887 research outputs found
Structure and Problem Hardness: Goal Asymmetry and DPLL Proofs in<br> SAT-Based Planning
In Verification and in (optimal) AI Planning, a successful method is to
formulate the application as boolean satisfiability (SAT), and solve it with
state-of-the-art DPLL-based procedures. There is a lack of understanding of why
this works so well. Focussing on the Planning context, we identify a form of
problem structure concerned with the symmetrical or asymmetrical nature of the
cost of achieving the individual planning goals. We quantify this sort of
structure with a simple numeric parameter called AsymRatio, ranging between 0
and 1. We run experiments in 10 benchmark domains from the International
Planning Competitions since 2000; we show that AsymRatio is a good indicator of
SAT solver performance in 8 of these domains. We then examine carefully crafted
synthetic planning domains that allow control of the amount of structure, and
that are clean enough for a rigorous analysis of the combinatorial search
space. The domains are parameterized by size, and by the amount of structure.
The CNFs we examine are unsatisfiable, encoding one planning step less than the
length of the optimal plan. We prove upper and lower bounds on the size of the
best possible DPLL refutations, under different settings of the amount of
structure, as a function of size. We also identify the best possible sets of
branching variables (backdoors). With minimum AsymRatio, we prove exponential
lower bounds, and identify minimal backdoors of size linear in the number of
variables. With maximum AsymRatio, we identify logarithmic DPLL refutations
(and backdoors), showing a doubly exponential gap between the two structural
extreme cases. The reasons for this behavior -- the proof arguments --
illuminate the prototypical patterns of structure causing the empirical
behavior observed in the competition benchmarks
An Atypical Survey of Typical-Case Heuristic Algorithms
Heuristic approaches often do so well that they seem to pretty much always
give the right answer. How close can heuristic algorithms get to always giving
the right answer, without inducing seismic complexity-theoretic consequences?
This article first discusses how a series of results by Berman, Buhrman,
Hartmanis, Homer, Longpr\'{e}, Ogiwara, Sch\"{o}ening, and Watanabe, from the
early 1970s through the early 1990s, explicitly or implicitly limited how well
heuristic algorithms can do on NP-hard problems. In particular, many desirable
levels of heuristic success cannot be obtained unless severe, highly unlikely
complexity class collapses occur. Second, we survey work initiated by Goldreich
and Wigderson, who showed how under plausible assumptions deterministic
heuristics for randomized computation can achieve a very high frequency of
correctness. Finally, we consider formal ways in which theory can help explain
the effectiveness of heuristics that solve NP-hard problems in practice.Comment: This article is currently scheduled to appear in the December 2012
issue of SIGACT New
On the Hardness of SAT with Community Structure
Recent attempts to explain the effectiveness of Boolean satisfiability (SAT)
solvers based on conflict-driven clause learning (CDCL) on large industrial
benchmarks have focused on the concept of community structure. Specifically,
industrial benchmarks have been empirically found to have good community
structure, and experiments seem to show a correlation between such structure
and the efficiency of CDCL. However, in this paper we establish hardness
results suggesting that community structure is not sufficient to explain the
success of CDCL in practice. First, we formally characterize a property shared
by a wide class of metrics capturing community structure, including
"modularity". Next, we show that the SAT instances with good community
structure according to any metric with this property are still NP-hard.
Finally, we study a class of random instances generated from the
"pseudo-industrial" community attachment model of Gir\'aldez-Cru and Levy. We
prove that, with high probability, instances from this model that have
relatively few communities but are still highly modular require exponentially
long resolution proofs and so are hard for CDCL. We also present experimental
evidence that our result continues to hold for instances with many more
communities. This indicates that actual industrial instances easily solved by
CDCL may have some other relevant structure not captured by the community
attachment model.Comment: 23 pages. Full version of a SAT 2016 pape
Backdoor Smoothing: Demystifying Backdoor Attacks on Deep Neural Networks
Backdoor attacks mislead machine-learning models to output an
attacker-specified class when presented a specific trigger at test time. These
attacks require poisoning the training data to compromise the learning
algorithm, e.g., by injecting poisoning samples containing the trigger into the
training set, along with the desired class label. Despite the increasing number
of studies on backdoor attacks and defenses, the underlying factors affecting
the success of backdoor attacks, along with their impact on the learning
algorithm, are not yet well understood. In this work, we aim to shed light on
this issue by unveiling that backdoor attacks induce a smoother decision
function around the triggered samples -- a phenomenon which we refer to as
\textit{backdoor smoothing}. To quantify backdoor smoothing, we define a
measure that evaluates the uncertainty associated to the predictions of a
classifier around the input samples.
Our experiments show that smoothness increases when the trigger is added to
the input samples, and that this phenomenon is more pronounced for more
successful attacks.
We also provide preliminary evidence that backdoor triggers are not the only
smoothing-inducing patterns, but that also other artificial patterns can be
detected by our approach, paving the way towards understanding the limitations
of current defenses and designing novel ones.Comment: 9 pages, 7 figures, under submissio
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