1 citations · 2 across the 9 of their papers we have counts for
10 papers
Representation Alignment Rests on Linear Structure
Kiril Bangachev, Guy Bresler, Yury Polyanskiy
We investigate the Platonic Representation Hypothesis (PRH) through a tripartite statistical framework of representations: signal, bias, and noise. {1) Signal:} We propose that Pla…
Is Dimensionality a Barrier for Retrieval Models?
Kiril Bangachev, Guy Bresler, Jonathan Kogan +1
Why does the low dimensionality of representations, typically , not prevent modern embedding-based retrieval models from scaling to billions, or even trillions, of d…
Global Minimizers of Sigmoid Contrastive Loss
Kiril Bangachev, Guy Bresler, Iliyas Noman +1
The meta-task of obtaining and aligning representations through contrastive pretraining is steadily gaining importance since its introduction in CLIP and ALIGN. In this paper we th…
Graph Quasirandomness for Hypothesis Testing of Stochastic Block Models
Kiril Bangachev, Guy Bresler
The celebrated theorem of Chung, Graham, and Wilson on quasirandom graphs implies that if the 4-cycle and edge counts in a graph are both close to their typical number in $\mat…
Partial and Exact Recovery of a Random Hypergraph from its Graph Projection
Guy Bresler, Chenghao Guo, Yury Polyanskiy +1
Consider a -uniform random hypergraph on vertices in which hyperedges are included iid so that the average degree is . The projection of a hypergraph is a graph on the…
Thresholds for Reconstruction of Random Hypergraphs From Graph Projections
Guy Bresler, Chenghao Guo, Yury Polyanskiy
The graph projection of a hypergraph is a simple graph with the same vertex set and with an edge between each pair of vertices that appear in a hyperedge. We consider the problem o…
Near-Optimal Time-Sparsity Trade-Offs for Solving Noisy Linear Equations
Kiril Bangachev, Guy Bresler, Stefan Tiegel +1
We present a polynomial-time reduction from solving noisy linear equations over in dimension with a un…
Sandwiching Random Geometric Graphs and Erdos-Renyi with Applications: Sharp Thresholds, Robust Testing, and Enumeration
Kiril Bangachev, Guy Bresler
The distribution is formed by sampling independent vectors uniformly on and placing an edge between pair…
On The Fourier Coefficients of High-Dimensional Random Geometric Graphs
Kiril Bangachev, Guy Bresler
The random geometric graph is formed by sampling i.i.d. vectors uniformly on and placing an edge be…
Detection of Geometry in Random Geometric Graphs: Suboptimality of Triangles and Cluster Expansion
Kiril Bangachev, Guy Bresler
In this paper we study the random geometric graph with distance where each vertex is sampled uniformly from the -dimen…