfident NN decisions, detects outlier points and learns to say ``I don't know'' when uncertain about a critical point between the top two predictions. In addition, we provide a mechanism to quantify class distributions overlap in the decision manifold and investigate its implications in model interpretability. Our method is two-step: in the first step, the proposed method builds a class distribution using Kernel Activation Vectors (kav) extracted from the Network. In the second step, the algorithm determines the confidence of a test point by a hierarchical decision rule based on the chi-squared distribution of squared Mahalanobis distances. Our method sits on top of a given Neural Network, requires a single scan of training data to estimate class distribution statistics, and is highly scalable to deep networks and wider pre-softmax layer. As a positive side effect, our method helps to prevent adversarial attacks without requiring any additional training. It is directly achieved when the Softmax layer is substituted by our robust uncertainty layer at the evaluation phase.

cs.LG↗

arXiv2013

Dyonic Black Hole and Holography

We study thermodynamic properties of dyonic black hole and its dual field theory. We observe that the phase diagram of a dyonic black hole in constant electric potential and magnetic charge ensemble is similar to that of a Van der Waals fluid with chemical potential. Phase transitions and other critical phenomena have been studied in presence of magnetic charge and chemical potential. We also analyse magnetic properties of dual conformal field theory and observe a ferromagnetic like behavior of boundary theory when the external magnetic field vanishes. Finally, we compute susceptibility of different phases of boundary CFT and find that, depending on the strength of the external magnetic field and temperature, these phases are either paramagnetic or diamagnetic.

hep-th↗