Search Results for author:
Found 13 papers, 0 papers with code
Exact objectives of random linear programs and mean widths of random polyhedrons
We consider \emph{random linear programs} (rlps) as a subclass of \emph{random optimization problems} (rops) and study their typical behavior.
Capacity of the Hebbian-Hopfield network associative memory
In \cite{Hop82}, Hopfield introduced a \emph{Hebbian} learning rule based neural network model and suggested how it can efficiently operate as an associative memory.
Exact capacity of the \emph{wide} hidden layer treelike neural networks with generic activations
We obtain explicit, closed form, capacity characterizations for a very generic class of the hidden layer activations.
Fixed width treelike neural networks capacity analysis -- generic activations
In more concrete terms, for each of these activations, we obtain both the RDT and pl RDT based memory capacities upper bound characterization for \emph{any} given (even) number of the hidden layer neurons, $d$.
Fl RDT based ultimate lowering of the negative spherical perceptron capacity
We here first show that the \emph{negative spherical perceptrons} can be fitted into the frame of the fl RDT and then employ the whole fl RDT machinery to characterize the capacity.
\emph{Lifted} RDT based capacity analysis of the 1-hidden layer treelike \emph{sign} perceptrons neural networks
Moreover, for particular \emph{treelike committee machines} (TCM) architectures with $d\leq 5$ neurons in the hidden layer, \cite{Stojnictcmspnncaprdt23} made a very first mathematically rigorous progress in over 30 years by lowering the previously best known capacity bounds of \cite{MitchDurb89}.
Capacity of the treelike sign perceptrons neural networks with one hidden layer -- RDT based upper bounds
We study the capacity of \emph{sign} perceptrons neural networks (SPNN) and particularly focus on 1-hidden layer \emph{treelike committee machine} (TCM) architectures.
Binary perceptrons capacity via fully lifted random duality theory
In particular, we rely on \emph{fully lifted} random duality theory (fl RDT) established in \cite{Stojnicflrdt23} to create a general framework for studying the perceptrons' capacities.
Causal Inference (C-inf) -- asymmetric scenario of typical phase transitions
In this paper, we revisit and further explore a mathematically rigorous connection between Causal inference (C-inf) and the Low-rank recovery (LRR) established in [10].
Causal Inference (C-inf) -- closed form worst case typical phase transitions
In this paper we establish a mathematically rigorous connection between Causal inference (C-inf) and the low-rank recovery (LRR).
Discrete perceptrons
An introductory statistical mechanics treatment of such perceptrons was given in \cite{GutSte90}.
Spherical perceptron as a storage memory with limited errors
In Gardner's original work the statistical mechanics predictions in this directions were presented sa well.
A problem dependent analysis of SOCP algorithms in noisy compressed sensing
In our recent work \cite{StojnicGenSocp10} we established an alternative framework that can be used for statistical performance analysis of the SOCP algorithms.
