diff --git a/core/include/jml/math/loss_functions.hpp b/core/include/jml/math/loss_functions.hpp
new file mode 100644
index 0000000..e3f7652
--- /dev/null
+++ b/core/include/jml/math/loss_functions.hpp
@@ -0,0 +1,46 @@
+/**
+ * This offers loss functions for a model. Only one such loss function exists
+ * right now, but we may need more in the future.
+ *
+ * Each loss function needs an actual calculation (put in a jml::Vector, get out
+ * a double), and a derivative with respect to a particular entry. That is, if
+ * we change the i-th entry of the input vector, how much the loss will change
+ * by. This will be very important later for gradient descent.
+ *
+ * Author: Adam Hutchings
+ * Date: 10-17-23
+*/
+
+#pragma once
+
+#include <functional>
+
+#include <jml/jmldefs.h>
+#include <jml/math/vector.hpp>
+
+namespace jml {
+
+typedef std::function<double(const jml::Vector&, const jml::Vector&)> LF;
+typedef std::function<double(const jml::Vector&, const jml::Vector&, int i)> DL;
+
+class JML_API LossFunction {
+
+private:
+	LF loss;
+	DL dl;
+
+public:
+	// Create a loss function with a given loss and derivative.
+	LossFunction(const LF& lf, const DL& dl);
+	double get_loss(const jml::Vector& actual, const jml::Vector& expected);
+	double get_loss_derivative(
+		const jml::Vector& actual, const jml::Vector& expected, int index
+	);
+
+};
+
+// Also, we provide an example set of loss functions (L^2 norm)
+extern JML_API LF l2lf;
+extern JML_API DL l2dl;
+
+}
diff --git a/core/meson.build b/core/meson.build
index 00f7bfc..ef4bcc4 100644
--- a/core/meson.build
+++ b/core/meson.build
@@ -10,7 +10,9 @@ endif
 
 # TODO: pkg-config stuff
 
-core_sources = ['src/math/matrix.cpp', 'src/math/vector.cpp', 'src/math/activation_functions.cpp', 'src/model.cpp', 'src/logger.cpp', 'capi/cjml.cpp']
+core_sources = ['src/math/matrix.cpp', 'src/math/vector.cpp',
+'src/math/activation_functions.cpp', 'src/model.cpp', 'src/logger.cpp',
+'capi/cjml.cpp', 'src/math/loss_functions.cpp']
 jmlcore = library('jmlcore',
                   core_sources,
                   include_directories: core_inc,
diff --git a/core/src/math/loss_functions.cpp b/core/src/math/loss_functions.cpp
new file mode 100644
index 0000000..8cbfdda
--- /dev/null
+++ b/core/src/math/loss_functions.cpp
@@ -0,0 +1,50 @@
+#include <jml/math/loss_functions.hpp>
+
+#include <cmath>
+
+#include <jml/internal/logger.hpp>
+
+namespace jml {
+
+LossFunction::LossFunction(const LF& lf, const DL& dl) {
+	this->loss = lf;
+	this->dl = dl;
+}
+
+double LossFunction::get_loss(
+	const Vector& actual, const Vector& expected
+) {
+	return this->loss(actual, expected);
+}
+
+double LossFunction::get_loss_derivative(
+	const Vector& actual, const Vector& expected, int index
+) {
+	return this->dl(actual, expected, index);
+}
+
+JML_API LF l2lf = [](const Vector& actual, const Vector& expected) {
+	int a = actual.get_size(), e = expected.get_size();
+	if (a != e) {
+		LOGGER->log(Log(WARN)
+	                    << "Tried to compare a vector of length " << a
+	                    << "to a vector of length " << e << ".\n");
+	}
+	double total = 0;
+	double diff;
+	for (int i = 0; i < a; ++i) {
+		diff = actual.get_entry(i) - expected.get_entry(i);
+		diff *= diff;
+		total += diff;
+	}
+	return sqrt(total);
+};
+
+JML_API DL l2dl = [](const Vector& actual, const Vector& expected, int i) {
+	double l = l2lf(actual, expected);
+	double ret = 1.0 / (2 * l);
+	ret *= 2 * (actual.get_entry(i) - expected.get_entry(i));
+	return ret;
+};
+
+}
diff --git a/tests/core/math/test_losses.cpp b/tests/core/math/test_losses.cpp
new file mode 100644
index 0000000..c005cf0
--- /dev/null
+++ b/tests/core/math/test_losses.cpp
@@ -0,0 +1,17 @@
+#include "catch2/catch_test_macros.hpp"
+#include <jml/math/loss_functions.hpp>
+#include <jml/math/vector.hpp>
+
+SCENARIO("Loss can be calculated from two vectors") {
+    GIVEN("Two vectors of the same size") {
+        jml::Vector vec1(3), vec2(3);
+        vec1.set_entry(0, 1.0);
+        vec1.set_entry(1, 2.0);
+        vec1.set_entry(2, 3.0);
+        vec2.set_entry(0, 4.0);
+        vec2.set_entry(1, 2.0);
+        vec2.set_entry(2,-1.0);
+        auto loss = jml::l2lf(vec1, vec2);
+        REQUIRE(loss == 5.0);
+    }
+}
\ No newline at end of file
diff --git a/tests/meson.build b/tests/meson.build
index 5d2749f..c5d8c0c 100644
--- a/tests/meson.build
+++ b/tests/meson.build
@@ -2,6 +2,7 @@ core_test_sources = [
     'core/math/test_matrix.cpp',
     'core/math/test_vector.cpp',
     'core/math/test_activation_functions.cpp',
+    'core/math/test_losses.cpp',
     'core/test_model.cpp',
 ]