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Universal Approximation Under Constraints is Possible with Transformers [article]

Anastasis Kratsios, Behnoosh Zamanlooy, Tianlin Liu, Ivan Dokmanić
2022 arXiv   pre-print
Our results imply the first universal approximation theorem for classical transformers with exact convex constraint satisfaction.  ...  The result guarantees that given an objective function L, a constraint set K, and a family of soft constraint sets, there is a probabilistic transformer F̂ that approximately minimizes L and whose outputs  ...  University of Zürich for his helpful feedback in the rebuttal phase.  ... 
arXiv:2110.03303v2 fatcat:2bnbxkaf7fhhrptscjz3453moy

Discrete R symmetries and anomalies

Michael Dine, Angelo Monteux
2014 Journal of High Energy Physics  
We review the Green-Schwarz cancellation of discrete anomalies, providing a heuristic explanation why, in the heterotic string, only the "model-independent dilaton" transforms non-linearly under discrete  ...  symmetries; this argument suggests that, in other theories, multiple fields might play a role in anomaly cancellations, further weakening any anomaly constraints at low energies.  ...  It is perfectly possible that the axion-like fields a i cancel various non-universal anomalies while precision gauge unification is achieved with 1/g 2 i ∼ s 0 .  ... 
doi:10.1007/jhep01(2014)011 fatcat:k776h56pnzhnvaye3fdhy3ngwy

Constraints on the universal contact interaction

W. Buchmüller, D. Wyler
1997 Physics Letters B  
Constraints from LEP2 imply that this universal contact interaction cannot be the origin of the recently observed high-Q^2 events at HERA.  ...  If these new forces are independent of colour and flavour quantum numbers including baryon and lepton number, then all low energy constraints, arising from quark-lepton universality, flavour-changing neutral  ...  which is significantly larger than the value needed to explain the HERA data.  ... 
doi:10.1016/s0370-2693(97)00734-x fatcat:czpw2pq3tjb5pa6sfsjjwtetnq

On Constraint Problems with Incomplete or Erroneous Data [chapter]

Neil Yorke-Smith, Carmen Gervet
2002 Lecture Notes in Computer Science  
Real-world constraint problems abound with uncertainty.  ...  We define the certainty closure to an uncertain constraint problem and show how it can be derived by transformation to an equivalent certain problem.  ...  The framework is complementary to stochastic data models (e.g. [6] ). Our current research looks at finding uncertain constraint classes and their corresponding tractable transformation operators.  ... 
doi:10.1007/3-540-46135-3_54 fatcat:5wu4dyjhlfbcvagjai7xsr2fga

On Constraint Problems with Incomplete or Erroneous Data [chapter]

Neil Yorke-Smith
2002 Lecture Notes in Computer Science  
Real-world constraint problems abound with uncertainty.  ...  We define the certainty closure to an uncertain constraint problem and show how it can be derived by transformation to an equivalent certain problem.  ...  The framework is complementary to stochastic data models (e.g. [6] ). Our current research looks at finding uncertain constraint classes and their corresponding tractable transformation operators.  ... 
doi:10.1007/3-540-46135-3_64 fatcat:r7vjlooe75earmuirernivpwcq

Page 36 of Bulletin of the American Physical Society Vol. 30, Issue 1 [page]

1955 Bulletin of the American Physical Society  
is invariant under a transformation group depending on arbitrary functions or when the Lagran- gian is linear in the time derivatives.  ...  However, if there are any first-class constraints, then the group of transformations contains an invariant subgroup, those transformations having a vanishing generator.  ... 

Page 1175 of None Vol. 98, Issue 4 [page]

1955 None  
is invariant under a transformation group depending on arbitrary functions or when the Lagran- gian is linear in the time derivatives.  ...  With each kinematic structure is associated a simplest possible Lagran- gian, and several are presented with their spectra.  ... 

Chance-Constrained Programming

A. Charnes, W. W. Cooper
1959 Management science  
Both projects are under contract with the U. 8. Office of Naval Research Reproduction of this paper in whole or in part is permitted for any purpose of the United States Government.  ...  More loosely, the problem is to determine optimal stochastic decision rules under these circumstances. An example is supplied in [2].  ... 
doi:10.1287/mnsc.6.1.73 fatcat:hnup7nnk65didp7ojxblwnnrei

Alternating Direction Method of Multipliers for Generalized Low-Rank Tensor Recovery

Jiarong Shi, Qingyan Yin, Xiuyun Zheng, Wei Yang
2016 Algorithms  
linear constraints.  ...  Low-Rank Tensor Recovery (LRTR), the higher order generalization of Low-Rank Matrix Recovery (LRMR), is especially suitable for analyzing multi-linear data with gross corruptions, outliers and missing  ...  ˚is a convex function with respect to A.  ... 
doi:10.3390/a9020028 fatcat:bj7c7fwkjzgflemz4vkvzt4xcm

Application of the no-signaling principle to obtain quantum cloners for any allowed value of fidelity

Z. Gedik, B. Çakmak
2013 Physical Review A. Atomic, Molecular, and Optical Physics  
Using only the no-signaling principle and an assumption about the form of the Schmidt decomposition, we show that for "any" allowed fidelity there is a "unique" approximate qubit cloner which can be written  ...  We introduce the prime cloners whose fidelities have multiplicative property and show that the fidelity of the prime cloners for the infinite copy limit is 1/2.  ...  ACKNOWLEDGMENTS This work has been partially supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) under Grant No. 111T232. The authors would like to thankİ. Adagideli,Ö.  ... 
doi:10.1103/physreva.87.042314 fatcat:5vsue3vpvzghjjbm2s5fhi6lca

Anisotropic separate universe and Weinberg's adiabatic mode [article]

Takahiro Tanaka, Yuko Urakawa
2021 arXiv   pre-print
In this paper, we show that the separate universe approach can be generically used, as long as a theory under consideration is local and preserves the spatial diffeomorphism invariance.  ...  In the separate universe approach, an inhomogeneous universe is rephrased as a set of glued numerous homogeneous local patches.  ...  under the slow-roll approximation [45].  ... 
arXiv:2101.05707v1 fatcat:t5tjbqirfbhb3few3rvksuyjjq

PID synthesis under probabilistic parametric uncertainty

Pedro Mercader, Kristian Soltesz, Alfonso Banos
2016 2016 American Control Conference (ACC)  
In this work, the problem is instead approximated by a deterministic one, through the unscented transform (UT), and its conjugate extension (CUT).  ...  The conventional way to find an approximate solution to the extended problem is through Monte Carlo (MC) methods, resulting in high computational cost.  ...  It is well-known that any Gaussian can be transformed into one with zero expectation and unitary covariance, through an affine transformation.  ... 
doi:10.1109/acc.2016.7526527 dblp:conf/amcc/MercaderSB16 fatcat:ktanm4kribf63iz2wq4vu7vqae

Page 22 of Bulletin of the American Physical Society Vol. 27, Issue 3 [page]

1952 Bulletin of the American Physical Society  
Canonical Coordinate Transformations and Constraints in Nonlinear Theories.* RALPH SCHILLER AND PETER G. BERGMANN, Syracuse University.  ...  BERGMANN, Syracuse University—In the approximation method intro- duced by Einstein and Infeld, the velocities of the particles are assumed to be small compared with the velocity of light.’  ... 

Page 198 of Physical Review Vol. 87, Issue 1 [page]

1952 Physical Review  
Canonical Coordinate Transformations and Constraints in Nonlinear Theories.* RALPH SCHILLER AND PETER G. BERGMANN, Syracuse University.  ...  A New Approximation for the Gravitational Field Equations.* JosHuUA GOLDBERG AND PETER G. BERGMANN, Syracuse University.  ... 

Page 34 of Bulletin of the American Physical Society Vol. 26, Issue 1 [page]

1951 Bulletin of the American Physical Society  
The final general formula is complicated, so that some numerical results as well as approximate expres- sions valid under various limiting conditions will be given. * Now at Northwestern University and  ...  To make a comparison with experi- ment possible, the cross section for the double Compton Effect (absorption of one photon followed by emission of two) is computed and integrated over the energy of one  ... 
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