diff --git a/compute/arena_size_test.go b/compute/arena_size_test.go
new file mode 100644
index 0000000..c21ca43
--- /dev/null
+++ b/compute/arena_size_test.go
@@ -0,0 +1,60 @@
+package compute
+
+import (
+	"testing"
+
+	"github.com/zerfoo/ztensor/log"
+)
+
+func TestArenaSizeBytes_Default(t *testing.T) {
+	t.Setenv("ZERFOO_ARENA_SIZE_GB", "")
+	got := arenaSizeBytes(log.Nop())
+	want := int64(defaultArenaSizeGB) * 1024 * 1024 * 1024
+	if got != want {
+		t.Fatalf("default arena size: got %d, want %d", got, want)
+	}
+}
+
+func TestArenaSizeBytes_EnvOverride(t *testing.T) {
+	tests := []struct {
+		name  string
+		env   string
+		wantG int64
+	}{
+		{"min", "1", 1},
+		{"training-typical", "32", 32},
+		{"max", "128", 128},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			t.Setenv("ZERFOO_ARENA_SIZE_GB", tt.env)
+			got := arenaSizeBytes(log.Nop())
+			want := tt.wantG * 1024 * 1024 * 1024
+			if got != want {
+				t.Fatalf("env=%q: got %d, want %d", tt.env, got, want)
+			}
+		})
+	}
+}
+
+func TestArenaSizeBytes_InvalidFallsBackToDefault(t *testing.T) {
+	tests := []struct {
+		name string
+		env  string
+	}{
+		{"non-integer", "lots"},
+		{"below-min", "0"},
+		{"above-max", "256"},
+		{"negative", "-5"},
+	}
+	wantDefault := int64(defaultArenaSizeGB) * 1024 * 1024 * 1024
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			t.Setenv("ZERFOO_ARENA_SIZE_GB", tt.env)
+			got := arenaSizeBytes(log.Nop())
+			if got != wantDefault {
+				t.Fatalf("env=%q: got %d, want default %d", tt.env, got, wantDefault)
+			}
+		})
+	}
+}
diff --git a/compute/gpu_engine.go b/compute/gpu_engine.go
index b1d5e7d..68d8a19 100644
--- a/compute/gpu_engine.go
+++ b/compute/gpu_engine.go
@@ -4,6 +4,7 @@ import (
 	"context"
 	"fmt"
 	"os"
+	"strconv"
 	"sync/atomic"
 	"unsafe"
 
@@ -16,6 +17,45 @@ import (
 	"github.com/zerfoo/ztensor/tensor"
 )
 
+// defaultArenaSizeGB is the per-GPUEngine arena capacity when the
+// ZERFOO_ARENA_SIZE_GB env var is unset. Sized for single-pass inference
+// on typical 1-7B LLMs; larger training workloads (e.g. multi-scale
+// walk-forward with hundreds of batches) should raise this via env var
+// to keep per-step intermediates inside the arena and avoid spill to
+// the unbounded MemPool fallback.
+const defaultArenaSizeGB = 2
+
+// minArenaSizeGB and maxArenaSizeGB bound user-supplied values so a typo
+// can't request a TB-sized arena or a zero-size one.
+const (
+	minArenaSizeGB = 1
+	maxArenaSizeGB = 128
+)
+
+// arenaSizeBytes resolves the arena capacity in bytes. ZERFOO_ARENA_SIZE_GB,
+// if set to an integer in [minArenaSizeGB, maxArenaSizeGB], overrides the
+// default. Invalid / out-of-range values are logged and ignored.
+func arenaSizeBytes(l log.Logger) int64 {
+	gb := int64(defaultArenaSizeGB)
+	if raw := os.Getenv("ZERFOO_ARENA_SIZE_GB"); raw != "" {
+		parsed, err := strconv.ParseInt(raw, 10, 64)
+		switch {
+		case err != nil:
+			l.Warn("ZERFOO_ARENA_SIZE_GB is not an integer; using default",
+				"value", raw, "default", fmt.Sprintf("%d", defaultArenaSizeGB))
+		case parsed < minArenaSizeGB || parsed > maxArenaSizeGB:
+			l.Warn("ZERFOO_ARENA_SIZE_GB out of range; using default",
+				"value", fmt.Sprintf("%d", parsed),
+				"min", fmt.Sprintf("%d", minArenaSizeGB),
+				"max", fmt.Sprintf("%d", maxArenaSizeGB),
+				"default", fmt.Sprintf("%d", defaultArenaSizeGB))
+		default:
+			gb = parsed
+		}
+	}
+	return gb * 1024 * 1024 * 1024
+}
+
 // DType selects the compute precision for GPU operations.
 type DType int
 
@@ -169,11 +209,14 @@ func NewGPUEngine[T tensor.Numeric](ops numeric.Arithmetic[T], deviceID ...int)
 	fallbackPool := cuda.NewMemPool()
 	cuda.SetDefaultMemPool(fallbackPool)
 
-	// Arena pool: 2GB pre-allocated region for per-inference intermediates.
-	// On DGX Spark with 128GB unified memory, this is a small fraction.
-	// Falls back to MemPool if arena is exhausted.
-	const arenaSize = 2 * 1024 * 1024 * 1024 // 2 GB
-	arenaPool, err := gpuapi.NewCUDAArenaPool(dev, arenaSize, fallbackPool)
+	// Arena pool: pre-allocated region for per-inference / per-step
+	// intermediates. Defaults to 2GB (sized for 1-7B LLM inference).
+	// Override via ZERFOO_ARENA_SIZE_GB for larger training workloads
+	// whose per-step working set would otherwise spill to the unbounded
+	// MemPool fallback and leak through StepScope.Close(). On DGX Spark
+	// with 128GB unified memory, sizes up to 128GB are valid.
+	arenaSize := arenaSizeBytes(l)
+	arenaPool, err := gpuapi.NewCUDAArenaPool(dev, int(arenaSize), fallbackPool)
 	if err == nil {
 		cuda.SetDefaultArenaPool(arenaPool.Inner())
 	}