[{"content":"This post verifies the core writing surface for a deep learning research blog: mathematical notation, code blocks, external links, generated math artifacts, and a JavaScript simulation.\nInline math works with passthrough delimiters: ∇θL(θ) \\nabla_\\theta \\mathcal{L}(\\theta) .\nDisplay math works as well:\nL(θ)=−∑i=1nyilog⁡pθ(yi∣xi) \\mathcal{L}(\\theta) = - \\sum_{i=1}^{n} y_i \\log p_\\theta(y_i \\mid x_i) Code blocks use Hugo syntax highlighting and PaperMod copy controls:\nimport torch def cosine_similarity(x: torch.Tensor, y: torch.Tensor) -\u0026gt; torch.Tensor: x = torch.nn.functional.normalize(x, dim=-1) y = torch.nn.functional.normalize(y, dim=-1) return x @ y.T External links such as Hugo are rendered with safer external-link attributes.\nStatic artifacts can live next to the post.\nLoading simulation... This simulation requires JavaScript. ","permalink":"https://827dc29b.blog-c55.pages.dev/posts/research-blog-smoke-test/","summary":"\u003cp\u003eThis post verifies the core writing surface for a deep learning research blog: mathematical notation, code blocks, external links, generated math artifacts, and a JavaScript simulation.\u003c/p\u003e\n\u003cp\u003eInline math works with passthrough delimiters: \u003cspan class=\"katex\"\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003csemantics\u003e\u003cmrow\u003e\u003cmsub\u003e\u003cmi mathvariant=\"normal\"\u003e∇\u003c/mi\u003e\u003cmi\u003eθ\u003c/mi\u003e\u003c/msub\u003e\u003cmi mathvariant=\"script\"\u003eL\u003c/mi\u003e\u003cmo stretchy=\"false\"\u003e(\u003c/mo\u003e\u003cmi\u003eθ\u003c/mi\u003e\u003cmo stretchy=\"false\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cannotation encoding=\"application/x-tex\"\u003e \\nabla_\\theta \\mathcal{L}(\\theta) \u003c/annotation\u003e\u003c/semantics\u003e\u003c/math\u003e\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eDisplay math works as well:\u003c/p\u003e\n\u003cspan class=\"katex\"\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"\u003e\u003csemantics\u003e\u003cmrow\u003e\u003cmi mathvariant=\"script\"\u003eL\u003c/mi\u003e\u003cmo stretchy=\"false\"\u003e(\u003c/mo\u003e\u003cmi\u003eθ\u003c/mi\u003e\u003cmo stretchy=\"false\"\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmo\u003e−\u003c/mo\u003e\u003cmunderover\u003e\u003cmo\u003e∑\u003c/mo\u003e\u003cmrow\u003e\u003cmi\u003ei\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mrow\u003e\u003cmi\u003en\u003c/mi\u003e\u003c/munderover\u003e\u003cmsub\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmi\u003ei\u003c/mi\u003e\u003c/msub\u003e\u003cmi\u003elog\u003c/mi\u003e\u003cmo\u003e⁡\u003c/mo\u003e\u003cmsub\u003e\u003cmi\u003ep\u003c/mi\u003e\u003cmi\u003eθ\u003c/mi\u003e\u003c/msub\u003e\u003cmo stretchy=\"false\"\u003e(\u003c/mo\u003e\u003cmsub\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmi\u003ei\u003c/mi\u003e\u003c/msub\u003e\u003cmo\u003e∣\u003c/mo\u003e\u003cmsub\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmi\u003ei\u003c/mi\u003e\u003c/msub\u003e\u003cmo stretchy=\"false\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cannotation encoding=\"application/x-tex\"\u003e\n\\mathcal{L}(\\theta) = - \\sum_{i=1}^{n} y_i \\log p_\\theta(y_i \\mid x_i)\n\u003c/annotation\u003e\u003c/semantics\u003e\u003c/math\u003e\u003c/span\u003e\u003cp\u003eCode blocks use Hugo syntax highlighting and PaperMod copy controls:\u003c/p\u003e\n\u003cdiv class=\"highlight\"\u003e\u003cpre tabindex=\"0\" class=\"chroma\"\u003e\u003ccode class=\"language-python\" data-lang=\"python\"\u003e\u003cspan class=\"line\"\u003e\u003cspan class=\"cl\"\u003e\u003cspan class=\"kn\"\u003eimport\u003c/span\u003e \u003cspan class=\"nn\"\u003etorch\u003c/span\u003e\n\u003c/span\u003e\u003c/span\u003e\u003cspan class=\"line\"\u003e\u003cspan class=\"cl\"\u003e\n\u003c/span\u003e\u003c/span\u003e\u003cspan class=\"line\"\u003e\u003cspan class=\"cl\"\u003e\u003cspan class=\"k\"\u003edef\u003c/span\u003e \u003cspan class=\"nf\"\u003ecosine_similarity\u003c/span\u003e\u003cspan class=\"p\"\u003e(\u003c/span\u003e\u003cspan class=\"n\"\u003ex\u003c/span\u003e\u003cspan class=\"p\"\u003e:\u003c/span\u003e \u003cspan class=\"n\"\u003etorch\u003c/span\u003e\u003cspan class=\"o\"\u003e.\u003c/span\u003e\u003cspan class=\"n\"\u003eTensor\u003c/span\u003e\u003cspan class=\"p\"\u003e,\u003c/span\u003e \u003cspan class=\"n\"\u003ey\u003c/span\u003e\u003cspan class=\"p\"\u003e:\u003c/span\u003e \u003cspan class=\"n\"\u003etorch\u003c/span\u003e\u003cspan class=\"o\"\u003e.\u003c/span\u003e\u003cspan class=\"n\"\u003eTensor\u003c/span\u003e\u003cspan class=\"p\"\u003e)\u003c/span\u003e \u003cspan class=\"o\"\u003e-\u0026gt;\u003c/span\u003e \u003cspan class=\"n\"\u003etorch\u003c/span\u003e\u003cspan class=\"o\"\u003e.\u003c/span\u003e\u003cspan class=\"n\"\u003eTensor\u003c/span\u003e\u003cspan class=\"p\"\u003e:\u003c/span\u003e\n\u003c/span\u003e\u003c/span\u003e\u003cspan class=\"line\"\u003e\u003cspan class=\"cl\"\u003e    \u003cspan class=\"n\"\u003ex\u003c/span\u003e \u003cspan class=\"o\"\u003e=\u003c/span\u003e \u003cspan class=\"n\"\u003etorch\u003c/span\u003e\u003cspan class=\"o\"\u003e.\u003c/span\u003e\u003cspan class=\"n\"\u003enn\u003c/span\u003e\u003cspan class=\"o\"\u003e.\u003c/span\u003e\u003cspan class=\"n\"\u003efunctional\u003c/span\u003e\u003cspan class=\"o\"\u003e.\u003c/span\u003e\u003cspan class=\"n\"\u003enormalize\u003c/span\u003e\u003cspan class=\"p\"\u003e(\u003c/span\u003e\u003cspan class=\"n\"\u003ex\u003c/span\u003e\u003cspan class=\"p\"\u003e,\u003c/span\u003e \u003cspan class=\"n\"\u003edim\u003c/span\u003e\u003cspan class=\"o\"\u003e=-\u003c/span\u003e\u003cspan class=\"mi\"\u003e1\u003c/span\u003e\u003cspan class=\"p\"\u003e)\u003c/span\u003e\n\u003c/span\u003e\u003c/span\u003e\u003cspan class=\"line\"\u003e\u003cspan class=\"cl\"\u003e    \u003cspan class=\"n\"\u003ey\u003c/span\u003e \u003cspan class=\"o\"\u003e=\u003c/span\u003e \u003cspan class=\"n\"\u003etorch\u003c/span\u003e\u003cspan class=\"o\"\u003e.\u003c/span\u003e\u003cspan class=\"n\"\u003enn\u003c/span\u003e\u003cspan class=\"o\"\u003e.\u003c/span\u003e\u003cspan class=\"n\"\u003efunctional\u003c/span\u003e\u003cspan class=\"o\"\u003e.\u003c/span\u003e\u003cspan class=\"n\"\u003enormalize\u003c/span\u003e\u003cspan class=\"p\"\u003e(\u003c/span\u003e\u003cspan class=\"n\"\u003ey\u003c/span\u003e\u003cspan class=\"p\"\u003e,\u003c/span\u003e \u003cspan class=\"n\"\u003edim\u003c/span\u003e\u003cspan class=\"o\"\u003e=-\u003c/span\u003e\u003cspan class=\"mi\"\u003e1\u003c/span\u003e\u003cspan class=\"p\"\u003e)\u003c/span\u003e\n\u003c/span\u003e\u003c/span\u003e\u003cspan class=\"line\"\u003e\u003cspan class=\"cl\"\u003e    \u003cspan class=\"k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"n\"\u003ex\u003c/span\u003e \u003cspan class=\"o\"\u003e@\u003c/span\u003e \u003cspan class=\"n\"\u003ey\u003c/span\u003e\u003cspan class=\"o\"\u003e.\u003c/span\u003e\u003cspan class=\"n\"\u003eT\u003c/span\u003e\n\u003c/span\u003e\u003c/span\u003e\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\u003cp\u003eExternal links such as \u003ca href=\"https://gohugo.io/\" target=\"_blank\" rel=\"noopener noreferrer external\"\u003eHugo\u003c/a\u003e\n are rendered with safer external-link attributes.\u003c/p\u003e","title":"Research Blog Smoke Test"},{"content":"This site collects deep learning research notes, technical experiments, and implementation write-ups.\n","permalink":"https://827dc29b.blog-c55.pages.dev/about/","summary":"\u003cp\u003eThis site collects deep learning research notes, technical experiments, and implementation write-ups.\u003c/p\u003e","title":"About"}]