54 research outputs found
Message passing for the coloring problem: Gallager meets Alon and Kahale
Message passing algorithms are popular in many combinatorial optimization
problems. For example, experimental results show that {\em survey propagation}
(a certain message passing algorithm) is effective in finding proper
-colorings of random graphs in the near-threshold regime. In 1962 Gallager
introduced the concept of Low Density Parity Check (LDPC) codes, and suggested
a simple decoding algorithm based on message passing. In 1994 Alon and Kahale
exhibited a coloring algorithm and proved its usefulness for finding a
-coloring of graphs drawn from a certain planted-solution distribution over
-colorable graphs. In this work we show an interpretation of Alon and
Kahale's coloring algorithm in light of Gallager's decoding algorithm, thus
showing a connection between the two problems - coloring and decoding. This
also provides a rigorous evidence for the usefulness of the message passing
paradigm for the graph coloring problem. Our techniques can be applied to
several other combinatorial optimization problems and networking-related
issues.Comment: 11 page
On the random satisfiable process
In this work we suggest a new model for generating random satisfiable k-CNF
formulas. To generate such formulas -- randomly permute all 2^k\binom{n}{k}
possible clauses over the variables x_1, ..., x_n, and starting from the empty
formula, go over the clauses one by one, including each new clause as you go
along if after its addition the formula remains satisfiable. We study the
evolution of this process, namely the distribution over formulas obtained after
scanning through the first m clauses (in the random permutation's order).
Random processes with conditioning on a certain property being respected are
widely studied in the context of graph properties. This study was pioneered by
Ruci\'nski and Wormald in 1992 for graphs with a fixed degree sequence, and
also by Erd\H{o}s, Suen, and Winkler in 1995 for triangle-free and bipartite
graphs. Since then many other graph properties were studied such as planarity
and H-freeness. Thus our model is a natural extension of this approach to the
satisfiability setting.
Our main contribution is as follows. For m \geq cn, c=c(k) a sufficiently
large constant, we are able to characterize the structure of the solution space
of a typical formula in this distribution. Specifically, we show that typically
all satisfying assignments are essentially clustered in one cluster, and all
but e^{-\Omega(m/n)} n of the variables take the same value in all satisfying
assignments. We also describe a polynomial time algorithm that finds with high
probability a satisfying assignment for such formulas
The condensation phase transition in random graph coloring
Based on a non-rigorous formalism called the "cavity method", physicists have
put forward intriguing predictions on phase transitions in discrete structures.
One of the most remarkable ones is that in problems such as random -SAT or
random graph -coloring, very shortly before the threshold for the existence
of solutions there occurs another phase transition called "condensation"
[Krzakala et al., PNAS 2007]. The existence of this phase transition appears to
be intimately related to the difficulty of proving precise results on, e.g.,
the -colorability threshold as well as to the performance of message passing
algorithms. In random graph -coloring, there is a precise conjecture as to
the location of the condensation phase transition in terms of a distributional
fixed point problem. In this paper we prove this conjecture for exceeding a
certain constant
Data Augmentation for Modeling Human Personality: The Dexter Machine
Modeling human personality is important for several AI challenges, from the
engineering of artificial psychotherapists to the design of persona bots.
However, the field of computational personality analysis heavily relies on
labeled data, which may be expensive, difficult or impossible to get. This
problem is amplified when dealing with rare personality types or disorders
(e.g., the anti-social psychopathic personality disorder). In this context, we
developed a text-based data augmentation approach for human personality
(PEDANT). PEDANT doesn't rely on the common type of labeled data but on the
generative pre-trained model (GPT) combined with domain expertise. Testing the
methodology on three different datasets, provides results that support the
quality of the generated data
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