Scientific computing is undergoing rapid transformation as advances in artificial intelligence, heterogeneous computing, automation, and data-intensive research reshape not only computational tools but also the institutions, workforce models, and collaborative practices that support scientific discovery. This report synthesizes insights from the 2026 Workshop on Next-Generation Ecosystems for Scientific Computing, the second in a three-year series focused on strengthening scientific computing ecosystems through socio-technical co-design. Workshop discussions identified four interdependent strategic themes: software ecosystems for AI-enabled scientific discovery; trust, validation, and traceability; human-AI teaming and paradigm shifts; and workforce, pedagogy, and governance. The report translates these themes into eight priorities for community action spanning shared research infrastructure, trust and traceability, user experience, human-AI teaming, workforce development, cross-sector coordination, stewardship and sustainability, and evaluation of scientific value. Together, these priorities outline directions for building scientific computing ecosystems that remain trustworthy, sustainable, innovative, and resilient as AI assumes a growing role in scientific work.
L. McInnes, Dorian Arnold, Prasanna Balaprakash et al.· 0 citations
We consider the problem of minimizing error in quantized matrix multiplication $C=AB$. Scalar quantization of the factors introduces rounding errors whose scale depends on the maximum absolute entries -- the ranges -- of their rows and columns. These ranges determine the quantization grid steps. To reduce the error, we optimize over product-preserving transformations that alter the factor ranges and grid steps without changing $C$. Specifically, we seek the smallest leading expected squared error over invertible inner changes of basis and orthogonal outer rotations. Under independent, zero-mean subtractive dither noise on an unbounded lattice, we prove the output-only bound $E_{\rm lead} \ge (c_A+c_B)/K \Vert AB\Vert_*^2$, where $K$ is the inner dimension, $c_A$ and $c_B$ are normalized noise variances, and $\Vert AB\Vert_*$ is the nuclear norm. The bound is tight: an SVD-aligned Hadamard construction attains the infimum whenever a Hadamard matrix of order $K$ exists, including every power of two, while an SVD-aligned DCT construction is within a factor of two for every $K$. Without outer rotations, Gram-matrix balancing minimizes factorization energy, and finite-set flattening achieves the bound within $C\log(K(m+n))$. For power-of-two $K$, conditional expectations deterministically select the Hadamard signs in $O((m+n)K^2)$ exact-real operations. Synthetic experiments verify both constructions and illustrate the tradeoff between regularization and conditioning. These results characterize the full-gauge optimum and quantify the cost of preserving row and column indices.
Piyush Sao, N. Miniskar, Pedro Valero-Lara et al.· 0 citations
An exact finite-dimensional identity is derived for the expected squared product error under independent, zero-mean entrywise errors with known variance fields; it holds exactly for non-overloading subtractive dither and for independent stochastic rounding, and is empirically assess deterministic round-to-nearest (RTN).
Piyush Sao, N. Miniskar, Pedro Valero-Lara et al.· arXiv.org· 1 citation
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