17 Search Results for "Ramya, C."

Document
Research
DOI: 10.4230/TGDK.4.1.1
On the Computational Cost of Knowledge Graph Embeddings

Authors: Victor Charpenay, Mansour Zoubeirou A Mayaki, and Antoine Zimmermann

Published in: TGDK, Volume 4, Issue 1 (2026). Transactions on Graph Data and Knowledge, Volume 4, Issue 1

Abstract
Over a decade, numerous Knowledge Graph Embedding (KGE) models have been designed and evaluated on reference datasets, always with increasing performance. In this paper, we re-evaluate these models with respect to their computational efficiency during training, by estimating the computational cost of the procedure expressed in floating-point operations. We design a cost model based on analytical expressions and apply it on a collection of 20 KGE models, representative of the state-of-the-art. We show that dimensionality or parameter efficiency, used in the literature to compare models with each other, are not suitable to evaluate the true cost of models. Through fixed-budget experiments, a novel approach to evaluate KGE models based on cost estimates, we re-assess the relative performance of model families compared to the state-of-the-art. Bilinear models such as ComplEx underperform with a low computational budget while hyperbolic linear models appear to offer no particular benefit compared to simpler Euclidian models, especially the MuRE model. Neural models, such as ConvE or CompGCN, achieve reasonable performance in the literature but their high computational cost appears unnecessary when compared with other models. The trade-off between efficiency and expressivity of both linear and neural models is to be further explored.
Cite as

Victor Charpenay, Mansour Zoubeirou A Mayaki, and Antoine Zimmermann. On the Computational Cost of Knowledge Graph Embeddings. In Transactions on Graph Data and Knowledge (TGDK), Volume 4, Issue 1, pp. 1:1-1:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@Article{charpenay_et_al:TGDK.4.1.1,
  author =	{Charpenay, Victor and Zoubeirou A Mayaki, Mansour and Zimmermann, Antoine},
  title =	{{On the Computational Cost of Knowledge Graph Embeddings}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{1:1--1:30},
  ISSN =	{2942-7517},
  year =	{2026},
  volume =	{4},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.4.1.1},
  URN =		{urn:nbn:de:0030-drops-256863},
  doi =		{10.4230/TGDK.4.1.1},
  annote =	{Keywords: Knowledge Graph Embedding, Parameter Efficiency, Computational Budget, Green AI}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.28
Conditional Complexity Hardness: Monotone Circuit Size, Matrix Rigidity, and Tensor Rank

Authors: Nikolai Chukhin, Alexander S. Kulikov, Ivan Mihajlin, and Arina Smirnova

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Proving complexity lower bounds remains a challenging task: currently, we only know how to prove conditional uniform (algorithm) lower bounds and nonuniform (circuit) lower bounds in restricted circuit models. About a decade ago, Williams (STOC 2010) showed how to derive nonuniform lower bounds from uniform upper bounds: roughly, by designing a fast algorithm for checking satisfiability of circuits, one gets a lower bound for this circuit class. Since then, a number of results of this kind have been proved. For example, Jahanjou et al. (ICALP 2015) and Carmosino et al. (ITCS 2016) proved that if NSETH fails, then E^{NP} has series-parallel circuit size ω(n). One can also derive nonuniform lower bounds from nondeterministic uniform lower bounds. Perhaps the most well-known example is the Karp-Lipton theorem (STOC 1980): if Σ₂ ≠ Π₂, then NP ⊄ P/poly. Some recent examples include the following. Nederlof (STOC 2020) proved a lower bound on the matrix multiplication tensor rank under an assumption that TSP cannot be solved faster than in 2ⁿ time. Belova et al. (SODA 2024) proved that there exists an explicit polynomial family of arithmetic circuit size Ω(n^{δ}), for any δ > 0, assuming that MAX-3-SAT cannot be solved faster than in 2ⁿ nondeterministic time. Williams (FOCS 2024) proved an exponential lower bound for ETHR ∘ ETHR circuits under the Orthogonal Vectors conjecture. Whereas all the lower bounds above are proved under strong assumptions that might eventually be refuted, the revealed connections are of great interest and may still give further insights: one may be able to weaken the used assumptions or to construct generators from other fine-grained reductions. In this paper, we continue developing this line of research and show how uniform nondeterministic lower bounds can be used to construct generators of various types of combinatorial objects that are notoriously hard to analyze: Boolean functions of high circuit size, matrices of high rigidity, and tensors of high rank. Specifically, we prove the following. - If, for some ε and k, k-SAT cannot be solved in input-oblivious co-nondeterministic time O(2^{(1/2+ε)n}), then there exists a monotone Boolean function family in coNP of monotone circuit size 2^{Ω(n / log n)}. Combining this with the result above, we get win-win circuit lower bounds: either E^{NP{}} requires series-parallel circuits of size ω(n) or coNP requires monotone circuits of size 2^{Ω(n / log n)}. - If, for all ε > 0, MAX-3-SAT cannot be solved in co-nondeterministic time O(2^{(1 - ε)n}), then there exist small families of matrices with rigidity exceeding the best known constructions as well as small families of three-dimensional tensors of rank n^{1+Δ}, for some Δ > 0.
Cite as

Nikolai Chukhin, Alexander S. Kulikov, Ivan Mihajlin, and Arina Smirnova. Conditional Complexity Hardness: Monotone Circuit Size, Matrix Rigidity, and Tensor Rank. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{chukhin_et_al:LIPIcs.STACS.2026.28,
  author =	{Chukhin, Nikolai and Kulikov, Alexander S. and Mihajlin, Ivan and Smirnova, Arina},
  title =	{{Conditional Complexity Hardness: Monotone Circuit Size, Matrix Rigidity, and Tensor Rank}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{28:1--28:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.28},
  URN =		{urn:nbn:de:0030-drops-255177},
  doi =		{10.4230/LIPIcs.STACS.2026.28},
  annote =	{Keywords: computational complexity, circuit complexity, lower bounds, conditional lower bounds, monotone circuits, matrix rigidity, tensor rank, arithmetic circuits, fine-grained complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.9
On Closure Properties of Read-Once Oblivious Algebraic Branching Programs

Authors: Robert Andrews, Jules Armand, Prateek Dwivedi, Magnus Rahbek Dalgaard Hansen, Nutan Limaye, Srikanth Srinivasan, and Sébastien Tavenas

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We investigate the closure properties of read-once oblivious Algebraic Branching Programs (roABPs) under various natural algebraic operations and prove the following. - Non-closure under factoring: There is a sequence of explicit polynomials (f_n(x₁,…, x_n))_n that have poly(n)-sized roABPs such that some irreducible factor of f_n requires roABPs of superpolynomial size in any order. - Non-closure under powering: There is a sequence of polynomials (f_n(x₁,…, x_n))_n with poly(n)-sized roABPs such that any super-constant power of f_n does not have roABPs of polynomial size in any order (and f_nⁿ requires exponential size in any order). - Non-closure under symmetric operations: There are symmetric polynomials (f_n(e₁,…, e_n))_n that have roABPs of polynomial size such that f_n(x₁,…, x_n) do not have roABPs of subexponential size. (Here, e₁,…, e_n denote the elementary symmetric polynomials in n variables.) These results should be viewed in light of known results on models such as algebraic circuits, (general) algebraic branching programs, formulas and constant-depth circuits, all of which are known to be closed under these operations. To prove non-closure under factoring, we construct hard polynomials based on expander graphs using gadgets that lift their hardness from sparse polynomials to roABPs. For symmetric compositions, we show that the circulant polynomial requires roABPs of exponential size in every variable order.
Cite as

Robert Andrews, Jules Armand, Prateek Dwivedi, Magnus Rahbek Dalgaard Hansen, Nutan Limaye, Srikanth Srinivasan, and Sébastien Tavenas. On Closure Properties of Read-Once Oblivious Algebraic Branching Programs. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{andrews_et_al:LIPIcs.ITCS.2026.9,
  author =	{Andrews, Robert and Armand, Jules and Dwivedi, Prateek and Hansen, Magnus Rahbek Dalgaard and Limaye, Nutan and Srinivasan, Srikanth and Tavenas, S\'{e}bastien},
  title =	{{On Closure Properties of Read-Once Oblivious Algebraic Branching Programs}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.9},
  URN =		{urn:nbn:de:0030-drops-252964},
  doi =		{10.4230/LIPIcs.ITCS.2026.9},
  annote =	{Keywords: Factoring, Closure Properties, Sparsity Bounds, Symmetric Polynomials, roABP, Expander Graphs}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.49
On the Hardness of Order Finding and Equivalence Testing for ROABPs

Authors: C. Ramya and Pratik Shastri

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
The complexity of representing a polynomial by a Read-Once Oblivious Algebraic Branching Program (ROABP) is highly dependent on the chosen variable ordering. Bhargava et al. [Bhargava et al., 2024] prove that finding the optimal ordering is NP-hard, and provide some evidence (based on the Small Set Expansion hypothesis) that it is also hard to approximate the optimal ROABP width. In another work, Baraskar et al. [Baraskar et al., 2024] show that it is NP-hard to test whether a polynomial is in the GL_n orbit of a polynomial of sparsity at most s. Building upon these works, we show the following results: first, we prove that approximating the minimum ROABP width up to any constant factor is NP-hard, when the input is presented as a circuit. This removes the reliance on stronger conjectures in the previous work [Bhargava et al., 2024]. Second, we show that testing if an input polynomial given in the sparse representation is in the affine GL_n orbit of a width-w ROABP is NP-hard. Furthermore, we show that over fields of characteristic 0, the problem is NP-hard even when the input polynomial is homogeneous. This provides the first NP-hardness results for membership testing for a dense subclass of polynomial sized algebraic branching programs (VBP). Finally, we locate the source of hardness for the order finding problem at the lowest possible non-trivial degree, proving that the problem is NP-hard even for quadratic forms.
Cite as

C. Ramya and Pratik Shastri. On the Hardness of Order Finding and Equivalence Testing for ROABPs. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 49:1-49:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{ramya_et_al:LIPIcs.FSTTCS.2025.49,
  author =	{Ramya, C. and Shastri, Pratik},
  title =	{{On the Hardness of Order Finding and Equivalence Testing for ROABPs}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{49:1--49:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.49},
  URN =		{urn:nbn:de:0030-drops-251296},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.49},
  annote =	{Keywords: ROABP, Order Finding, Equivalence Testing, NP-hardness, Hardness of Approximation}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.56
Efficient Polynomial Identity Testing over Nonassociative Algebras

Authors: Partha Mukhopadhyay, C. Ramya, and Pratik Shastri

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We design the first efficient polynomial identity testing algorithms over the nonassociative polynomial algebra. In particular, multiplication among the formal variables is commutative but it is not associative. This complements the strong lower bound results obtained over this algebra by Hrubeš, Yehudayoff, and Wigderson [Pavel Hrubes et al., 2010] and Fijalkow, Lagarde, Ohlmann, and Serre [Fijalkow et al., 2021] from the identity testing perspective. Our main results are the following: - We construct nonassociative algebras (both commutative and noncommutative) which have no low degree identities. As a result, we obtain the first Amitsur-Levitzki type theorems [A. S. Amitsur and J. Levitzki, 1950] over nonassociative polynomial algebras. As a direct consequence, we obtain randomized polynomial-time black-box PIT algorithms for nonassociative polynomials which allow evaluation over such algebras. - On the derandomization side, we give a deterministic polynomial-time identity testing algorithm for nonassociative polynomials given by arithmetic circuits in the white-box setting. Previously, such an algorithm was known with the additional restriction of noncommutativity [Vikraman Arvind et al., 2017]. - In the black-box setting, we construct a hitting set of quasipolynomial-size for nonassociative polynomials computed by arithmetic circuits of small depth. Understanding the black-box complexity of identity testing, even in the randomized setting, was open prior to our work.
Cite as

Partha Mukhopadhyay, C. Ramya, and Pratik Shastri. Efficient Polynomial Identity Testing over Nonassociative Algebras. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 56:1-56:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{mukhopadhyay_et_al:LIPIcs.APPROX/RANDOM.2025.56,
  author =	{Mukhopadhyay, Partha and C. Ramya and Shastri, Pratik},
  title =	{{Efficient Polynomial Identity Testing over Nonassociative Algebras}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{56:1--56:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.56},
  URN =		{urn:nbn:de:0030-drops-244224},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.56},
  annote =	{Keywords: Polynomial identity testing, nonassociative algebra, arithmetic circuits, black-box algorithms, white-box algorithms}
}
Document
DOI: 10.4230/LIPIcs.DNA.31.4
Differentiable Programming of Indexed Chemical Reaction Networks and Reaction-Diffusion Systems

Authors: Inhoo Lee, Salvador Buse, and Erik Winfree

Published in: LIPIcs, Volume 347, 31st International Conference on DNA Computing and Molecular Programming (DNA 31) (2025)

Abstract
Many molecular systems are best understood in terms of prototypical species and reactions. The central dogma and related biochemistry are rife with examples: gene i is transcribed into RNA i, which is translated into protein i; kinase n phosphorylates substrate m; protein p dimerizes with protein q. Engineered nucleic acid systems also often have this form: oligonucleotide i hybridizes to complementary oligonucleotide j; signal strand n displaces the output of seesaw gate m; hairpin p triggers the opening of target q. When there are many variants of a small number of prototypes, it can be conceptually cleaner and computationally more efficient to represent the full system in terms of indexed species (e.g. for dimerization, M_p, D_pq) and indexed reactions (M_p + M_q → D_pq). Here, we formalize the Indexed Chemical Reaction Network (ICRN) model and describe a Python software package designed to simulate such systems in the well-mixed and reaction-diffusion settings, using a differentiable programming framework originally developed for large-scale neural network models, taking advantage of GPU acceleration when available. Notably, this framework makes it straightforward to train the models’ initial conditions and rate constants to optimize a target behavior, such as matching experimental data, performing a computation, or exhibiting spatial pattern formation. The natural map of indexed chemical reaction networks onto neural network formalisms provides a tangible yet general perspective for translating concepts and techniques from the theory and practice of neural computation into the design of biomolecular systems.
Cite as

Inhoo Lee, Salvador Buse, and Erik Winfree. Differentiable Programming of Indexed Chemical Reaction Networks and Reaction-Diffusion Systems. In 31st International Conference on DNA Computing and Molecular Programming (DNA 31). Leibniz International Proceedings in Informatics (LIPIcs), Volume 347, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{lee_et_al:LIPIcs.DNA.31.4,
  author =	{Lee, Inhoo and Buse, Salvador and Winfree, Erik},
  title =	{{Differentiable Programming of Indexed Chemical Reaction Networks and Reaction-Diffusion Systems}},
  booktitle =	{31st International Conference on DNA Computing and Molecular Programming (DNA 31)},
  pages =	{4:1--4:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-399-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{347},
  editor =	{Schaeffer, Josie and Zhang, Fei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.31.4},
  URN =		{urn:nbn:de:0030-drops-238534},
  doi =		{10.4230/LIPIcs.DNA.31.4},
  annote =	{Keywords: Differentiable Programming, Chemical Reaction Networks, Reaction-Diffusion Systems}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.26
Algebraic Metacomplexity and Representation Theory

Authors: Maxim van den Berg, Pranjal Dutta, Fulvio Gesmundo, Christian Ikenmeyer, and Vladimir Lysikov

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
In the algebraic metacomplexity framework we prove that the decomposition of metapolynomials into their isotypic components can be implemented efficiently, namely with only a quasipolynomial blowup in the circuit size. We use this to resolve an open question posed by Grochow, Kumar, Saks & Saraf (2017). Our result means that many existing algebraic complexity lower bound proofs can be efficiently converted into isotypic lower bound proofs via highest weight metapolynomials, a notion studied in geometric complexity theory. In the context of algebraic natural proofs, it means that without loss of generality algebraic natural proofs can be assumed to be isotypic. Our proof is built on the Poincaré-Birkhoff-Witt theorem for Lie algebras and on Gelfand-Tsetlin theory, for which we give the necessary comprehensive background.
Cite as

Maxim van den Berg, Pranjal Dutta, Fulvio Gesmundo, Christian Ikenmeyer, and Vladimir Lysikov. Algebraic Metacomplexity and Representation Theory. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 26:1-26:35, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{vandenberg_et_al:LIPIcs.CCC.2025.26,
  author =	{van den Berg, Maxim and Dutta, Pranjal and Gesmundo, Fulvio and Ikenmeyer, Christian and Lysikov, Vladimir},
  title =	{{Algebraic Metacomplexity and Representation Theory}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{26:1--26:35},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.26},
  URN =		{urn:nbn:de:0030-drops-237209},
  doi =		{10.4230/LIPIcs.CCC.2025.26},
  annote =	{Keywords: Algebraic complexity theory, metacomplexity, representation theory, geometric complexity theory}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.14
Model Ensembling for Constrained Optimization

Authors: Ira Globus Harris, Varun Gupta, Michael Kearns, and Aaron Roth

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
Many instances of decision making under objective uncertainty can be decomposed into two steps: predicting the objective function and then optimizing for the best feasible action under the estimate of the objective vector. We study the problem of ensembling models for optimization of uncertain linear objectives under arbitrary constraints. We imagine we are given a collection of predictive models mapping a feature space to multi-dimensional real-valued predictions, which form the coefficients of a linear objective that we would like to optimize. We give two ensembling methods that can provably result in transparent decisions that strictly improve on all initial policies. The first method operates in the "white box" setting in which we have access to the underlying prediction models and the second in the "black box" setting in which we only have access to the induced decisions (in the downstream optimization problem) of the constituent models, but not their underlying point predictions. They are transparent or trustworthy in the sense that the user can reliably predict long-term ensemble rewards even if the instance by instance predictions are imperfect.
Cite as

Ira Globus Harris, Varun Gupta, Michael Kearns, and Aaron Roth. Model Ensembling for Constrained Optimization. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{globusharris_et_al:LIPIcs.FORC.2025.14,
  author =	{Globus Harris, Ira and Gupta, Varun and Kearns, Michael and Roth, Aaron},
  title =	{{Model Ensembling for Constrained Optimization}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.14},
  URN =		{urn:nbn:de:0030-drops-231412},
  doi =		{10.4230/LIPIcs.FORC.2025.14},
  annote =	{Keywords: model ensembling, trustworthy AI, decision-making under uncertainty}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2024.10
Explicit Commutative ROABPs from Partial Derivatives

Authors: Vishwas Bhargava and Anamay Tengse

Published in: LIPIcs, Volume 323, 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)

Abstract
The dimension of partial derivatives (Nisan and Wigderson, 1997) is a popular measure for proving lower bounds in algebraic complexity. It is used to give strong lower bounds on the Waring decomposition of polynomials (called Waring rank). This naturally leads to an interesting open question: does this measure essentially characterize the Waring rank of any polynomial? The well-studied model of Read-once Oblivious ABPs (ROABPs for short) lends itself to an interesting hierarchy of "sub-models": Any-Order-ROABPs (ARO), Commutative ROABPs, and Diagonal ROABPs. It follows from previous works that for any polynomial, a bound on its Waring rank implies an analogous bound on its Diagonal ROABP complexity (called the duality trick), and a bound on its dimension of partial derivatives implies an analogous bound on its "ARO complexity": ROABP complexity in any order (Nisan, 1991). Our work strengthens the latter connection by showing that a bound on the dimension of partial derivatives in fact implies a bound on the commutative ROABP complexity. Thus, we improve our understanding of partial derivatives and move a step closer towards answering the above question. Our proof builds on the work of Ramya and Tengse (2022) to show that the commutative-ROABP-width of any homogeneous polynomial is at most the dimension of its partial derivatives. The technique itself is a generalization of the proof of the duality trick due to Saxena (2008).
Cite as

Vishwas Bhargava and Anamay Tengse. Explicit Commutative ROABPs from Partial Derivatives. In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{bhargava_et_al:LIPIcs.FSTTCS.2024.10,
  author =	{Bhargava, Vishwas and Tengse, Anamay},
  title =	{{Explicit Commutative ROABPs from Partial Derivatives}},
  booktitle =	{44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)},
  pages =	{10:1--10:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-355-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{323},
  editor =	{Barman, Siddharth and Lasota, S{\l}awomir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2024.10},
  URN =		{urn:nbn:de:0030-drops-221994},
  doi =		{10.4230/LIPIcs.FSTTCS.2024.10},
  annote =	{Keywords: Partial derivatives, Apolar ideals, Commuting matrices, Branching programs}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.91
Lower Bounds for Planar Arithmetic Circuits

Authors: C. Ramya and Pratik Shastri

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
Arithmetic circuits are a natural well-studied model for computing multivariate polynomials over a field. In this paper, we study planar arithmetic circuits. These are circuits whose underlying graph is planar. In particular, we prove an Ω(nlog n) lower bound on the size of planar arithmetic circuits computing explicit bilinear forms on 2n variables. As a consequence, we get an Ω(nlog n) lower bound on the size of arithmetic formulas and planar algebraic branching programs computing explicit bilinear forms. This is the first such lower bound on the formula complexity of an explicit bilinear form. In the case of read-once planar circuits, we show Ω(n²) size lower bounds for computing explicit bilinear forms. Furthermore, we prove fine separations between the various planar models of computations mentioned above. In addition to this, we look at multi-output planar circuits and show Ω(n^{4/3}) size lower bound for computing an explicit linear transformation on n-variables. For a suitable definition of multi-output formulas, we extend the above result to get an Ω(n²/log n) size lower bound. As a consequence, we demonstrate that there exists an n-variate polynomial computable by n^{1 + o(1)}-sized formulas such that any multi-output planar circuit (resp., multi-output formula) simultaneously computing all its first-order partial derivatives requires size Ω(n^{4/3}) (resp., Ω(n²/log n)). This shows that a statement analogous to that of Baur, Strassen[Walter Baur and Volker Strassen, 1983] does not hold in the case of planar circuits and formulas.
Cite as

C. Ramya and Pratik Shastri. Lower Bounds for Planar Arithmetic Circuits. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 91:1-91:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{ramya_et_al:LIPIcs.ITCS.2024.91,
  author =	{Ramya, C. and Shastri, Pratik},
  title =	{{Lower Bounds for Planar Arithmetic Circuits}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{91:1--91:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.91},
  URN =		{urn:nbn:de:0030-drops-196199},
  doi =		{10.4230/LIPIcs.ITCS.2024.91},
  annote =	{Keywords: Arithmetic circuit complexity, Planar circuits, Bilinear forms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.6
On Identity Testing and Noncommutative Rank Computation over the Free Skew Field

Authors: V. Arvind, Abhranil Chatterjee, Utsab Ghosal, Partha Mukhopadhyay, and C. Ramya

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
The identity testing of rational formulas (RIT) in the free skew field efficiently reduces to computing the rank of a matrix whose entries are linear polynomials in noncommuting variables [Hrubeš and Wigderson, 2015]. This rank computation problem has deterministic polynomial-time white-box algorithms [Ankit Garg et al., 2016; Ivanyos et al., 2018] and a randomized polynomial-time algorithm in the black-box setting [Harm Derksen and Visu Makam, 2017]. In this paper, we propose a new approach for efficient derandomization of black-box RIT. Additionally, we obtain results for matrix rank computation over the free skew field and construct efficient linear pencil representations for a new class of rational expressions. More precisely, we show: - Under the hardness assumption that the ABP (algebraic branching program) complexity of every polynomial identity for the k×k matrix algebra is 2^Ω(k) [Andrej Bogdanov and Hoeteck Wee, 2005], we obtain a subexponential-time black-box RIT algorithm for rational formulas of inversion height almost logarithmic in the size of the formula. This can be seen as the first "hardness implies derandomization" type theorem for rational formulas. - We show that the noncommutative rank of any matrix over the free skew field whose entries have small linear pencil representations can be computed in deterministic polynomial time. While an efficient rank computation was known for matrices with noncommutative formulas as entries [Ankit Garg et al., 2020], we obtain the first deterministic polynomial-time algorithms for rank computation of matrices whose entries are noncommutative ABPs or rational formulas. - Motivated by the definition given by Bergman [George M Bergman, 1976], we define a new class of rational functions where a rational function of inversion height at most h is defined as a composition of a noncommutative r-skewed circuit (equivalently an ABP) with inverses of rational functions of this class of inversion height at most h-1 which are also disjoint. We obtain a polynomial-size linear pencil representation for this class which gives a white-box deterministic polynomial-time identity testing algorithm for the class.
Cite as

V. Arvind, Abhranil Chatterjee, Utsab Ghosal, Partha Mukhopadhyay, and C. Ramya. On Identity Testing and Noncommutative Rank Computation over the Free Skew Field. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{arvind_et_al:LIPIcs.ITCS.2023.6,
  author =	{Arvind, V. and Chatterjee, Abhranil and Ghosal, Utsab and Mukhopadhyay, Partha and Ramya, C.},
  title =	{{On Identity Testing and Noncommutative Rank Computation over the Free Skew Field}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.6},
  URN =		{urn:nbn:de:0030-drops-175093},
  doi =		{10.4230/LIPIcs.ITCS.2023.6},
  annote =	{Keywords: Algebraic Complexity, Identity Testing, Non-commutative rank}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.44
If VNP Is Hard, Then so Are Equations for It

Authors: Mrinal Kumar, C. Ramya, Ramprasad Saptharishi, and Anamay Tengse

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
Assuming that the Permanent polynomial requires algebraic circuits of exponential size, we show that the class VNP does not have efficiently computable equations. In other words, any nonzero polynomial that vanishes on the coefficient vectors of all polynomials in the class VNP requires algebraic circuits of super-polynomial size. In a recent work of Chatterjee, Kumar, Ramya, Saptharishi and Tengse (FOCS 2020), it was shown that the subclasses of VP and VNP consisting of polynomials with bounded integer coefficients do have equations with small algebraic circuits. Their work left open the possibility that these results could perhaps be extended to all of VP or VNP. The results in this paper show that assuming the hardness of Permanent, at least for VNP, allowing polynomials with large coefficients does indeed incur a significant blow up in the circuit complexity of equations.
Cite as

Mrinal Kumar, C. Ramya, Ramprasad Saptharishi, and Anamay Tengse. If VNP Is Hard, Then so Are Equations for It. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 44:1-44:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{kumar_et_al:LIPIcs.STACS.2022.44,
  author =	{Kumar, Mrinal and Ramya, C. and Saptharishi, Ramprasad and Tengse, Anamay},
  title =	{{If VNP Is Hard, Then so Are Equations for It}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{44:1--44:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.44},
  URN =		{urn:nbn:de:0030-drops-158547},
  doi =		{10.4230/LIPIcs.STACS.2022.44},
  annote =	{Keywords: Computational Complexity, Algebraic Circuits, Algebraic Natural Proofs}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.53
On Finer Separations Between Subclasses of Read-Once Oblivious ABPs

Authors: C. Ramya and Anamay Tengse

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
Read-once Oblivious Algebraic Branching Programs (ROABPs) compute polynomials as products of univariate polynomials that have matrices as coefficients. In an attempt to understand the landscape of algebraic complexity classes surrounding ROABPs, we study classes of ROABPs based on the algebraic structure of these coefficient matrices. We study connections between polynomials computed by these structured variants of ROABPs and other well-known classes of polynomials (such as depth-three powering circuits, tensor-rank and Waring rank of polynomials). Our main result concerns commutative ROABPs, where all coefficient matrices commute with each other, and diagonal ROABPs, where all the coefficient matrices are just diagonal matrices. In particular, we show a somewhat surprising connection between these models and the model of depth-three powering circuits that is related to the Waring rank of polynomials. We show that if the dimension of partial derivatives captures Waring rank up to polynomial factors, then the model of diagonal ROABPs efficiently simulates the seemingly more expressive model of commutative ROABPs. Further, a commutative ROABP that cannot be efficiently simulated by a diagonal ROABP will give an explicit polynomial that gives a super-polynomial separation between dimension of partial derivatives and Waring rank. Our proof of the above result builds on the results of Marinari, Möller and Mora (1993), and Möller and Stetter (1995), that characterise rings of commuting matrices in terms of polynomials that have small dimension of partial derivatives. The algebraic structure of the coefficient matrices of these ROABPs plays a crucial role in our proofs.
Cite as

C. Ramya and Anamay Tengse. On Finer Separations Between Subclasses of Read-Once Oblivious ABPs. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 53:1-53:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{ramya_et_al:LIPIcs.STACS.2022.53,
  author =	{Ramya, C. and Tengse, Anamay},
  title =	{{On Finer Separations Between Subclasses of Read-Once Oblivious ABPs}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{53:1--53:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.53},
  URN =		{urn:nbn:de:0030-drops-158636},
  doi =		{10.4230/LIPIcs.STACS.2022.53},
  annote =	{Keywords: Algebraic Complexity Theory, Algebraic Branching Programs, Commutative Matrices}
}
Document
DOI: 10.4230/LITES.7.1.2
We know what you're doing! Application detection using thermal data

Authors: Philipp Miedl, Rehan Ahmed, and Lothar Thiele

Published in: LITES, Volume 7, Issue 1 (2021): Special Issue on Embedded System Security. Leibniz Transactions on Embedded Systems, Volume 7, Issue 1

Abstract
Modern mobile and embedded devices have high computing power which allows them to be used for multiple purposes. Therefore, applications with low security restrictions may execute on the same device as applications handling highly sensitive information. In such a setup, a security risk occurs if it is possible that an application uses system characteristics to gather information about another application on the same device.In this work, we present a method to leak sensitive runtime information by just using temperature sensor readings of a mobile device. We employ a Convolutional-Neural-Network, Long Short-Term Memory units and subsequent label sequence processing to identify the sequence of executed applications over time. To test our hypothesis we collect data from two state-of-the-art smartphones and real user usage patterns. We show an extensive evaluation using laboratory data, where we achieve labelling accuracies up to 90% and negligible timing error. Based on our analysis we state that the thermal information can be used to compromise sensitive user data and increase the vulnerability of mobile devices. A study based on data collected outside of the laboratory opens up various future directions for research.
Cite as

Philipp Miedl, Rehan Ahmed, and Lothar Thiele. We know what you're doing! Application detection using thermal data. In LITES, Volume 7, Issue 1 (2021): Special Issue on Embedded System Security. Leibniz Transactions on Embedded Systems, Volume 7, Issue 1, pp. 02:1-02:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@Article{miedl_et_al:LITES.7.1.2,
  author =	{Miedl, Philipp and Ahmed, Rehan and Thiele, Lothar},
  title =	{{We know what you're doing! Application detection using thermal data}},
  journal =	{Leibniz Transactions on Embedded Systems},
  pages =	{02:1--02:28},
  ISSN =	{2199-2002},
  year =	{2021},
  volume =	{7},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES.7.1.2},
  URN =		{urn:nbn:de:0030-drops-192850},
  doi =		{10.4230/LITES.7.1.2},
  annote =	{Keywords: Thermal Monitoring, Side Channel, Data Leak, Sequence Labelling}
}
Document
DOI: 10.4230/LIPIcs.CCC.2021.7
Separating ABPs and Some Structured Formulas in the Non-Commutative Setting

Authors: Prerona Chatterjee

Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)

Abstract
The motivating question for this work is a long standing open problem, posed by Nisan [Noam Nisan, 1991], regarding the relative powers of algebraic branching programs (ABPs) and formulas in the non-commutative setting. Even though the general question remains open, we make some progress towards its resolution. To that effect, we generalise the notion of ordered polynomials in the non-commutative setting (defined by Hrubeš, Wigderson and Yehudayoff [Hrubeš et al., 2011]) to define abecedarian polynomials and models that naturally compute them. Our main contribution is a possible new approach towards resolving the VF_{nc} vs VBP_{nc} question, via lower bounds against abecedarian formulas. In particular, we show the following. There is an explicit n²-variate degree d abecedarian polynomial f_{n,d}(𝐱) such that - f_{n, d}(𝐱) can be computed by an abecedarian ABP of size O(nd); - any abecedarian formula computing f_{n, log n}(𝐱) must have size at least n^{Ω(log log n)}. We also show that a super-polynomial lower bound against abecedarian formulas for f_{log n, n}(𝐱) would separate the powers of formulas and ABPs in the non-commutative setting.
Cite as

Prerona Chatterjee. Separating ABPs and Some Structured Formulas in the Non-Commutative Setting. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 7:1-7:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{chatterjee:LIPIcs.CCC.2021.7,
  author =	{Chatterjee, Prerona},
  title =	{{Separating ABPs and Some Structured Formulas in the Non-Commutative Setting}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{7:1--7:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.7},
  URN =		{urn:nbn:de:0030-drops-142812},
  doi =		{10.4230/LIPIcs.CCC.2021.7},
  annote =	{Keywords: Non-Commutative Formulas, Lower Bound, Separating ABPs and Formulas}
}
  • Refine by Type
  • 17 Document/PDF
  • 7 Document/HTML

  • Refine by Publication Year
  • 3 2026
  • 5 2025
  • 2 2024
  • 1 2023
  • 2 2022
  • Show More...

  • Refine by Author
  • 6 Ramya, C.
  • 3 Shastri, Pratik
  • 3 Tengse, Anamay
  • 2 Mukhopadhyay, Partha
  • 2 Rao, B. V. Raghavendra
  • Show More...

  • Refine by Series/Journal
  • 15 LIPIcs
  • 1 LITES
  • 1 TGDK

  • Refine by Classification
  • 11 Theory of computation → Algebraic complexity theory
  • 2 Theory of computation → Circuit complexity
  • 2 Theory of computation → Problems, reductions and completeness
  • 1 Computer systems organization → Molecular computing
  • 1 Computing methodologies → Learning settings
  • Show More...

  • Refine by Keyword
  • 2 Algebraic Complexity Theory
  • 2 Algebraic complexity theory
  • 2 Computational Complexity
  • 2 arithmetic circuits
  • 1 Algebraic Branching Programs
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact