Cool. Will definitely do 👍
May 27, 2025 at 5:18 AM
Cool. Will definitely do 👍
Interesting. I was not aware of aware if the challenges in the video subfield. But that makes sense given the context. We will definitely explore those benchmarks in the future. Thanks for the suggestions.
May 27, 2025 at 5:10 AM
Interesting. I was not aware of aware if the challenges in the video subfield. But that makes sense given the context. We will definitely explore those benchmarks in the future. Thanks for the suggestions.
Tnx. We did not test yet on any other benshmarks. You mean algorithmic or language type benchmarks?
May 27, 2025 at 4:57 AM
Tnx. We did not test yet on any other benshmarks. You mean algorithmic or language type benchmarks?
Interesting. I was not aware of this study. However, we did not just used tropical operations, we tried to simulate a concrete tropical circuit and do the message passing in the tropical space with the Generalized Hilbert metric as the kernel.
May 27, 2025 at 4:54 AM
Interesting. I was not aware of this study. However, we did not just used tropical operations, we tried to simulate a concrete tropical circuit and do the message passing in the tropical space with the Generalized Hilbert metric as the kernel.
7/ Our message ✍️
Better reasoning might come not from bigger models, but from choosing the right algebra/geometry 🌴.
@petar-v.bsky.social @jalonso.bsky.social
#TropicalGeometry #NeuralAlgorithmicReasoning #AI4Math
Better reasoning might come not from bigger models, but from choosing the right algebra/geometry 🌴.
@petar-v.bsky.social @jalonso.bsky.social
#TropicalGeometry #NeuralAlgorithmicReasoning #AI4Math
May 26, 2025 at 1:08 PM
7/ Our message ✍️
Better reasoning might come not from bigger models, but from choosing the right algebra/geometry 🌴.
@petar-v.bsky.social @jalonso.bsky.social
#TropicalGeometry #NeuralAlgorithmicReasoning #AI4Math
Better reasoning might come not from bigger models, but from choosing the right algebra/geometry 🌴.
@petar-v.bsky.social @jalonso.bsky.social
#TropicalGeometry #NeuralAlgorithmicReasoning #AI4Math
6/ We also show that each Tropical attention head can function as a tropical gate in a tropical circuit, simulating any max-plus circuit.
May 26, 2025 at 1:08 PM
6/ We also show that each Tropical attention head can function as a tropical gate in a tropical circuit, simulating any max-plus circuit.
5/ We benchmarked on 11 canonical combinatorial tasks. Tropical attention beat vanilla & adaptive softmax attention on all three OOD axes, Length, value and Adversarial attack generalization:
May 26, 2025 at 1:08 PM
5/ We benchmarked on 11 canonical combinatorial tasks. Tropical attention beat vanilla & adaptive softmax attention on all three OOD axes, Length, value and Adversarial attack generalization:
4/ Tropical Attention runs each head natively in max-plus. Result:
Strong OOD length generalization with sharp attention maps even in several algorithmic tasks, including the notorious Quickselect algorithm (Another settlement for the challenge identified by @mgalkin.bsky.social )
Strong OOD length generalization with sharp attention maps even in several algorithmic tasks, including the notorious Quickselect algorithm (Another settlement for the challenge identified by @mgalkin.bsky.social )
May 26, 2025 at 1:08 PM
4/ Tropical Attention runs each head natively in max-plus. Result:
Strong OOD length generalization with sharp attention maps even in several algorithmic tasks, including the notorious Quickselect algorithm (Another settlement for the challenge identified by @mgalkin.bsky.social )
Strong OOD length generalization with sharp attention maps even in several algorithmic tasks, including the notorious Quickselect algorithm (Another settlement for the challenge identified by @mgalkin.bsky.social )
3/ In the Tropical (max + ) geometry, “addition” is max, “multiplication” is +. Many algorithms already live here, carving exact polyhedral decision boundaries --> so why force them through exponential probabilities?
Let's ditch softmax, embrace the tropical semiring 🤯🍹.
Let's ditch softmax, embrace the tropical semiring 🤯🍹.
May 26, 2025 at 1:08 PM
3/ In the Tropical (max + ) geometry, “addition” is max, “multiplication” is +. Many algorithms already live here, carving exact polyhedral decision boundaries --> so why force them through exponential probabilities?
Let's ditch softmax, embrace the tropical semiring 🤯🍹.
Let's ditch softmax, embrace the tropical semiring 🤯🍹.
2/ We introduce Tropical Attention -- the first Neural Algorithmic reasoner that operates in the Tropical semiring, achieving SOTA OOD performance on executing several combinatorial algorithms
arxiv.org/abs/2505.17190
arxiv.org/abs/2505.17190
Tropical Attention: Neural Algorithmic Reasoning for Combinatorial Algorithms
Dynamic programming (DP) algorithms for combinatorial optimization problems work with taking maximization, minimization, and classical addition in their recursion algorithms. The associated value func...
arxiv.org
May 26, 2025 at 1:08 PM
2/ We introduce Tropical Attention -- the first Neural Algorithmic reasoner that operates in the Tropical semiring, achieving SOTA OOD performance on executing several combinatorial algorithms
arxiv.org/abs/2505.17190
arxiv.org/abs/2505.17190
Tnx. The probing methods were both linear and non-linear over the conjectural form of the large-genus asymptotic form of the intersections. If the model actually learned the underlying math, it must have internalized the parameters of the asymptotic formula. We found that this was the case.
February 8, 2025 at 8:34 PM
Tnx. The probing methods were both linear and non-linear over the conjectural form of the large-genus asymptotic form of the intersections. If the model actually learned the underlying math, it must have internalized the parameters of the asymptotic formula. We found that this was the case.